Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (delta(t) similar or equal to 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at delta similar or equal to 0.09 in case of T* = 1.0, phi = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at delta similar or equal to 0.10 (just beyond the solid-liquid transition density at T* = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Structure constants of beta deformed super Yang-Mills

We study the structure constants of the N = 1 beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS(5) x S-5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Auditory-motivated Gammatone wavelet transform

The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals. (C) 2013 Elsevier B.V. All rights reserved.

Regenerating codes: A reformulated storage-bandwidth trade-off and a new construction

In this paper, the storage-repair-bandwidth (SRB) trade-off curve of regenerating codes is reformulated to yield a tradeoff between two global parameters of practical relevance, namely information rate and repair rate. The new information-repair-rate (IRR) tradeoff provides a different and insightful perspective on regenerating codes. For example, it provides a new motivation for seeking to investigate constructions corresponding to the interior of the SRB tradeoff. Interestingly, each point on the SRB tradeoff corresponds to a curve in the IRR tradeoff setup. We characterize completely, functional repair under the IRR framework, while for exact repair, an achievable region is presented. In the second part of this paper, a rate-half regenerating code for the minimum storage regenerating point is constructed that draws upon the theory of invariant subspaces. While the parameters of this rate-half code are the same as those of the MISER code, the construction itself is quite different.

RIESZ-TRANSFORM-BASED DEMODULATION OF NARROWBAND SPECTROGRAMS OF VOICED SPEECH

Narrowband spectrograms of voiced speech can be modeled as an outcome of two-dimensional (2-D) modulation process. In this paper, we develop a demodulation algorithm to estimate the 2-D amplitude modulation (AM) and carrier of a given spectrogram patch. The demodulation algorithm is based on the Riesz transform, which is a unitary, shift-invariant operator and is obtained as a 2-D extension of the well known 1-D Hilbert transform operator. Existing methods for spectrogram demodulation rely on extension of sinusoidal demodulation method from the communications literature and require precise estimate of the 2-D carrier. On the other hand, the proposed method based on Riesz transform does not require a carrier estimate. The proposed method and the sinusoidal demodulation scheme are tested on real speech data. Experimental results show that the demodulated AM and carrier from Riesz demodulation represent the spectrogram patch more accurately compared with those obtained using the sinusoidal demodulation. The signal-to-reconstruction error ratio was found to be about 2 to 6 dB higher in case of the proposed demodulation approach.

Continuity equation based nonquasi-static charge model for independent double gate MOSFET

Using the numerical device simulation we show that the relationship between the surface potentials along the channel in any double gate (DG) MOSFET remains invariant in QS (quasistatic) and NQS (nonquasi-static) condition for the same terminal voltages. This concept along with the recently proposed `piecewise charge linearization' technique is then used to develop the intrinsic NQS charge model for a Independent DG (IDG) MOSFET by solving the governing continuity equation. It is also demonstrated that unlike the usual MOSFET transcapacitances, the inter-gate transcapacitance of a IDG-MOSFET initially increases with the frequency and then saturates, which might find novel analog circuit application. The proposed NQS model shows good agreement with numerical device simulations and appears to be useful for efficient circuit simulation.

Pressure-Induced Bond Rearrangement and Reversible Phase Transformation in a Metal-Organic Framework

Pressure-induced phase transformations (PIPTs) occur in a wide range of materials. In general, the bonding characteristics, before and after the PIPT, remain invariant in most materials, and the bond rearrangement is usually irreversible due to the strain induced under pressure. A reversible PIPT associated with a substantial bond rearrangement has been found in a metal-organic framework material, namely tmenH(2)]Er(HCOO)(4)](2) (tmenH(2)(2+) = N,N,N',N'-tetramethylethylenediammonium). The transition is first-order and is accompanied by a unit cell volume change of about 10%. High-pressure single-crystal X-ray diffraction studies reveal the complex bond rearrangement through the transition. The reversible nature of the transition is confirmed by means of independent nanoindentation measurements on single crystals.

Topological blocking in quantum quench dynamics

We study the nonequilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground-state degeneracies and associated topological sectors. We present the notion of ``topological blocking,'' experienced by the dynamics due to a mismatch in degeneracies between two phases, and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through nonlocal maps of each of these systems, we effectively study spinless fermionic p-wave paired topological superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.

Microscopic description of the evolution of the local structure and an evaluation of the chemical pressure concept in a solid solution

Extended x-ray absorption fine-structure studies have been performed at the Zn K and Cd K edges for a series of solid solutions of wurtzite Zn1-xCdxS samples with x = 0.0, 0.1, 0.25, 0.5, 0.75, and 1.0, where the lattice parameter as a function of x evolves according to the well-known Vegard's law. In conjunction with extensive, large-scale first-principles electronic structure calculations with full geometry optimizations, these results establish that the percentage variation in the nearest-neighbor bond distances are lower by nearly an order of magnitude compared to what would be expected on the basis of lattice parameter variation, seriously undermining the chemical pressure concept. With experimental results that allow us to probe up to the third coordination shell distances, we provide a direct description of how the local structure, apparently inconsistent with the global structure, evolves very rapidly with interatomic distances to become consistent with it. We show that the basic features of this structural evolution with the composition can be visualized with nearly invariant Zn-S-4 and Cd-S-4 tetrahedral units retaining their structural integrity, while the tilts between these tetrahedral building blocks change with composition to conform to the changing lattice parameters according to the Vegard's law within a relatively short length scale. These results underline the limits of applicability of the chemical pressure concept that has been a favored tool of experimentalists to control physical properties of a large variety of condensed matter systems.

Isotropic finite volume discretization

Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured Cartesian mesh in multiple dimensions. This simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution. The resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines. In this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error. Explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions, respectively. It is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next-nearest and next-next-nearest neighbors in three dimensions. Use of these isotropic expressions alone in a standard finite volume framework, however, is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and/or spatially non-uniform. The rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form. Various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms, while preserving the formal order of accuracy and discrete conservation of the original finite volume method, are developed. Numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method. Prominent anisotropic errors, such as spurious asymmetric distortions on a circular reaction-diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization. Furthermore, for a given spatial resolution, a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two-dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization. (C) 2014 Elsevier Inc. All rights reserved.

Nutritional benefits from domatia inhabitants in an ant-plant interaction: interlopers do pay the rent

1. How a symbiosis originates and is maintained are important evolutionary questions. Symbioses in myrmecophytes (plants providing nesting for ants) are believed to be maintained by protection and nutrients provided by specialist plant-ants in exchange for nesting spaces (called domatia) and nourishment offered by ant-plants. However, besides the benefits accrued from housing protective ants, the mechanisms contributing to the fitness advantages of bearing domatia have rarely been examined, especially because the domatia trait is usually constitutively expressed, and many myrmecophytes have obligate mutualisms with single ant species resulting in invariant conditions. 2. In the unspecialized ant-plant Humboldtia brunonis (Fabaceae) that offers extrafloral nectar to ants, only some plants produce domatia in the form of hollow internodes. These domatia have a self-opening slit making them more prone to interlopers and are occupied mostly by non-protective ants and other invertebrates, especially arboreal earthworms. The protection mutualism with ants is restricted in geographical extent, occurring only at a few sites in the southernmost part of this plant's range in the Western Ghats of India. 3. We examined nutrient flux from domatia residents to the plant using stable isotopes. We found that between 9% (earthworms) and 17% (protective or non-protective ants) of nitrogen of plant tissues nearest the domatium came from domatia inhabitants. Therefore, interlopers such as earthworms and non-protective ants contributed positively to the nitrogen budget of localized plant modules of this understorey tree. N-15-enriched feeding experiments with protective ants demonstrated that nutrients flowed from domatia inhabitants to nearby plant modules. Fruit set did not differ between paired hand-pollinated inflorescences on domatia and non-domatia bearing branches. This was possibly due to the nutrient flux from domatia to adjacent branches without domatia within localized modules. 4. This study has demonstrated the nutritive role of non-protective ants and non-ant invertebrates, hitherto referred to as interlopers, in an unspecialized myrmecophyte. Our study suggests that even before the establishment of a specialized ant-plant protection mutualism, nutritional benefits conferred by domatia inhabitants can explain the fitness benefits of bearing domatia, and thus the maintenance of a trait that facilitates the establishment of a specialized ant-plant symbiosis.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

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.