Later-life Effects of Mitochondrial DNA Damage During Development in the Whole Organism Model Caenorhabditis elegans by Maxwell C. K. Leung Environment Duke University Date:_______________________ Approved: ___________________________ Joel N. Meyer, Supervisor ___________________________ Shawn Ahmed ___________________________ Jonathan H. Freedman ___________________________ David E. Hinton An ...

This paper is concerned with the approximation of the time domain Maxwell equations in a dispersive propagation medium by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the medium. We adapt the locally implicit time integration method from [1] and derive a convergence analysis to prove that the locally implicit DGTD method for...

We prove that the Maxwell-Klein-Gordon equations on R relative to the Coulomb gauge are locally well-posed for initial data in H for all ε > 0. This builds on previous work by Klainerman and Machedon [3] who proved the corresponding result for a model problem derived from the Maxwell-Klein-Gordon system by ignoring the elliptic features of the system, as well as cubic terms.

this deals with the harmonic forced vibration of a circular plate surface bonded by two piezoelectric layers, based on the kirchhoff plate model. the form of electric potential field in the piezoelectric layer is assumed such that the maxwell static electricity equation is satisfied. the differential equations of motion are solved analytically for clamped edge boundary condition of the plate. t...

Maxwell-type models for non-linear kinetic equations have many applications in physics, dynamics of granular gases, economics, and other areas where statistical modeling is relevant. They model the evolution of probability measures (distribution functions) and relate to a class of non-linear space homogeneous Boltzmann equations for binary interactions where scattering probability rates of the ...

We consider the Dirac equation in flat Minkowski 3–space and rewrite it as the Maxwell equation in Minkowski 4–space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to “negative frequencies”: we produce a real scalar invariant (charge) which indicates whether we are l...

We present in this paper a numerical Maxwell–Schrödinger model to simulate intense ultrashort laser pulses interacting with a H 2 -gas in the nonlinear non-perturbative regime. After presentation of the model and a short mathematical study, we propose a numerical approach for its computation. In particular we focus on the polarization computation allowing the coupling between the Maxwell and Sc...

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact anal...

Two numerical schemes are developed for solutions of the bidimensional Maxwell-Bloch equations in nonlinear optical crystals. The Maxwell-Bloch model was recently extended [1] to treat anisotropic materials like nonlinear crystals. This semiclassical model seems to be adequate to describe the wave-matter interaction of ultrashort pulses in nonlinear crystals [2] as it is closer to the physics t...

SUMMARY In this paper an inverse scattering problem for the time-dependent Maxwell curl equations is considered. This problem is formulated as an optimal control problem governed by partial differential equations. First-order necessary optimality conditions are discussed. For the numerical solution a gradient-based algorithm is applied and successfully tested for some numerical examples. Finall...