Molecular theory of underdamped dielectric relaxation: understanding collective effects in dipolar liquids

A molecular theory of underdamped dielectric relaxation of a dense dipolar liquid is presented. This theory properly takes into account the collective effects that are present (due to strong intermolecular correlations) in a dipolar liquid. For small rigid molecules, the theory again leads to a three-variable description which, however, is somewhat different from the traditional version. In particular, two of the three parameters are collective in nature and are determined by the orientational pair correlation function. A detailed comparison between the theory and the computer simulation results of Neria and Nitzan is performed and an excellent agreement is obtained without the use of any adjustable or free parameter - the calculation is fully microscopic. The theory can also provide a systematic description of the Poley absorption often observed in dipolar liquids in the high-frequency regime.

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Theory of the non-Fermi-liquid transition point in the two-impurity Kondo model

We present an explicit solution of the problem of two coupled spin-1/2 impurities, interacting with a band of conduction electrons. We obtain an exact effective bosonized Hamiltonian, which is then treated by two different methods (low-energy theory and mean-field approach). Scale invariance is explicitly shown at the quantum critical point. The staggered susceptibility behaves like ln(T(K)/T) at low T, whereas the magnetic susceptibility and [S1.S2] are well behaved at the transition. The divergence of C(T)/T when approaching the transition point is also studied. The non-Fermi-liquid (actually marginal-Fermi-liquid) critical point is shown to arise because of the existence of anomalous correlations, which lead to degeneracies between bosonic and fermionic states of the system. The methods developed in this paper are of interest for studying more physically relevant models, for instance, for high-T(c) cuprates.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

A Microscopic Theory of the f.c.c.-b.c.c. Interface .

We present a first-principles theory of the equilibrium b.c.c.-f.c.c. interface at coexistence using the density functional method. We assume that the interfacial region has local body-centred tetragonal (b.c.t.) symmetry and predict typical interfacial widths to be of order 2 to 3 lattice spacings with typical energies close to 0.05 J/m2. These quantities are in good agreement with laboratory measurements on coherent interfaces.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

A new theory of gravitation with parity-violating propagating torsion

A new theory of gravitation has been proposed in a more general space-time than Riemannian. It is a generalization of the ECSK and Brans-Dicke (BD) theory of gravitation. It is found that, in contrast to the standard the ECSK theory, a parity-violating propagating torsion is generated by the BD scalar field. The interesting consequence of the theory is that it can successfully predict solar system experimental results to desired accuracy.

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/4 pi. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.

A Sub-Nyquist Sampling Method For Computing The Level-crossing-times Of An Analog Signal: Theory And Applications

We address the problem of computing the level-crossings of an analog signal from samples measured on a uniform grid. Such a problem is important, for example, in multilevel analog-to-digital (A/D) converters. The first operation in such sampling modalities is a comparator, which gives rise to a bilevel waveform. Since bilevel signals are not bandlimited, measuring the level-crossing times exactly becomes impractical within the conventional framework of Shannon sampling. In this paper, we propose a novel sub-Nyquist sampling technique for making measurements on a uniform grid and thereby for exactly computing the level-crossing times from those samples. The computational complexity of the technique is low and comprises simple arithmetic operations. We also present a finite-rate-of-innovation sampling perspective of the proposed approach and also show how exponential splines fit in naturally into the proposed sampling framework. We also discuss some concrete practical applications of the sampling technique.

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.