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Phase-sensitive coherent imaging exploits changes in the phases of backscattered light to observe tiny alterations of scattering structures or variations of the refractive index. But moving scatterers or a fluctuating refractive index…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
In this article, we derive off-diagonal estimates of the Bergman kernel associated to the tensor-powers of the cotangent bundle defined on a hyperbolic Riemann surface of finite volume, when the distance between the points is less than…
Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
In this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr\"odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Polymer mixtures fractionate between phases depending on their molecular weight. Consequently, by varying solvent conditions, a polydisperse polymer sample can be separated between phases so as to achieve a particular molecular weight…
We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system…
In a previous work [math.AP/0305408] three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the…
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive.…
By far, the fractional derivative model is mainly related to the modelling of complicated solid viscoelastic material. In this study, we try to build the fractional derivative PDE model for broadband ultrasound propagation through human…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the seventh paper, the usual structural analysis of beams on an elastic foundation…
We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…