Capacitive-Resistive Transients in terms of field quantities

Capacitive-resistive transients in extended media are discussed in tenns of electric field quantities. Obviously, in rhese problems, the contribution of the magnetlc field to the electric field is deemed negligible. For a simple lllusfratlve example, the field solution is compared with the circuit-theoretical resuit for the voltage and current. An algorithm for solving such transients in space and time doman with the help of a Laplace solver is presented. Any other Laplace solver can also be used far this purpose. Its applicability is demonstrated with three examples, one of which is chosen to have a circuit-theoretical solution.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.

Gel Sculpture: Moldable, Load-Bearing and Self-Healing Non-Polymeric Supramolecular Gel Derived from a Simple Organic Salt

An easy access to a library of simple organic salts derived from tert-butoxycarbonyl (Boc)-protected L-amino acids and two secondary amines (dicyclohexyl- and dibenzyl amine) are synthesized following a supramolecular synthon rationale to generate a new series of low molecular weight gelators (LMWGs). Out of the 12 salts that we prepared, the nitrobenzene gel of dicyclohexylammonium Boc-glycinate (GLY.1) displayed remarkable load-bearing, moldable and self-healing properties. These remarkable properties displayed by GLY.1 and the inability to display such properties by its dibenzylammonium counterpart (GLY.2) were explained using microscopic and rheological data. Single crystal structures of eight salts displayed the presence of a 1D hydrogen-bonded network (HBN) that is believed to be important in gelation. Powder X-ray diffraction in combination with the single crystal X-ray structure of GLY.1 clearly established the presence of a 1D hydrogen-bonded network in the xerogel of the nitrobenzene gel of GLY.1. The fact that such remarkable properties arising from an easily accessible (salt formation) small molecule are due to supramolecular (non-covalent) interactions is quite intriguing and such easily synthesizable materials may be useful in stress-bearing and other applications.

Bulk Majorana mass terms and Dirac neutrinos in the Randall-Sundrum model

We present a novel scheme where Dirac neutrinos are realized even if lepton number violating Majorana mass terms are present. The setup is the Randall-Sundrum framework with bulk right-handed neutrinos. Bulk mass terms of both Majorana and Dirac type are considered. It is shown that massless zero mode solutions exist when the bulk Dirac mass term is set to zero. In this limit, it is found that the effective 4D small neutrino mass is primarily of Dirac nature, with the Majorana-type contributions being negligible. Interestingly, this scenario is very similar to the one known with flat extra dimensions. Neutrino phenomenology is discussed by fitting both charged lepton masses and neutrino masses simultaneously. A single Higgs localized on the IR brane is highly constrained, as unnaturally large Yukawa couplings are required to fit charged lepton masses. A simple extension with two Higgs doublets is presented, which facilitates a proper fit for the lepton masses.

ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados-Teitelboim-Zanelli (BTZ) black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

Comprehending the Formation of Eutectics and Cocrystals in Terms of Design and Their Structural Interrelationships

The phenomenon of cocrystallization, which encompasses the art of making multicomponent organic solids such as cocrystals, solid solutions, eutectics, etc. for novel applications, has been less studied in terms of reliably and specifically obtaining a desired cocrystallization product and the issues that govern their formation. Further, the design, structural, and functional aspects of organic eutectics have been relatively unexplored as compared to solid solutions and cocrystals well-established by crystal engineering principles. Recently, eutectics were proposed to be designable materials on par with cocrystals, and herein we have devised a systematic approach, based on the same crystal engineering principles, to specifically and desirably make both eutectics and cocrystals for a given system. The propensity for strong homomolecular synthons over weak heteromolecular synthons and vice versa during supramolecular growth was successfully utilized to selectively obtain eutectics and cocrystals, respectively, in two model systems and in two drug systems. A molecular level understanding of the formation of eutectics and cocrystals and their structural interrelationships which is significant from both fundamental and application viewpoints is discussed. On the other hand, the obscurity in establishing a low melting combination as a eutectic or a cocrystal is resolved through phase diagrams.

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian (PN) order. We further extend these results for compact binaries in quasielliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current-type multipole moments, we compute the spin-weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasielliptical orbits.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

A Cip/Multi-Moment Finite Volume Method For Shallow Water Equations With Source Terms

A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments. Copyright (c) 2007 John Wiley & Sons, Ltd.

The role of the terms of trade in the trade channel of transmission of oil price shocks

This paper highlights the role of the terms of trade in the trade channel of propagation of oil price shocks both empirically and theoretically. Empirically, I show that oil price shocks have a large, persistent and statistically significant impact on the US terms of trade. Theoretically, I add oil in the model by Corsetti and Pesenti (2005) and analyse under what conditions the terms of trade plays a relevant role in the international transmission of oil price shocks. With nominal price rigidities and full exchange rate pass-through positive oil price shocks depreciate the currency of the oil importing country. The subsequent negative wealth effect adds to the recessive effect of the supply channel and may trongly reduce the consumption in the oil importing country economy. Without exchange rate pass-through oil shocks transmit to the economy only through the supply channel. The model suggests that a change in the exchange rate pass-through might contribute to explain the evidence of a weaker impact of oil price shocks on the macroeconomic activity in recent times.