Encontrados 2972213 resultado(s)

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Encontradas 29723 página(s)

#### Pseudospin lifetime in relaxed-shape armchair graphene nanoribbons due to in-plane phonon modes

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Prabhakar, S., Melnik, R., Bonilla, L.

We study the influence of ripple waves on the band structures of strained armchair graphene nanoribbons. We argue that the Zeeman pseudospin (p-spin) splitting energy induced by ripple waves might not be neglected for smaller widths of armchair graphene nanoribbons (GNRs). We show that the p-spin splitting energy breaks the symmetry of degeneracy due to the ripple-induced Zeeman effect in GNRs, originating from electromechanical coupling. We estimate the p-spin lifetime in strained armchair…

#### Computer software for understanding resonances and resonance-related phenomena in chemical reactions

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Sokolovski, D., Akhmatskaya, E.

In numerical modelling of chemical reactions one calculates the scattering matrix for the required values of energy and angular momentum. Having done so, one still faces the non-trivial task of extracting detailed information about the reaction mechanism. We discuss the methods and numerical tools for such an analysis in terms of resonance poles and semiclassical trajectories. Our approach avoids calculating the scattering matrix in semiclassical approximation, and employs its numerical values…

#### Three Dimensional Metallic Carbon from Distorting sp3-Bond

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Cheng, Y., Melnik, R., Kawazoe, Y., Wen, B.

Owing to the outstanding properties of metallic carbon as well as their great potential applications, design and synthesis of metallic carbon have long attracted considerable attention. In this work, a new three-dimensional metallic carbon (dubbed as Tri-C9) has been built by distorting the sp3 hybridization bond. Our first-principles calculations results indicate that Tri-C9 is a metastable metallic carbon, and that the metallic behavior of Tri-C9 originates from the Ï€ bonds near Fermi level…

#### Electrochemical Potential Derived from Atomic Cluster Structures

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Du, J., Xiao, D., Wen, B., Melnik, R., Kawazoe, Y.

Based on the atomic cluster structures and free electron approximation model, it is revealed that the electrochemical potential (ECP) for the system of interest is proportional to the reciprocal of atomic cluster radius squared, i.e., Ïˆ = kÂ·(1/r2). Applied to elemental crystals, the correlation between atomic cluster radii and the ECP that we have predicted agrees well with the previously reported results. In addition, some other physicochemical properties associated with the ECP have also…

#### Radiation of water waves by a submerged nearly circular plate

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Farina, L., da Gama, R.L., Korotov, S., Ziebell, J.S.

A thin nearly circular plate is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the surface of the plate which is conformally mapped onto the unit disc. The solution is computed by a spectral method proved to be efficient for the case of a circular disc. Numerical results are presented for the heave added mass and damping coefficients for two types of nearly circular plates.

#### Corrections to finite-size scaling in the $\varphi^4$ model on square lattices

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Kaupuzs, J., Melnik, R., Rimsans, J.

Corrections to scaling in the two-dimensional (2D) scalar (Formula presented.) model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L ((Formula presented.)) and different values of the (Formula presented.) coupling constant (Formula presented.), i.e. (Formula presented.), 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correctionâ€“toâ€“scaling exponents (Formula presented.)…

#### Tuning $g$-factor of electrons through spin-orbit coupling in GaAs/AlGaAs conical quantum dots

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Prabhakar, S., Melnik, R.

We investigate band structures of (Formula presented.) three-dimensional conical quantum dots (QDs). In particular, we explore the influence of the Rashba and Dresselhaus spinâ€“orbit couplings in the variation of effective (Formula presented.)-factor of electrons in such QDs. We demonstrate that the interplay between the Rashba and Dresselhaus spinâ€“orbit couplings can provide further insight into underlying physical phenomena and assist in the design of quantum logic gates for the…

#### Mathematical modelling as a tool to understand cell self-renewal and differentiation

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Getto, P., Marciniak-Czochra, A.

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle…

#### Multiple-time-stepping generalized hybrid Monte Carlo methods

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Escribano, B., Akhmatskaya, E., Reich, S., Azpiroz, J.M.

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the…

#### Constant pressure hybrid Monte Carlo simulations in GROMACS

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Fernández-Pendás, M., Escribano, B., Radivojevic, T., Akhmatskaya, E.

Adaptation and implementation of the Generalized Shadow Hybrid Monte Carlo (GSHMC) method for molecular simulation at constant pressure in the NPT ensemble are discussed. The resulting method, termed NPT-GSHMC, combines Andersen barostat with GSHMC to enable molecular simulations in the environment natural for biological applications, namely, at constant pressure and constant temperature. Generalized Hybrid Monte Carlo methods are designed to maintain constant temperature and volume and…

#### Stability analysis of a renewal equation for cell population dynamics with quiescence

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Alarcon, T., Getto, P., Nakata, Y.

We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a…

#### Numerical Regge pole analysis of resonance structures in elastic, inelastic and reactive state-to-state integral cross sections

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Akhmatskaya, E., Sokolovski, D., Echeverria-Arrondo, C.

We present a detailed description of a FORTRAN code for evaluation of the resonance contribution a Regge trajectory makes to the integral state-to-state cross section (ICS) within a specified range of energies. The contribution is evaluated with the help of the Mulholland formula (Macek et al., 2004) and its variants (Sokolovski et al., 2007; Sokolovski and Akhmatskaya, 2011). Regge pole positions and residues are obtained by analytically continuing S-matrix element, evaluated numerically for…

#### Impact of competitive processes on controlled radical polymerization

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Ballard, N., Rusconi, S., Akhmatskaya, E., Sokolovski, D., de La Cal, J.C., Asua, J.M.

The kinetics of radical polymerization have been systematically studied for nearly a century and in general are well understood. However, in light of recent developments in controlled radical polymerization many kinetic anomalies have arisen. These unexpected results have been largely considered separate, and various, as yet inconclusive, debates as to the cause of these anomalies are ongoing. Herein we present a new theory on the cause of changes in kinetics under controlled radical…

#### Computing the eigenvalues of realistic Daphnia models by pseudospectral methods

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Breda, D., Getto, P., Sanchez Sanz, J., Vermiglio, R.

This work deals with physiologically structured populations of the Daphnia type. Their biological modeling poses several computational challenges. In such models, indeed, the evolution of a size structured consumer described by a Volterra functional equation (VFE) is coupled to the evolution of an unstructured resource described by a delay differential equation (DDE), resulting in dynamics over an infinite dimensional state space. As additional complexities, the right-hand sides are both of…

#### From chemical gardens to chemobrionics

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Barge, L.M., Cardoso, S.S.S., Cartwright, J.H.E., Cooper, G.J.T., Cronin, L., de Wit, A., Doloboff, I.J., Escribano, B., Goldstein, R.E., Haudin, F., Jones, D.E.H., Mackay, A.L., Maselko, J., Pagano, J.J., Pantaleone, J., Russell, M.J., Sainz-Díaz, C.I., Steinbock, O., Stone, D.A., Tanimoto, Y., Thomas, N.

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to…

#### Macroscopic conductivity of free fermions in disordered media

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W., Hertling, C.

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint starting with [1-3]. We show, in particular, the existence and finiteness of the conductivity measure ŒºŒ£ for macroscopic scales. Then we prove that, similar…

#### Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

We apply Liebâ€“Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations of the external electromagnetic field. This analysis leads to an extension of the results for quasi-free fermions of (Bru etÂ al. Commun Pure Appl Math 68(6):964â€“1013, 2015; Bru etÂ al. J Math Phys…

#### Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bach, V., Breteaux, S., Petrat, S., Pickl, P., Tzaneteas, T.

We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system.

#### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

We generalize to multi–commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expan- sions) in order to estimate time–dependent multi–commutators for interact- ing fermions. Lieb–Robinson bounds for multi–commutators are effective mathematical tools to handle analytic aspects of the dynamics of quantum particles with interactions which are non–vanishing in the whole…

#### Universal Bounds for Large Determinants from Non–Commutative Ho ̈lder Inequalities in Fermionic Constructive Quantum Field Theory

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

Efficiently bounding large determinants is an essential step in non–relati- vistic fermionic constructive quantum field theory, because, together with the summability of the interaction and the covariance, it implies the abso- lute convergence of the perturbation expansion of all correlation functions in terms of powers of the strength u ∈ R of the interparticle interaction. We provide, for large determinants of fermionic convariances, sharp bounds which hold for all (bounded and unbounded, the…

#### From the 2nd Law of Thermodynamics to AC–Conductivity Measures of Interacting Fermions in Disordered Media

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of time-dependent electromagnetic fields. The interparticle interaction is short-range and translation invariant. Electromagnetic fields are compactly supported in time and space. In the limit of infinite space supports (macroscopic limit) of electromagnetic fields, we derive Ohm and Joule's laws in the AC-regime. An important outcome is the extension to…

#### Heat production of noninteracting fermions subjected to electric fields

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W., Hertling, C.

Electric resistance in conducting media is related to heat (or entropy) production in the presence of electric fields. In this paper, by using Araki's relative entropy for states, we mathematically define and analyze the heat production of free fermions within external potentials. More precisely, we investigate the heat production of the nonautonomous C*-dynamical system obtained from the fermionic second quantization of a discrete SchrÃ¶dinger operator with bounded static potential in the…

#### AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W., Hertling, C.

We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium…

#### Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

From quantum mechanical first principles only, we rigorously study the time-evolution of a N-level atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at thermal equilibrium (reservoir). In particular, we establish the relation between the full dynamics of the compound system and the effective dynamics for the N-level atom, which is studied in detail in Bru etÂ al. (Ann Henri PoincarÃ© 13(6):1305â€“1370, 2012). Together with Bru…

#### Microscopic conductivity of lattice fermions at equilibrium. I. Non-interacting particles

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W., Hertling, C.

We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent electric field. For any bounded convex region R âŠ‚ â„ (d (d â‰¥ 1) of space, electric fields Îµ within R drive currents. At leading order, uniformly with respect to the volume |R| of R and the particular choice of the static potential, the dependency on E of the current is linear and described by a conductivity (tempered, operator-valued) distribution. Because of the positivity of the heat…

#### D-Wave pairing driven by bipolaric modes related to giant electron-phonon anomalies in high-Tc superconductors

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Pasquale, A.D., de Siqueira Pedra, W.

Taking into account microscopic properties of most usual high-Tc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the two-dimensional square lattice. We establish that these model Hamiltonians can show d-wave pairing at the bottom of their spectrum, despite their space isotropy. This phenomenon appears when a 'giant electron-phonon anomaly' is present at the boundaries of the…

#### Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bru, J.-B., de Siqueira Pedra, W.

We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations of the external electromagnetic field. This analysis leads to an extension of the results for quasi-free fermions of (Bru et al. Commun Pure Appl Math 68(6):964–1013, 2015; Bru et al. J Math Phys 56:051901…

#### Diagonalizing quadratic bosonic operators by non-autonomous flow equations volker bach

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bach, V., Bru, J.-B.

We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal infinity. We demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous…

#### Equisingularity in One-Parameter Families of Generically Reduced Curves

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Fernández de Bobadilla, J., Snoussi, J., Spivakovsky, M.

We explore some equisingularity criteria in one-parameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality implies smoothness of the normalized surface. Examples are given to show that Witney regularity and equisaturation are not stable under the blow-up of the singular locus nor under the Nash modification.

#### Modelling wildland fire propagation by tracking random fronts

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Pagnini, G., Mentrelli, A.

Abstract. Wildland fire propagation is studied in the liter- ature by two alternative approaches, namely the reaction– diffusion equation and the level-set method. These two ap- proaches are considered alternatives to each other because the solution of the reaction–diffusion equation is generally a continuous smooth function that has an exponential de- cay, and it is not zero in an infinite domain, while the level- set method, which is a front tracking technique, generates a sharp function that…

#### Turbulence and fire-spotting effects into wild-land fire simulators

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Kaur, I., Mentrelli, A., Bosseur, F., Filippi, J.-B., Pagnini, G.

This paper presents a mathematical approach to model the effects and the role of phenomena with random nature such as turbulence and fire-spotting into the existing wildfire simulators. The formulation proposes that the propagation of the fire-front is the sum of a drifting component (obtained from an existing wildfire simulator without turbulence and fire-spotting) and a random fluctuating component. The modelling of the random effects is embodied in a probability density function accounting…

#### Modelling and simulation of wildland fire in the framework of the level set method

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Mentrelli, A., Pagnini, G.

Among the modelling approaches that have been proposed for the simulation of wildfire propagation, two have gained considerable attention in recent years: the one based on a reaction-diffusion equation, and the one based on the level set method. These two approaches, traditionally seen in competition, do actually lead to similar equation models when the level set method is modified taking into account random effects as those due to turbulent hot air transport and fire spotting phenomena. The…

#### Fractional relaxation with time-varying coefficient

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Garra, R., Giusti, A., Mainardi, F., Pagnini, G.

From the point of view of the general theory of the hyper-Bessel operators, we consider a particular operator that is suitable to generalize the standard process of relaxation by taking into account both memory effects of power law type and time variability of the characteristic coefficient. According to our analysis, the solutions are still expressed in terms of functions of the Mittag-Leffler type as in case of fractional relaxation with constant coefficient but exhibit a further stretching…

#### Front propagation in anomalous diffusive media governed by time-fractional diffusion

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Mentrelli, A., Pagnini, G.

In this paper, a multi-dimensional model is proposed to study the propagation of random fronts in media in which anomalous diffusion takes place. The front position is obtained as the weighted mean of fronts calculated by means of the level set method, using as weight-function the probability density function which characterizes the anomalous diffusion process. Since anomalous diffusion is assumed to be governed by a time-fractional diffusion equation, its fundamental solution is the required…

#### Self-similar stochastic models with stationary increments for symmetric space-time fractional diffusion

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Pagnini, G.

An approach to develop stochastic models for studying anomalous diffusion is proposed. In particular, in this approach the stochastic particle trajectory is based on the fractional Brownian motion but, for any realization, it is multiplied by an independent random variable properly distributed. The resulting probability density function for particle displacement can be represented by an integral formula of subordination type and, in the single-point case, it emerges to be equal to the solution…

#### Short note on the emergence of fractional kinetics

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Pagnini, G.

In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian and described by the Continuous Time Random Walk model. But, as a consequence of the complexity of the medium, each trajectory is supposed to scale in time according to a particular random timescale. The link from this framework to microscopic dynamics is…

#### A renewal model for the emergence of anomalous solute crowding in liposomes

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Paradisi, P., Allegrini, P., Chiarugi, D.

A fundamental evolutionary step in the onset of living cells is thought to be the spontaneous formation of lipid vesicles (liposomes) in the pre-biotic mixture. Even though it is well known that hydrophobic forces drive spontaneous liposome formation in aqueous solutions, how the components of the earliest biochemical pathways were trapped and concentrated in the forming vesicles is an issue that still needs to be clarified. In recent years, some authors carried out a set of experiments where a…

#### Velocity and energy distributions in microcanonical ensembles of hard spheres

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Scalas, E., Gabriel, A.T., Martin, E., Germano, G.

In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a d-dimensional volume V having a total energy E, a total momentum P, and an overall center of mass position G, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d, N, E, the boundary…

#### Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Paradisi, P., Allegrini, P.

In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth-death process of cooperation. This is found to be described by a renewal point process, i.e., a sequence of crucial birth-death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occurrence of crucial events is…

#### The emergence of self-organization in complex systems-Preface

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Paradisi, P., Kaniadakis, G., Scarfone, A.M.

[No abstract available]

#### Almost periodic parameters for the second moment stability of linear stochastic systems

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Vargas, A.N., Do Val, J.B.R.

The technical note presents conditions to assure the uniform second moment stability for a class of linear time-varying stochastic systems. The system parameters are assumed to be almost periodic, a concept that is weaker than the periodic one. Under the existence of the long-run average cost associated with the stochastic system, we apply the almost periodicity to prove the desired stability result. An application illustrates the usefulness of the approach by implementing an almost periodic…

#### Weak observability estimates for 1-D wave equations with rough coefficients

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Fanelli, F., Zuazua, E.

In this paper we prove observability estimates for 1-dimensional wave equations with non-Lipschitz coefficients. For coefficients in the Zygmund class we prove a "classical" estimate, which extends the well-known observability results in the energy space for BV regularity. When the coefficients are instead log-Lipschitz or log-Zygmund, we prove observability estimates "with loss of derivatives": in order to estimate the total energy of the solutions, we need measurements on…

#### On the exact controllability of hyperbolic magnetic Schrödinger equations

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lu, X., Tu, Z., Lv, X.

In this paper, we address the exact controllability problem for the hyperbolic magnetic Schr√∂dinger equation, which plays an important role in the research of electromagnetics. Typical techniques, such as Hamiltonian induced Hilbert spaces and pseudodifferential operators are introduced. By choosing an appropriate multiplier, we proved the observability inequality with sharp constants. In particular, a genuine compactness-uniqueness argument is applied to obtain the minimal time. In the final…

#### Robust ‚H-2 static output feedback to control an automotive throttle valve

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Vargas, A.N., Acho, L., Pujol, G., Oliveira, R.C.L.F., Do Val, J.B.R., Peres, P.L.D.

The paper presents a control strategy for an automotive electronic throttle body, a device largely used into vehicles to increase the efficiency of the combustion engines. The synthesis of the proposed controller is based on a linear matrix inequality (LMI) formulation, which allows us to deal with uncertainties on the measurements of the position of the throttle valve. The LMI approach generates a suboptimal solution for the robust ‚Ñã2 static output feedback control problem, and the…

#### Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Ignat, L.I., Pozo, A., Zuazua, E.

In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are consistent with the one-sided Lipschitz condition (OSLC): Lax-Friedrichs, Engquist-Osher and Godunov. We mainly focus on the inviscid Burgers equation, for which we know that the large time behavior is of a self-similar nature, described by a two-parameter family of N-waves. We…

#### Averaged control and observation of parameter-depending wave equations

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lazar, M., Zuazua, E.

We analyze the problem of averaged observability and control of wave equations.This topic is motivated by the control of parameter-dependent systems of wave equations. We look for controls ensuring the controllability of the averages of the states with respect to the parameter. This turns out to be equivalent to the problem of averaged observation in which one aims at recovering the energy of the initial data of the adjoint system by measurements done on its averages, under the assumption that…

#### Averaged control

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Zuazua, E.

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but…

#### Estimating the division rate of the growth-fragmentation equation with a self-similar kernel

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bourgeron, T., Doumic, M., Escobedo, M.

We consider the growth-fragmentation equation and we address the problem of estimating the division rate from the stable size distribution of the population, which is easily measured, but non-smooth. We propose a method based on the Mellin transform for growth-fragmentation equations with self-similar kernels. We build a sequence of functions which converges to the density of the population in division, simultaneously in several weighted L2 spaces, as the measurement error goes to 0. This…

#### Unsteady mixed flows in non uniform closed water pipes: a Full Kinetic Approach

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Bourdarias, C., Ersoy, M., Gerbi, S.

We recall the Pressurized and Free Surface model constructed for the modeling of unsteady mixed flows in closed water pipes where transition points between the free surface and pressurized flow are treated as a free boundary associated to a discontinuity of the gradient of pressure. Then we present a numerical kinetic scheme for the computations of unsteady mixed flows in closed water pipes. This kinetic method that we call FKA for ‚ÄúFull Kinetic Approach‚Äù is an easy and mathematically…

#### A note on complete hyperbolic operators with log-Zygmund coefficients

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Colombini, F., del Santo, D., Fanelli, F., Métivier, G.

The present paper is the continuation of the recent work [7], and it is devoted to strictly hyperbolic operators with non-regular coefficients. We focus here on the case of complete operators whose second-order coefficients are log-Zygmund continuous in time, and we investigate the $H^{\inf}$ well-posedness of the associate Cauchy problem.

#### Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Carvalho, A.N., Sonner, S.

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

#### Global Attractor for a Generalized Discrete Nonlinear Schrödinger Equation

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Pereira, J.M.

A generalized discrete nonlinear Schr√∂dinger equation (Formula presented.) with long-range interactions in weighted spaces (Formula presented.) is considered. Under suitable assumptions on the coupling constants J(m), the damping Œ≥ and the weight (Formula presented.), the existence of a global attractor is proved.

#### Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Corrias, L., Escobedo, M., Matos, J.

In the present article we consider several issues concerning the doubly parabolic Keller-Segel system (1.1)-(1.2) in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global existence of integral solutions, their optimal time decay, uniqueness and positivity, together with the uniqueness of self-similar solutions. In particular, we prove that there exist integral solutions of any mass, provided that Œµ>0 is sufficiently…

#### A Hyperbolic system and the cost of the controllability for the Stokes system

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chaves-Silva, F.W.

This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time $T$ is of order $e^{CIT} when T⟶0+ , i.e., the same order of controllability as for the heat equation. For this to be possible, we prove a new exact controllability result for a hyperbolic system with a resistance term, which will be done under assumptions on the control region.

#### Null controllability of a system of viscoelasticity with a moving control

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chaves-Silva, F.W., Rosier, L., Zuazua, E.

In this paper, we consider the wave equation with both viscous Kelvin-Voigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null controllability when the control region, driven by the flow of an ODE, covers all the domain. The proof is based upon the interpretation of the system as, roughly, the coupling of a heat equation with an ordinary differential equation (ODE). The presence of the ODE for which there is…

#### Transmutation techniques and observability for time-discrete approximation schemes of conservative systems

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Ervedoza, S., Zuazua, E.

In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding time-discrete one. As an application, we show how observability properties for the time continuous model yield uniform (with respect to the time-step) observability results for its time-discrete approximation counterparts, provided the initial data are suitably…

#### Recovery of an initial temperature from discrete sampling

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Devore, R., Zuazua, E.

The problem of recovering the initial temperature of a body from discrete temperature measurements made at later times is studied. While this problem has a general formulation, the results of this paper are only given in the simplest setting of a finite (one-dimensional), constant coefficient, linear rod. It is shown that with a judicious placement of a thermometer on this rod, the initial temperature profile of the rod can be completely determined by later time measurements. The paper then…

#### On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Escobedo, M., Velazquez, J.J.L.

In this paper we prove that the solutions of the isotropic, spatially homogeneous Nordheim equation for bosons with bounded initial data blow up in finite time in the L‚àû norm if the values of the energy and particle density are in the range of values where the corresponding equilibria contain a Dirac mass. We also prove that, in the weak solutions, whose initial data are measures with values of particle and energy densities satisfying the previous condition, a Dirac measure at the origin…

#### A functional limit theorem for stochastic integrals driven by a time-changed symmetric sigma-stable Levy process

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Scalas, E., Viles, N.

Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the $M_1$-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric Œ±-stable Lévy process. The time change is given by the inverse Œ≤-stable subordinator.

#### Controllability of fast diffusion coupled parabolic systems

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chaves-Silva, F.W., Guerrero, S., Puel, J.P.

In this work we are concerned with the null controllability of coupled parabolic systems depending on a parameter and converging to a parabolic-elliptic system. We show the uniform null controllability of the family of coupled parabolic systems with respect to the degenerating parameter.

#### Generation of two-dimensional water waves by moving bottom disturbances

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Nersisyan, H., Dutykh, D., Zuazua, E.

In this study we investigate the potential and limitations of the wave genera- tion by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to a prescribed trajectory. The practical question we address in this study is how to compute the wavemaker shape and its trajectory in order to generate a wave with prescribed char- acteristics? For the sake of simplicity we model the…

#### Attractors met X-elliptic operators

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Kogoj, A.E., Sonner, S.

We consider degenerate parabolic and damped hyperbolic equations involving an operator L, that is X-elliptic with respect to a family of locally Lipschitz continuous vector fields X={X1,... Xm}. The local well-posedness is established under subcritical growth restrictions on the nonlinearity f, which are determined by the geometry and functional setting naturally associated with the family of vector fields X. Assuming additionally that f is dissipative, the global existence of solutions follows…

#### Gradient-based optimization techniques for the design of static controllers for Markov jump linear systems with unobservable modes

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Vargas, A.N., Bortolin, D.C., Costa, E.F., Do Val, J.B.R.

The paper formulates the static control problem of Markov jump linear systems, assuming that the controller does not have access to the jump variable. We derive the expression of the gradient for the cost motivated by the evaluation of 10 gradient-based optimization techniques. The numerical efficiency of these techniques is verified by using the data obtained from practical experiments. The corresponding solution is used to design a scheme to control the velocity of a real-time DC motor device…

#### Topological degree in the generalized gause prey-predator model

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Makarenkov, O.

We consider a generalized Gause prey-predator model with T-periodic continuous coefficients. In the case where the Poincar√© map P over time T is well defined, the result of the paper can be explained as follows: we locate a subset U of R2 such that the topological degree d(I-P,U) equals to +1. The novelty of the paper is that the later is done under only continuity and (some) monotonicity assumptions for the coefficients of the model. A suitable integral operator is used in place of the…

#### The behavior of domain decomposition methods when the overlapping length is large

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Tran, M.-B.

In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.

#### Control of underwater vehicles in inviscid fluids: I. Irrotational flows

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lecaros, R., Rosier, L.

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron's return method, we establish some local…

#### Parallel Schwarz wave form relaxation algorithm for an n-dimensional semilinear heat equation

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Tran, M.-B.

We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods,…

#### Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Marica, A., Zuazua, E.

This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are…

#### A multilayer method for the hydrostatic Navier-Stokes equations: A particular weak solution

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Fernandez-Nieto, E.D., Kone, E.H., Chacon-Rebollo, T.

In this work we present a multilayer approach to the solution of non-stationary 3D Navier-Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulation and by considering a reduced family of test functions. The procedure naturally provides the mass…

#### On the Structure of $\infty$-Harmonic Maps

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Katzourakis, N.I.

Let H ‚àà C 2(‚ÑùN√ón), H ‚â• 0. The PDE system (Formula presented.) arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ‚àû(u, Œ©) = {norm of matrix}H(Du){norm of matrix}L ‚àû(Œ©) defined on maps u: Œ© ‚äÜ ‚Ñùn ‚Üí ‚ÑùN. (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ‚â§ N with H the Euclidean norm on ‚ÑùN√ón, which…

#### On the existence and asymptotic stability of solutions for unsteady mixing-layer models

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chacon-Rebollo, T., Gomez-Marmol, M., Rubino, S.

We introduce in this paper some elements for the mathematical analysis of turbulence models for oceanic surface mixing layers. We consider Richardson-number based vertical eddy diffusion models. We prove the existence of unsteady solutions if the initial condition is close to an equilibrium, via the inverse function theorem in Banach spaces. We use this result to prove the non-linear asymptotic stability of equilibrium solutions.

#### Optimal shape and location of sensors or actuators in PDE models

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Privat, Y., Trélat, E., Zuazua, E.

We investigate the problem of optimizing the shape and location of sensors and actuators for evolution systems driven by distributed parameter systems or partial differential equations (PDE). We consider wave, Schr√∂dinger and heat equations on an arbitrary domain Œ©, in any space dimension, and with suitable boundary conditions (if there is a boundary) which can be of Dirichlet, Neumann, mixed or Robin type. This kind of problem is frequently encountered in applications where one aims, for…

#### Optimal sensor location for wave and Schrödinger equations

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Privat, Y., Trélat, E., Zuazua, E.

This paper summarizes the research we have carried out recently on the problem of the optimal location of sensors and actuators for wave equa- tions, which has been the object of the talk of the third author at the Hyp2012 Conference held in Padova (Italy). We also address the same issues for the Schro ̈dinger equations and present some possible perspectives of future re- search.
We consider the multi-dimensional wave or Schro ̈dinger equations in a bounded domain Ω, with usual boundary…

#### Mode-independent H2-control of a DC motor modeled as a Markov jump linear system

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Oliveira, R.C.L.F., Vargas, A.N., Val, J.B.R.D., Peres, P.L.D.

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H2 -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that…

#### Global exact controllability in infinite time of Schrodinger equation: multidimensional case

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Nersesyan, V., Nersisyan, H.

In this paper, we study the problem of controllability of Schrödinger equation. We prove that the system is exactly controllable in infinite time to any po- sition. The proof is based on an inverse mapping theorem for multivalued functions. We show also that the system is not exactly controllable in finite time in lower Sobolev spaces.

#### Boundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Marica, A., Zuazua, E.

In this paper, we consider the boundary stabilization problem associated to the 1- d wave equation with both variable density and diffusion coefficients and to its finite difference semi-discretizations. It is well-known that, for the finite difference semi-discretization of the constant coefficients wave equation on uniform meshes (T√©bou and Zuazua, Adv. Comput. Math. 26:337‚Äì365, 2007) or on somenon-uniform meshes (Marica and Zuazua, BCAM, 2013, preprint), the discrete decay rate fails to…

#### The turnpike property infinite-dimensional nonlinear optimal control

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Trélat, E., Zuazua, E.

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated…

#### Internal control for non-local Schrodinger and wave equations involving the fractional Laplace operator

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Biccari, U.

We analyse the interior controllability problem for a non-local Schr\"odinger equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability from a neighbourhood of the boundary of the domain is obtained for exponents $s$ in the interval $[1/2,1)$, while for $s<1/2$ the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a non-local wave…

#### Derivation of a homogenized nonlinear plate theory from 3d elasticity

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Hornung, P., Neukamm, S., Velcic, I.

We derive, via simultaneous homogenization and dimension reduction, the (Formula presented.)-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff‚Äôs nonlinear bending theory of plates.

#### Propagation of 1D Waves in Regular Discrete Heterogeneous Media: A Wigner Measure Approach

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Marica, A., Zuazua, E.

In this article, we describe the propagation properties of the one-dimensional wave and transport equations with variable coefficients semi-discretized in space by finite difference schemes on non-uniform meshes obtained as diffeomorphic transformations of uniform ones. In particular, we introduce and give a rigorous meaning to notions like the principal symbol of the discrete wave operator and the corresponding bi-characteristic rays. The main mathematical tool we employ is the discrete Wigner…

#### A hyperbolic system and the cost of the null controllability for the Stokes system

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chaves-Silva, F.W.

This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time $T$ is of order $e^{C/T}$ when $T \to 0^+$, i.e., the same order of controllability as for the heat equation. For this to be possible, we prove a new exact controllability result for a hyperbolic system with a resistance term, which will be done under assumptions on the control region.

#### Hard-type inequalities for $\Delta_{\lambda}$-Laplacians

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Kogoj, A.E., Sonner, S.

We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of (Formula presented.) -Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin-type operators (Formula presented.) which were proved to be sharp.

#### Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lescarret, V., Zuazua, E.

We develop finite difference numerical schemes for a model arising in multi-body structures, previously analyzed by H. Koch and E. Zuazua, constituted by two n-dimensional wave equations coupled with a (n - 1)- dimensional one along a flexible interface. That model, under suitable assumptions on the speed of propagation in each media, is well-posed in asymmetric spaces in which the regularity of solutions differs by one derivative from one medium to the other. Here we consider a flat interface…

#### Finite time blow-up for the bosonic Nordheim equation

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Escobedo, M., Velazquez, J.J.L.

The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.

#### On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Kogut, P.I.

We study an optimal boundary control problem (OCP) associated to a linear elliptic equation -div (‚àáy + A(x)‚àáy) = f. The characteristic feature of this equation is the fact that the matrix A(x) = [aij (x)] i;j=1;

#### Critical points and symmetries of a free energy function for biaxial nematic liquid crystals

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chillingworth, D.R.J.

We describe a general mean field model for the free energy function for a homogeneous medium of mutually interacting molecules, based on the formalism for a biaxial nematic liquid crystal set out by Katriel et al (1986) in an influential paper in Liquid Crystals 1 and subsequently called the KKLS formalism. The free energy is expressed as the sum of an entropy term and an interaction (Hamiltonian) term. Using the language of group representation theory we identify the order parameters as…

#### Sparse initial data identification for parabolic PDE and its finite element approximations

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Casas, E., Vexler, B., Zuazua, E.

We address the problem of inverse source identication for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on…

#### Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Escobedo, M., Tran, M.-B.

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasipar-ticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither bounded from below nor from above. We prove the ex-istence and uniqueness of solutions satisfying the conservation of energy. We show that these solutions converge to the corresponding stationary state, at an algebraic rate as time tends to infinity.

#### Emergence of cooperation in phenotypically heterogeneous populations: A replicator dynamics analysis

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Barreira Da Silva Rocha, A., Escobedo, R., Laruelle, A.

The emergence of cooperation is analyzed in heterogeneous populations where two kinds of individuals exist according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type. Individuals thus behave under partial information conditions. The interactions between individuals are described by the snowdrift game, where individuals can either cooperate or defect. The…

#### Molien series and low-degree invariants for a natural action of $SO(3) \wr Z_2$

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chillingworth, D.R.J., Lauterbach, R., Turzi, S.S.

We investigate the invariants of the 25-dimensional real representation of the group SO(3) ? Z2 given by the left and right actions of SO(3) on 5 5 matrices together with matrix transposition; the action on column vectors is the irreducible five-dimensional representation of SO(3). The 25-dimensional representation arises naturally in the study of nematic liquid crystals, where the second-rank orientational order parameters of a molecule are represented by -rfaut symmetric 3 Ã—3 traceless…

#### A uniform controllability result for the Keller-Segel system

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Chaves-Silva, F.W., Guerrero, S.

In this paper we study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic system when the control is acting on the component of the chemical.

#### Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Privat, Y., Trélat, E., Zuazua, E.

In this article, we consider parabolic equations on a bounded open connected subset Rn. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem is motivated by the question of knowing how to shape and place sensors in some domain in order to maximize the quality of the observation: for instance, what is the optimal location and shape of a thermometer? We show that it is relevant to consider a spectral optimal design…

#### Complexity and regularity of maximal energy domains for the wave equation with fixed initial data

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Privat, Y., Trélat, E., Zuazua, E.

We consider the homogeneous wave equation on a bounded open connected subset Î© of IRn. Some initial data being specified, we consider the problem of determining a measurable subset Ï‰ of Î© maximizing the L2-norm of the restriction of the corresponding solution to Ï‰ over a time interval [0, T], over all possible subsets of Î© having a certain prescribed measure. We prove that this problem always has at least one solution and that, if the initial data satisfy some analyticity assumptions, then…

#### A Systematization of the Unscented Kalman Filter Theory

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Menegaz, H.M.T., Ishihara, J.Y., Borges, G.A., Vargas, A.N.

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (…

#### Control of a hysteresis model subject to random failures

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lévano, E., Vargas, A.N.

The note presents conditions to assure weak stability in the mean for a hysteresis Bouc-Wen model controlled by a proportional-integral controller subject to random failures. When a failure happens, the controller turns off and remains off for a while. After that the controller turns on and keeps on until the occurrence of the next failure. The failures occur according to a Poisson distributed process. A numerical example illustrates the result.

#### Counterexample of loss of regularity for fractional order evolution equations with both degenerating and oscillating coefficients

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Lu, X., Tu, Z., Liu, X.

For weak evolution models of fractional order with singularity near the origin, the joint influence from the principal œÉ-Laplacian operator, degenerating part and oscillating part is of prime concern in the discussion of regularity behavior of the solutions. We apply the techniques from the micro-local analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, a delicate counterexample with periodic coefficients will be…

#### On the well-posedness of mathematical models for multicomponent biofilms

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Sonner, S., Efendiev, M.A., Eberl, H.J.

Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects: (i) a porous medium equation like degeneracy where the biomass density vanishes and (ii) a super-diffusion singularity if the biomass density reaches its threshold density. In the case of multispecies interactions, several such equations are coupled, both in the reaction terms and in the nonlinear diffusion operator. In…

#### Long time dynamics of a multidimensional nonlinear lattice with memory

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Oliveira, J.C., Pereira, J.M., Menzala, G.P.

This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction on the nonlinear term we obtain decay rates of the total energy. These rates could be exponential, polynomial or several other intermediate types.

#### Optimal strategies for driving a mobile agent in a "guidance by repulsion" model

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Escobedo, R., Ibañez, A., Zuazua, E.

We present a guidance by repulsion model based on a driver-evader interaction where the driver, assumed to be faster than the evader, follows the evader but cannot be arbitrarily close to it, and the evader tries to move away from the driver beyond a short distance. The key ingredient allowing the driver to guide the evader is that the driver is able to display a circumvention maneuver around the evader, in such a way that the trajectory of the evader is modified in the direction of the…

#### An ADER-type scheme for a class of equations arising from the water-wave theory

**Repositorio: **BIRD: BCAM's Institutional Repository Data

Montecinos, G.I., López-Rios, J.C., Lecaros, R., Ortega, J.H., Toro, E.F.

In this work we propose a numerical strategy to solve a family of partial differential equations arising from the water-wave theory. These problems may contain four terms; a source which is an algebraic function of the solution, a convective part involving first order spatial derivatives of the solution, a diffusive part involving second order spatial derivatives and the transient part. Unlike partial differential equations of hyperbolic or parabolic type, where the transient part is the time…