Related papers: Higher Order Continuum Wave Equation Calibrated on…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…
The main purpose of the present paper is to solve the thermodynamic inconsistencies that result when deriving equivalent micropolar models of periodic beam-lattice materials through standard continualization schemes. In fact, this technique…
The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are…
In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections.…
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…
Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of…
We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a…
We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…
A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of the homogeneous reference state is studied in detail using methods of non-equilibrium statistical mechanics. A…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
Recent results relating to ray dynamics in ocean acoustics are reviewed. Attention is focussed on long-range propagation in deep ocean environments. For this class of problems, the ray equations may be simplified by making use of a one-way…