Can an observer really catch up with light

Given a null geodesic $\gamma_0(\lambda)$ with a point $r$ in $(p,q)$ conjugate to $p$ along $\gamma_0(\lambda)$, there will be a variation of $\gamma_0(\lambda)$ which will give a time-like curve from $p$ to $q$. This is a well-known theory proved in the famous book\cite{2}. In the paper we prove that the time-like curves coming from the above-mentioned variation have a proper acceleration which approaches infinity as the time-like curve approaches the null geodesic. This means no observer can be infinitesimally near the light and begin at the same point with the light and finally catch the light. Only separated from the light path finitely, does the observer can begin at the same point with the light and finally catch the light.Comment: 6 pages, no figures, submited to Physical Review

A Fully Parameterized Fem Model for Electromagnetic Optimization of an RF Mems Wafer Level Package

In this work, we present a fully parameterized capped transmission line model for electromagnetic optimization of a wafer level package (WLP) for RF MEMS applications using the Ansoft HFSS-TM electromagnetic simulator. All the degrees of freedom (DoF's) in the package fabrication can be modified within the model in order to optimize for losses and mismatch (capacitive and inductive couplings) introduced by the cap affecting the MEMS RF behaviour. Ansoft HFSS-TM was also validated for the simulation of capped RF MEMS devices by comparison against experimental data. A test run of capped 50 transmission lines and shorts was fabricated and tested.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

Parasitic Effects Reduction for Wafer-Level Packaging of RF-Mems

In RF-MEMS packaging, next to the protection of movable structures, optimization of package electrical performance plays a very important role. In this work, a wafer-level packaging process has been investigated and optimized in order to minimize electrical parasitic effects. The RF-MEMS package concept used is based on a wafer-level bonding of a capping silicon substrate to an RF-MEMS wafer. The capping silicon substrate resistivity, substrate thickness and the geometry of through-substrate electrical interconnect vias have been optimized using finite-element electromagnetic simulations (Ansoft HFSS). Test structures for electrical characterization have been designed and after their fabrication, measurement results will be compared with simulations.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstr\"om black holes in $(n+1)$-dimensional anti-de Sitter spacetime is studied in details using the thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid gas system. We first investigate critical phenomena of the RN-AdS black hole. The critical exponents of relevant thermodynamical quantities are evaluated. We find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas system. This suggests a possible universality in the phase transitions of these systems. We finally study the thermodynamic behavior using the equilibrium thermodynamic state space geometry and find that the scalar curvature diverges exactly at the van der Waals-like critical point where the heat capacity at constant charge of the black hole diverges.Comment: 18 pages, 5 figure

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

Flat bidifferential ideals and semihamiltonian PDEs

In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural interpretation in the theory of flat bifferential ideals. The class of systems we consider contains important well-known examples of semihamiltonian systems. Other examples, like genus 1 Whitham modulation equations for KdV, are related to this class by a reciprocal trasformation.Comment: 18 pages. v5: formula (36) corrected; minor change

Heat capacity anomaly at the quantum critical point of the Transverse Ising Magnet CoNb_2O_6

The transverse Ising magnet Hamiltonian describing the Ising chain in a transverse magnetic field is the archetypal example of a system that undergoes a transition at a quantum critical point (QCP). The columbite CoNb$_2$O$_6$ is the closest realization of the transverse Ising magnet found to date. At low temperatures, neutron diffraction has observed a set of discrete collective spin modes near the QCP. We ask if there are low-lying spin excitations distinct from these relatively high energy modes. Using the heat capacity, we show that a significant band of gapless spin excitations exists. At the QCP, their spin entropy rises to a prominent peak that accounts for 30$\%$ of the total spin degrees of freedom. In a narrow field interval below the QCP, the gapless excitations display a fermion-like, temperature-linear heat capacity below 1 K. These novel gapless modes are the main spin excitations participating in, and affected, by the quantum transition.Comment: 14 pages total, 8 figure