Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Thermodynamics of ideal gas in doubly special relativity

We study thermodynamics of an ideal gas in doubly special relativity. A new type of special functions (which we call ``incomplete modified Bessel functions'') emerge. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that doubly special relativity thermodynamics is nonperturbative in the special relativity and massless limits. A stiffer equation of state is found.

A Novel Cache Architecture and Placement Framework for Packet Forwarding Engines

Packet forwarding is a memory-intensive application requiring multiple accesses through a trie structure. With the requirement to process packets at line rates, high-performance routers need to forward millions of packets every second with each packet needing up to seven memory accesses. Earlier work shows that a single cache for the nodes of a trie can reduce the number of external memory accesses. It is observed that the locality characteristics of the level-one nodes of a trie are significantly different from those of lower level nodes. Hence, we propose a heterogeneously segmented cache architecture (HSCA) which uses separate caches for level-one and lower level nodes, each with carefully chosen sizes. Besides reducing misses, segmenting the cache allows us to focus on optimizing the more frequently accessed level-one node segment. We find that due to the nonuniform distribution of nodes among cache sets, the level-one nodes cache is susceptible t high conflict misses. We reduce conflict misses by introducing a novel two-level mapping-based cache placement framework. We also propose an elegant way to fit the modified placement function into the cache organization with minimal increase in access time. Further, we propose an attribute preserving trace generation methodology which emulates real traces and can generate traces with varying locality. Performanc results reveal that our HSCA scheme results in a 32 percent speedup in average memory access time over a unified nodes cache. Also, HSC outperforms IHARC, a cache for lookup results, with as high as a 10-fold speedup in average memory access time. Two-level mappin further enhances the performance of the base HSCA by up to 13 percent leading to an overall improvement of up to 40 percent over the unified scheme.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

On Network-Error Correcting Convolutional Codes under the BSC Edge Error Model

Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error pe(0 <= p(e) < 0.5). We obtain bounds on the performance of such CNECCs based on a modified generating function (the transfer function) of the CNECCs. For a given network, we derive a mathematical condition on how small p(e) should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low p(e) and high p(e) regimes. For the low p(e) regime, convolutional codes with good distance properties show good performance. For the high p(e) regime, convolutional codes that have a good slope ( the minimum normalized cycle weight) are seen to be good. We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.

Nonlinear dynamics of a rigid block on a rigid base

The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.

Small signal Nonquasi-Static Model for Common Double-Gate MOSFETs Adapted to Gate Oxide Thickness Asymmetry

We present a physics-based closed form small signal Nonquasi-static (NQS) model for a long channel Common Double Gate MOSFET (CDG) by taking into account the asymmetry that may prevail between the gate oxide thickness. We use the unique quasi-linear relationship between the surface potentials along the channel to solve the governing continuity equation (CE) in order to develop the analytical expressions for the Y parameters. The Bessel function based solution of the CE is simplified in form of polynomials so that it could be easily implemented in any circuit simulator. The model shows good agreement with the TCAD simulation at-least till 4 times of the cut-off frequency for different device geometries and bias conditions.

A modified sulphide capacity function

The sulphide capacity as originally defined by Fincham and Richardson is a strong function of composition in pseudobinary oxide melts of interest in extractive metallurgy. From an analysis of data available in the literature, it is shown that sulphide capacity is directly proportional to the activity of the basic oxide in the melt, within the uncertainty of experimental data. A single parameter is sufficient to describe the sulphide capacity of a binary slag system under isothermal and isobaric conditions. The correlation indicates that the activity coefficient of the sulphide ion or the neutral base metal sulphide dissolved in the melt is independent of composition in pseudobinary melts within experimental uncertainty. Structural variations in the melt with composition do not seem to affect the activity coefficient of the sulphide. A modified sulphide capacity function is defined which makes the treatment more elegant and greatly simplifies data storage and retrieval. The modified function is not based on any model for the melt.

Implementation of a modified CVSD coder

This paper describes the implementation of the modified continuously variable slope delta modulator (MCVSD), in which the basic step size δ0 is made to vary as a function of input signal level. The information needed to carry out this is extracted at the local decoder output so that the coder and the decoder track each other. The result is a significant improvement in the dynamic range (about 15dB) as compared to CVSD coder without degrading the peak signal to noise ratio.

Potential functions for hydrogen bond interactions - III. Empirical Potential Function for the Peptide N-H...O=C Hydrogen Bond

A careful comparison of the distribution in the (R, θ)-plane of all NH ... O hydrogen bonds with that for bonds between neutral NH and neutral C=O groups indicated that the latter has a larger mean R and a wider range of θ and that the distribution was also broader than for the average case. Therefore, the potential function developed earlier for an average NH ... O hydrogen bond was modified to suit the peptide case. A three-parameter expression of the form {Mathematical expression}, with △ = R - Rmin, was found to be satisfactory. By comparing the theoretically expected distribution in R and θ with observed data (although limited), the best values were found to be p1 = 25, p3 = - 2 and q1 = 1 × 10-3, with Rmin = 2·95 Å and Vmin = - 4·5 kcal/mole. The procedure for obtaining a smooth transition from Vhb to the non-bonded potential Vnb for large R and θ is described, along with a flow chart useful for programming the formulae. Calculated values of ΔH, the enthalpy of formation of the hydrogen bond, using this function are in reasonable agreement with observation. When the atoms involved in the hydrogen bond occur in a five-membered ring as in the sequence[Figure not available: see fulltext.] a different formula for the potential function is needed, which is of the form Vhb = Vmin +p1△2 +q1x2 where x = θ - 50° for θ ≥ 50°, with p1 = 15, q1 = 0·002, Rmin = 2· Å and Vmin = - 2·5 kcal/mole. © 1971 Indian Academy of Sciences.

Medium access control schemes for local area networks with multiple priority function

This paper deals with the development and performance evaluation of three modified versions of a scheme proposed for medium access control in local area networks. The original scheme implements a collision-free and fair medium arbitration by using a control wire in conjunction with a data bus. The modifications suggested in this paper are intended to realize the multiple priority function in local area networks.

Modified conformation and physical properties in conducting polymers due to varying conjugation and solvent interactions

Small angle X-ray scattering (SAXS) studies of poly2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) with varying conjugation, and polyethylene dioxythiophene complexed with polystyrene sulfonate (PEDOT-PSS) in different solvents have shown the importance of the role of pi-electron conjugation and solvent-chain interactions in controlling the chain conformation and assembly. In MEH-PPV, by increasing the extent of conjugation from 30 to 100%, the persistence length (l(p)) increases from 20 to 66 angstrom. Moreover, a pronounced second peak in the pair distribution function has been observed in the fully conjugated chain, at larger length scales. This feature indicates that the chain segments tend to self-assemble as the conjugation along the chain increases. In the case of PEDOT-PSS, the chains undergo solvent induced expansion and enhanced chain organization. The clusters formed by chains are better correlated in dimethyl sulfoxide (DMSO) solution than water, as observed in the scattered intensity profiles. The values of radius of gyration and the exponent (water: 2.6, DMSO: 2.31) of power-law decay, obtained from the unified scattering function (Beaucage) analysis, give evidence for chain expansion from compact (in water) to an extended coil in DMSO solutions, which is consistent with the Kratky plot analysis. The mechanism of this transition and the increase in dc conductivity of PEDOT-PSS in DMSO solution are discussed. The onset frequency for the increase in ac conduction, as well as its temperature dependence, probes the extent of the connectivity in the PEDOT-PSS system. The enhanced charge transport in PEDOT-PSS in DMSO is attributed to the extended chain conformation, as observed in the SAXS results.

Deblurring in a noncoherent optical processing system: pupil function synthesis and experimental implementation

The bipolar point spread function (PSF) corresponding to the Wiener filter tor correcting linear-motion-blurred pictures is implemented in a noncoherent optical processor. The following two approaches are taken for this implementation: (1) the PSF is modulated and biased so that the resulting function is non-negative and (2) the PSF is split into its positive and sign-reversed negative parts, and these two parts are dealt with separately. The phase problem associated with arriving at the pupil function from these modified PSFs is solved using both analytical and combined analytical-iterative techniques available in the literature. The designed pupil functions are experimentally implemented, and deblurring in a noncoherent processor is demonstrated. The postprocessing required (i.e., demodulation in the first approach to modulating the PSF and intensity subtraction in the second approach) are carried out either in a coherent processor or with the help of a PC-based vision system. The deblurred outputs are presented.

Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.