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The discrete unified gas kinetic scheme (DUGKS) with a force term is a finite volume solver for the Boltzmann equation. Unlike the standard lattice Boltzmann method (LBM), DUGKS can be applied on nonuniform grids. For both the LBM and DUGKS, the boundary conditions need to be processed through the density distribution function. So researchers introduced the boundary conditions from the LBM frame into the DUGKS. However, the accuracy of these boundary conditions in the DUGKS has not been studied thoroughly. Through strict theoretical deduction, we find that the bounce-back (BB) scheme leads to a different dependence of the numerical error term in the DUGKS as compared to the LBM. VX-661 The error term is influenced by the relaxation time and the body force. And it can be reduced by lowering the kinetic viscosity. Unlike the BB scheme, the nonequilibrium bounce-back scheme has the ability to implement real no-slip boundary condition. Furthermore, two slip boundary conditions incorporated with Navier's slip model are introduced from the LBM framework into the DUGKS. The tangential momentum change-based (TMAC) scheme can be used directly in the DUGKS because it generates no numerical error term in the DUGKS. For the combination of the bounce-back and specular reflection schemes (BSR), the relation between the slip length and the combination parameter should be modified in accordance with the numerical error term. Analysis shows that the TMAC scheme can simulate a wider range of slip length than the BSR scheme. Numerical simulations of the Couette flow and the Poiseuille flow confirm our theoretical analysis.We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.The Ott-Antonsen ansatz is a powerful tool to extract the behaviors of coupled phase oscillators, but it imposes a strong restriction on the initial condition. Herein, an extension of the Ott-Antonsen ansatz is proposed to relax the restriction, enabling the systematic approximation of the behavior of a globally coupled phase oscillator system with an arbitrary initial condition. The proposed method is validated on the Kuramoto-Sakaguchi model of identical phase oscillators. The method yields cluster and chimera-like solutions that are not obtained by the conventional ansatz.Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semiclassical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited s-state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the d-state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of ∼1/r^d+σ (denoted as LTDP), where r is the separation, d is the spatial dimension, and σ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension d_c=min(3,1.5σ). We numerically obtain a set of critical exponents in the LTDP class and determine the interval of σ for the LTDP class. Finally, we construct a diagram of universality classes in the space (d,σ).The lattice Boltzmann method often involves small numerical time steps due to the acoustic scaling (i.e., scaling between time step and grid size) inherent to the method. In this work, a second-order dual-time-stepping lattice Boltzmann method is proposed in order to avoid any time-step restriction. The implementation of the dual time stepping is based on an external source in the lattice Boltzmann equation, related to the time derivatives of the macroscopic flow quantities. Each time step is treated as a pseudosteady problem. The convergence rate of the steady lattice Boltzmann solver is improved by implementing a multigrid method. The developed solver is based on a two-relaxation time model coupled to an immersed-boundary method. The reliability of the method is demonstrated for steady and unsteady laminar flows past a circular cylinder, either fixed or towed in the computational domain. In the steady-flow case, the multigrid method drastically increases the convergence rate of the lattice Boltzmann method.hod.In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. Here we propose and study a class of random walks defined on such higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterization of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalized random-walk Laplace operator that reduces to the standard random-walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have full control of the high-order structures and on real-world networks where higher-order interactions are at play.
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