Dissipation in holographic superfluids

We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global U(1). By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. Finally, we study the pseudo-Goldstone mode that emerges upon introducing a perturbative symmetry breaking source and we determine its resonant frequency and decay rate.

Global small data solutions for semilinear waves with two dissipative terms

In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity $$|u|^p$$ | u | p or nonlinearity of derivative type $$|u_t|^p$$ | u t | p , in any space dimension $$n\geqslant 1$$ n ⩾ 1 , for supercritical powers $$p>{\bar{p}}$$ p > p ¯ . The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive $$L^r-L^q$$ L r - L q long time decay estimates for the solution in the full range $$1\leqslant r\leqslant q\leqslant \infty $$ 1 ⩽ r ⩽ q ⩽ ∞ . The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers $$p<{\bar{p}}$$ p < p ¯ .

Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.

Intrinsically symmetric cosmological model in the presence of dissipative fluids

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter components.

A regularity criterion for a 2D tropical climate model with fractional dissipation

Tropical climate model derived by Frierson et al. (Commun Math Sci 2:591–626, 2004) and its modified versions have been investigated in a number of papers [see, e.g., Li and Titi (Discrete Contin Dyn Syst Series A 36(8):4495–4516, 2016), Wan (J Math Phys 57(2):021507, 2016), Ye (J Math Anal Appl 446:307–321, 2017) and more recently Dong et al. (Discrete Contin Dyn Syst Ser B 24(1):211–229, 2019)]. Here, we deal with the 2D tropical climate model with fractional dissipative terms in the equation of the barotropic mode u and in the equation of the first baroclinic mode v of the velocity, but without diffusion in the temperature equation, and we establish a regularity criterion for this system.

Asymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domains

This paper is concerned with the asymptotic behaviour of solutions to a class of non-autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space $\mathbb {R}^n$ . The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors are proved in $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$ when the growth rate of the nonlinearity has a subcritical range, the density of the noise is suitably controllable, and the time-dependent force converges to a time-independent function in some sense. The main difficulty to establish the time-semi-uniform pullback asymptotic compactness of the solutions in $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$ is caused by the lack of compact Sobolev embeddings on $\mathbb {R}^n$ , as well as the weak dissipativeness of the equations is surmounted at light of the idea of uniform tail-estimates and a spectral decomposition approach. The measurability of random attractors is proved by using an argument which considers two attracting universes developed by Wang and Li (Phys. D 382: 46–57, 2018).

A Passivity Approach to the Stabilization of Free-Radical Polymerization Reactor

This work proposes a tracking error passivity-based multivariable control viafeedback passivation for a class of free-radical polymerization systems in a continuouslystirred tank reactor (CSTR). Firstly, this system dynamics with high nonlinearity ispassivized by input coordinate transformations, the resulting passive system is then rewritten into a canonical form strongly related to the so-called Port Control Hamiltonianstructure. Actually, this representation allows to show the physical meanings of systemdynamics such as dissipative, non-dissipative terms and supply rate. From this, a feedbackcontroller based on tracking error is designed for the globally exponential stabilization atan arbitrarily chosen reference trajectory passing the desired equilibrium point. Thetheoretical developments are then illustrated for polystyrene polymerization system inthe CSTR. The numerical simulations show that the trajectories of styrene polymerizationsystem considered as an illustrative example of FRP system converges globallyexponentially to the imposed trajectories.