Non-Gaussianity of Inflationary Gravitational Waves from the Field Equation

We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green's function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.Comment: 17 pages, 2 figures; comments welcom

How happy is your web browsing? A model to quantify satisfaction of an Internet user, searching for desired information

We feel happy when web-browsing operations provide us with necessary information; otherwise, we feel bitter. How to measure this happiness (or bitterness)? How does the profile of happiness grow and decay during the course of web-browsing? We propose a probabilistic framework that models evolution of user satisfaction, on top of his/her continuous frustration at not finding the required information. It is found that the cumulative satisfaction profile of a web-searching individual can be modeled effectively as the sum of random number of random terms, where each term is mutually independent random variable, originating from 'memoryless' Poisson flow. Evolution of satisfaction over the entire time interval of user's browsing was modeled with auto-correlation analysis. A utilitarian marker, magnitude of greater than unity of which describe happy web-searching operations; and an empirical limit that connects user's satisfaction with his frustration level - are proposed too. Presence of pertinent information in the very first page of a web-site and magnitude of the decay parameter of user satisfaction (frustration, irritation etc.), are found to be two key aspects that dominate web-browser's psychology. The proposed model employed different combination of decay parameter, searching time and number of helpful web-sites. Obtained results are found to match the results from three real-life case-studies

Performance analysis of nanostructured Peltier coolers

Employing non-equilibrium quantum transport models, we investigate the details and operating conditions of nano-structured Peltier coolers embedded with an energy filtering barrier. Our investigations point out non-trivial aspects of Peltier cooling which include an inevitable trade-off between the cooling power and the coefficient of performance, the coefficient of performance being high at a low voltage bias and subsequently deteriorating with increasing voltage bias. We point out that there is an optimum energy barrier height for nanowire Peltier coolers at which the cooling performance is optimized. However, for bulk Peltier coolers, the cooling performance is enhanced with the height of the energy filtering barrier. Exploring further, we point out that a degradation in cooling performance with respect to bulk is inevitable as a single moded nanowire transitions to a multi-moded one. The results discussed here can provide theoretical insights for optimal design of nano Peltier coolers

Incoherent scattering can favorably influence energy filtering in nanostructured thermoelectrics

Investigating in detail the physics of energy filtering through a single planar energy barrier in nanostructured thermoelectric generators, we reinforce the non-trivial result that the anticipated enhancement in generated power at a given efficiency via energy filtering is a characteristic of systems dominated by incoherent scattering and is absent in ballistic devices. In such cases, assuming an energy dependent relaxation time $\tau(E)=kE^r$, we show that there exists a minimum value $r_{min}$ beyond which generation can be enhanced by embedding nanobarriers. For bulk generators with embedded nanobarriers, we delve into the details of inter sub-band scattering and show that it has finite contribution to the enhancement in generation. We subsequently discuss the realistic aspects, such as the effect of smooth transmission cut-off and show that for $r>r_{min}$, the optimized energy barrier is just sufficiently wide enough to scatter off low energy electrons, a very wide barrier being detrimental to the performance. Analysis of the obtained results should provide general design guidelines for enhancement in thermoelectric generation via energy filtering. Our non-equilibrium approach is typically valid in the absence of local quasi-equilibrium and hence sets the stage for future advancements in thermoelectric device analysis, for example, Peltier cooling near a barrier interface.Comment: This article is related to our earlier submission arXiv:1609.07894 (Role of incoherent scattering on energy filtering in nanostructured thermoelectric generators

Out of Equilibrium Characteristics of a Forced Translocating Chain through a Nanopore

Polymer translocation through a nano-pore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the $cis$ and the $trans$ side separately either as a function of the time during the translocation process or as as function of the monomer index $m$ inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the $cis$ side are distinctly different from those at the $trans$ side. During the translocation, and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier, and the chain immediately after translocation is described by an effective Flory exponent $0.45 \pm 0.01$. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the $cis$ to the $trans$ side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.Comment: 35 pages, 16 figures. Submitted to Phys. Rev.

Realtime Multilevel Crowd Tracking using Reciprocal Velocity Obstacles

We present a novel, realtime algorithm to compute the trajectory of each pedestrian in moderately dense crowd scenes. Our formulation is based on an adaptive particle filtering scheme that uses a multi-agent motion model based on velocity-obstacles, and takes into account local interactions as well as physical and personal constraints of each pedestrian. Our method dynamically changes the number of particles allocated to each pedestrian based on different confidence metrics. Additionally, we use a new high-definition crowd video dataset, which is used to evaluate the performance of different pedestrian tracking algorithms. This dataset consists of videos of indoor and outdoor scenes, recorded at different locations with 30-80 pedestrians. We highlight the performance benefits of our algorithm over prior techniques using this dataset. In practice, our algorithm can compute trajectories of tens of pedestrians on a multi-core desktop CPU at interactive rates (27-30 frames per second). To the best of our knowledge, our approach is 4-5 times faster than prior methods, which provide similar accuracy