A new power MEMS component with variable capacitance

Autonomous devices such as wireless sensors and sensor networks need a long battery lifetime in a small volume. Incorporating micro-power generators based on ambient energy increases the lifetime of these systems while reducing the volume. This paper describes a new approach to the conversion of mechanical energy, available in vibrations, to electrical energy. The conversion principle is based on charge transportation between two parallel capacitors. An electret is used to polarize the device. A large-signal model was developed, allowing simulations of the behavior of the generator. A small-signal model was then derived in order to quantify the output power as a function of the design parameters. These models show the possibility of generating up to 40 muW with a device of 10 mm 2. A layout was made based on a standard SOI-technology, available in an MPW. With this design a power of 1 muW at 1020 Hz is expected

Reply to Comment on "Existence of Internal Modes of sine-Gordon Kinks"

In this reply to the comment by C. R. Willis, we show, by quoting his own statements, that the simulations reported in his original work with Boesch [Phys. Rev. B 42, 2290 (1990)] were done for kinks with nonzero initial velocity, in contrast to what Willis claims in his comment. We further show that his alleged proof, which assumes among other approximations that kinks are initially at rest, is not rigorous but an approximation. Moreover, there are other serious misconceptions which we discuss in our reply. As a consequence, our result that quasimodes do not exist in the sG equation [Phys. Rev. E 62, R60 (2000)] remains true.Comment: Reply to a comment by C. R. Willis on Phys. Rev. E 62, R60 (2000), to appear in Physical Review

Pariah moonshine

Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate--Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.Comment: 20 page

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential

We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\bar{\Psi} \Psi)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find that, for all three cases, after a short transit time, the initial pulse breaks into two pulses which are solutions of the massless linear Dirac equation traveling in opposite directions with the speed of light. During this splitting the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation.Comment: 11 pages, 7 figure

Nonlinear Dirac equation solitary waves under a spinor force with different components

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar selfinteraction in the presence of external forces as well as damping of the form γͦf(x-t) - ιμγͦψ, where both f, {fj = rieiKjx} and ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. In our previous paper we assumed Kj = K, j = 1,2 which allowed a transformation to a simplifying coordinate system, and we also assumed the "small" component of the external force was zero. Here we include the effects of the small component and also the case K1 ≠ K2 which dramatically modi es the behavior of the solitary wave in the presence of these external forces.United States Department of EnergySanta Fe InstituteNational Natural Science Foundation of China (Nos. 11471025 and 11421101)Alexander von Humboldt Foundation (Germany) through Research Fellowship for Experienced Researchers SPA 1146358 STPMinisterio de Economía y Competitividad (Spain) through FIS2014-54497-PJunta de Andalucía (Spain) under Projects No. FQM207Excellent Grant P11-FQM-7276Mathematical Institute of the University of Seville (IMUS)Theoretical Division and Center for Nonlinear Studies at Los Alamos National LaboratoryPlan Propio of the University of Sevill

Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise

We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional classical, ferromagnetic, anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise both have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a non-trivial result, as multiplicative and additive noises usually modify the dynamics quite differently. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.Comment: 10 pages, 6 figure