Related papers: Mathematical analysis of an age structured problem…
In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there…
Synaptic plasticity is metabolically expensive, yet animals continuously update their internal models without exhausting energy reserves. However, when artificial neural networks are trained, the network parameters are typically updated on…
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single…
We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
Understanding how living organisms spontaneously develop complex functional structures inspires innovative approaches in engineering design. Here, we introduce a decentralized generative model based on morphogenesis to autonomously grow…
This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
Aging behavior is an important effect in the friction properties of solid surfaces. In this paper we investigate the temporal evolution of the static properties of a granular medium by studying the aging over time of the maximum stability…
In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…
Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic…
We define regularised Poisson brackets for the monodromy matrix of classical string theory on R x S^3. The ambiguities associated with Non-Ultra Locality are resolved using the symmetrisation prescription of Maillet. The resulting brackets…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
An unexpected dichotomic long time aging behaviour is observed in a glassy colloidal clay suspension investigated by X-Ray Photon Correlation Spectroscopy and Dynamic Light Scattering. In the long time aging regime the intensity…
We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…