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While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the…
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish…
We theoretically analyze three-mode opto-acoustic parametric interactions in a coupled Fabry-Perot cavity, where one acoustic mode interacts with two optical modes. We show explicitly that extra degrees of freedom in a coupled cavity allow…
A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the…
Parametric excitation in coupled mechanical systems has enabled advances in sensing, computation, and phonon control. The function of distinct phase modes using parametric driving remains insufficiently explored. Here, we investigate the…
The existence of a symmetric mode in an elastic solid wedge for all admissible values of the Poisson ratio and arbitrary openings close to $\pi$ has been proven.
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
A numerical solver for the elastic wave eigenmodes in acoustic waveguides of inhomogeneous cross-section is presented. Operating under the assumptions of linear, isotropic materials, it utilizes a finite-difference method on a staggered…
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly…
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent…
A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector…
The interactions between parametrically and directly driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric…
Threshold of the transverse mode coupling instability is calculated in frameworks of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique.…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
A computational fluid dynamics methodology for the simulation of electromagnetic interactions in compressible reacting flows has been formulated. The developed code, named EMI, is based on the SENGA Direct Numerical Simulation (DNS)…
A four dimensional systematic mathematical approach for investigating propagation and coupling of wave modes in a slowly varying (in all space directions and time) anisotropic, absorbing plasma is represented. The formalism is especially…
We show experimentally that parametric interaction can induce a cooperative oscillation of non simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially…