Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Relation between the work function and Young's modulus of RhSi and estimate of Schottky-barrier height at RhSi/Si interface: An ab-initio study

Density-functional calculations are performed to explore the relationship between the work function and Young's modulus of RhSi, and to estimate the p-Schottky-barrier height (SBH) at the Si/RhSi(010) interface. It is shown that the Young's modulus and the workfunction of RhSi satisfy the generic sextic relation, proposed recently for elemental metals. The calculated p-SBH at the Si/RhSi interface is found to differ only by 0.04 eV in opposite limits, viz., no-pinning and strong pinning. We find that the p-SBH is reduced as much as by 0.28 eV due to vacancies at the interface. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4761994]

SOLVING VOLUME INTEGRAL EQUATION USING ScaLAPACK

In this article, we investigate the performance of a volume integral equation code on BlueGene/L system. Volume integral equation (VIE) is solved for homogeneous and inhomogeneous dielectric objects for radar cross section (RCS) calculation in a highly parallel environment. Pulse basis functions and point matching technique is used to convert the volume integral equation into a set of simultaneous linear equations and is solved using parallel numerical library ScaLAPACK on IBM's distributed-memory supercomputer BlueGene/L by different number of processors to compare the speed-up and test the scalability of the code.

Site-specific N-Linked Glycosylation of Receptor Guanylyl Cyclase C Regulates Ligand Binding, Ligand-mediated Activation and Interaction with Vesicular Integral Membrane Protein 36, VIP36

Guanylyl cyclase C (GC-C) is a multidomain, membrane-associated receptor guanylyl cyclase. GC-C is primarily expressed in the gastrointestinal tract, where it mediates fluid-ion homeostasis, intestinal inflammation, and cell proliferation in a cGMP-dependent manner, following activation by its ligands guanylin, uroguanylin, or the heat-stable enterotoxin peptide (ST). GC-C is also expressed in neurons, where it plays a role in satiation and attention deficiency/hyperactive behavior. GC-C is glycosylated in the extracellular domain, and differentially glycosylated forms that are resident in the endoplasmic reticulum (130 kDa) and the plasma membrane (145 kDa) bind the ST peptide with equal affinity. When glycosylation of human GC-C was prevented, either by pharmacological intervention or by mutation of all of the 10 predicted glycosylation sites, ST binding and surface localization was abolished. Systematic mutagenesis of each of the 10 sites of glycosylation in GC-C, either singly or in combination, identified two sites that were critical for ligand binding and two that regulated ST-mediated activation. We also show that GC-C is the first identified receptor client of the lectin chaperone vesicular integral membrane protein, VIP36. Interaction with VIP36 is dependent on glycosylation at the same sites that allow GC-C to fold and bind ligand. Because glycosylation of proteins is altered in many diseases and in a tissue-dependent manner, the activity and/or glycan-mediated interactions of GC-C may have a crucial role to play in its functions in different cell types.

Frequency detection from multiplexed compressed sensing of noisy signals

Signal acquisition under a compressed sensing scheme offers the possibility of acquisition and reconstruction of signals sparse on some basis incoherent with measurement kernel with sub-Nyquist number of measurements. In particular when the sole objective of the acquisition is the detection of the frequency of a signal rather than exact reconstruction, then an undersampling framework like CS is able to perform the task. In this paper we explore the possibility of acquisition and detection of frequency of multiple analog signals, heavily corrupted with additive white Gaussian noise. We improvise upon the MOSAICS architecture proposed by us in our previous work to include a wider class of signals having non-integral frequency components. This makes it possible to perform multiplexed compressed sensing for general frequency sparse signals.

Some questions on integral geometry on noncompact symmetric spaces of higher rank

Let be a noncompact symmetric space of higher rank. We consider two types of averages of functions: one, over level sets of the heat kernel on and the other, over geodesic spheres. We prove injectivity results for functions in which extend the results in Pati and Sitaram (Sankya Ser A 62:419-424, 2000).

Tensile flow and work hardening behavior of hot cross-rolled AA7010 aluminum alloy sheets

The present work describes the tensile flow and work hardening behavior of a high strength 7010 aluminum alloy by constitutive relations. The alloy has been hot rolled by three different cross-rolling schedules. Room temperature tensile properties have been evaluated as a function of tensile axis orientation in the as-hot rolled as well as peak aged conditions. It is found that both the Ludwigson and a generalized Voce-Bergstrom relation adequately describe the tensile flow behavior of the present alloy in all conditions compared to the Hollomon relation. The variation in the Ludwigson fitting parameter could be correlated well with the microstructural features and anisotropic contribution of strengthening precipitates in the as-rolled and peak aged conditions, respectively. The hardening rate and the saturation stress of the first Voce-Bergstrom parameter, on the other hand, depend mainly on the crystallographic texture of the specimens. It is further shown that for the peak aged specimens the uniform elongation (epsilon(u)) derived from the Ludwigson relation matches well with the measured epsilon(u) irrespective of processing and loading directions. However, the Ludwigson fit overestimates the epsilon(u) in case of the as-rolled specimens. The Hollomon fit, on the other hand, predicts well the measured epsilon(u), of the as-rolled specimens but severely underestimates the epsilon(u), for the peak aged specimens. Contrarily, both the relations significantly overestimate the UTS of the as-rolled and the peak aged specimens. The Voce-Bergstrom parameters define the slope of e Theta-sigma plots in the stage-III regime when the specimens show a classical linear decrease in hardening rate in stage-III. Further analysis of work hardening behavior throws some light on the effect of texture on the dislocation storage and dynamic recovery.

Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression

Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p, r, t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p, r, t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t -> infinity. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.

A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.

Time-Optimal Convergence to a Rectilinear Path in the Presence of Wind

This paper considers the problem of determining the time-optimal path of a fixed-wing Miniature Air Vehicle (MAV), in the presence of wind. The MAV, which is subject to a bounded turn rate, is required to eventually converge to a straight line starting from a known initial position and orientation. Earlier work in the literature uses Pontryagin's Minimum Principle (PMP) to solve this problem only for the no-wind case. In contrast, the present work uses a geometric approach to solve the problem completely in the presence of wind. In addition, it also shows how PMP can be used to partially solve the problem. Using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for cases with steady and time-varying wind. Some issues on real-time path planning are also addressed.

Optimal Trajectory Generation for Convergence to a Rectilinear Path

This paper presents a strategy to determine the shortest path of a fixed-wing Miniature Air Vehicle (MAV), constrained by a bounded turning rate, to eventually fly along a given straight line, starting from an arbitrary but known initial position and orientation. Unlike the work available in the literature that solves the problem using the Pontryagin's Minimum Principle (PMP) the trajectory generation algorithm presented here considers a geometrical approach which is intuitive and easy to understand. This also computes the explicit solution for the length of the optimal path as a function of the initial configuration. Further, using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for different cases.

Socio-cultural protection of endemic trees in humanised landscape

Culturally protected forest patches or sacred groves have been the integral part of many traditional societies. This age old tradition is a classic instance of community driven nature conservation sheltering native biodiversity and supporting various ecosystem functions particularly hydrology. The current work in Central Western Ghats of Karnataka, India, highlights that even small sacred groves amidst humanised landscapes serve as tiny islands of biodiversity, especially of rare and endemic species. Temporal analysis of landuse dynamics reveals the changing pattern of the studied landscape. There is fast reduction of forest cover (15.14-11.02 %) in last 20 years to meet up the demand of agricultural land and plantation programs. A thorough survey and assessment of woody endemic species distribution in the 25 km(2) study area documented presence of 19 endemic species. The distribution of these species is highly skewed towards the culturally protected patches in comparison to other land use elements. It is found that, among the 19 woody endemic species, those with greater ecological amplitude are widely distributed in the studied landscape in groves as well as other land use forms whereas, natural population of the sensitive endemics are very much restricted in the sacred grove fragments. The recent degradation in the sacred grove system is perhaps, due to weakening of traditional belief systems and associated laxity in grove protection leading to biotic disturbances. Revitalisation of traditional practices related to conservation of sacred groves can go a long way in strengthening natural ecological systems of fragile humid tropical landscape.

Room temperature electrical spin injection into GaAs by an oxide spin injector

Spin injection, manipulation and detection are the integral parts of spintronics devices and have attracted tremendous attention in the last decade. It is necessary to judiciously choose the right combination of materials to have compatibility with the existing semiconductor technology. Conventional metallic magnets were the first choice for injecting spins into semiconductors in the past. So far there is no success in using a magnetic oxide material for spin injection, which is very important for the development of oxide based spintronics devices. Here we demonstrate the electrical spin injection from an oxide magnetic material Fe3O4, into GaAs with the help of tunnel barrier MgO at room temperature using 3-terminal Hanle measurement technique. A spin relaxation time tau similar to 0.9 ns for n-GaAs at 300 K is observed along with expected temperature dependence of t. Spin injection using Fe3O4/MgO system is further established by injecting spins into p-GaAs and a tau of similar to 0.32 ns is obtained at 300 K. Enhancement of spin injection efficiency is seen with barrier thickness. In the field of spin injection and detection, our work using an oxide magnetic material establishes a good platform for the development of room temperature oxide based spintronics devices.

In a hot bubble: why does superbubble feedback work, but isolated supernovae do not?

Using idealized one-dimensional Eulerian hydrodynamic simulations, we contrast the behaviour of isolated supernovae with the superbubbles driven by multiple, collocated supernovae. Continuous energy injection via successive supernovae exploding within the hot/dilute bubble maintains a strong termination shock. This strong shock keeps the superbubble over-pressured and drives the outer shock well after it becomes radiative. Isolated supernovae, in contrast, with no further energy injection, become radiative quite early (less than or similar to 0.1Myr, tens of pc), and stall at scales less than or similar to 100 pc. We show that isolated supernovae lose almost all of their mechanical energy by 1 Myr, but superbubbles can retain up to similar to 40 per cent of the input energy in the form of mechanical energy over the lifetime of the star cluster (a few tens of Myr). These conclusions hold even in the presence of realistic magnetic fields and thermal conduction. We also compare various methods for implementing supernova feedback in numerical simulations. For various feedback prescriptions, we derive the spatial scale below which the energy needs to be deposited in order for it to couple to the interstellar medium. We show that a steady thermal wind within the superbubble appears only for a large number (greater than or similar to 10(4)) of supernovae. For smaller clusters, we expect multiple internal shocks instead of a smooth, dense thermalized wind.

An integral fluctuation theorem for systems with unidirectional transitions

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where R-ij > 0 but R-ji = 0, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution, which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically and found to show the same qualitative features as systems exhibiting microreversibility.