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The temperonic crystal, a periodic structure with a unit cell made of two slabs sustaining temperature wave-like oscillations on short time-scales, is introduced. The complex-valued dispersion relation for the temperature scalar field is…
We investigate the in-plane oscillations of the relaxed shape graphene due to externally applied tensile edge stress along both the armchair and zigzag directions. We show that the total elastic energy density is enhanced with temperature…
We derive sufficient conditions for the existence of a periodic traveling wave solution to an integro-difference equation with a piecewise constant growth function exhibiting a stable period2 cycle and strong Allee effect. The mean…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
This paper concerns the global propagation of impact-induced tensile waves in a kind of phase-transforming materials. It is well-known that the governing system of partial differential equations is hyperbolic-elliptic and the…
In this paper we analyze the wavefront solutions of parabolic partial differential equations of the type \[ g(u)u_{\tau}+f(u)u_{x}=\left(D(u)u_{x}\right)_{x}+\rho(u),\quad u\left(\tau,x\right)\in[0,1] \] where the reaction term $\rho$ is of…
We demonstrate the high stability of simulated graphene hyperbolic pseudospheres under large externally imposed deformations and high temperature annealing. Hyperbolic pseudospheres are produced in a two-step Molecular Dynamics simulation…
In this work, we present a comprehensive investigation of graphene's thermal conductivity using first-principles density functional perturbation theory calculations, with a focus on the phonon and lattice vibrational properties underlying…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
Position measurements at the quantum level are vital for many applications, but also challenging. Typically, methods based on optical phase shifts are used, but these methods are often weak and difficult to apply to many materials. An…
We demonstrate a substrate-supported thermometry platform to measure thermal conduction in nanomaterials like graphene, with no need to suspend them. We use three-dimensional simulations and careful uncertainty analysis to optimize the…
Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a "side-contact" geometry which causes the current to flow perpendicular to the sheets within the device. Such…
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional…
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…
We propose an on-chip CMOS compatible graphene plasmonic photodetector based on the photo-thermoelectric effect (PTE) that occurs across an entire homogeneous graphene channel. The proposed photodetector incorporates the long-range…