相关论文: Small inertia regularization of an anisotropic agg…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…

The semiclassical backreaction equations are solved in closed Robertson-Walker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stress-energy tensor results in…

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the…

In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator…

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226]…

A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…

This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…

An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and…

We consider the Ising model on a small-world network, where the long-range interaction strength $J_2$ is in general different from the local interaction strength $J_1$, and examine its relaxation behaviors as well as phase transitions. As…

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…

In systems displaying a bulk first-order transition the order parameter may vanish continuously at a free surface, a phenomenon which is called surface-induced disorder. In the presence of surface-induced disorder the correlation lengths,…

We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods for proving hypocoercivity of the linearized equations. Exponential decay of…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction…

In practical applications, the efficacy of a control algorithm relies critically on the accurate knowledge of the parameters and states of the underlying system. However, obtaining these quantities in practice is often challenging. Adaptive…

We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of novel type: jump of the order parameter coincides with its power-law singularity. Some…

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational…

We study the asymptotic behaviour, as the small parameter $\varepsilon$ tends to zero, of the resolvents of uniformly elliptic second-order differential operators with locally periodic coefficients depending on the slow variable $x$ and the…