arXiv subjects

Abhishek Kumar

Publications and source records attributed to Abhishek Kumar.

At least 199 records · Page 11Linked to original sources

arXiv2018

Scaling of a Fast Fourier Transform and a Pseudo-spectral Fluid Solver up to 196608 cores

In this paper we present scaling results of a FFT library, FFTK, and a pseudospectral code, Tarang, on grid resolutions up to $8192^3$ grid using 65536 cores of Blue Gene/P and 196608 cores of Cray XC40 supercomputers. We observe that communication dominates computation, more so on the Cray XC40. The computation time scales as $T_\mathrm{comp} \sim p^{-1}$, and the communication time as $T_\mathrm{comm} \sim n^{-γ_2}$ with $γ_2$ ranging from 0.7 to 0.9 for Blue Gene/P, and from 0.43 to 0.73 for Cray XC40. FFTK, and the fluid and convection solvers of Tarang exhibit weak as well as strong scaling nearly up to 196608 cores of Cray XC40. We perform a comparative study of the performance on the Blue Gene/P and Cray XC40 clusters.

physics.comp-ph↗

arXiv2018

Large eddy simulations using renormalized viscosity

In this paper, we have used renormalized viscosity for performing large eddy simulations (LES) of decaying homogeneous and isotropic turbulence inside a periodic cube on coarse grids ($32^3$, $64^3$ and $128^3$) at initial Taylor Reynolds number ${\mathrm{Re}_λ \approx 315} $. The LES results were compared with direct numerical simulation (DNS) results on $512^3$ grid. We observe good agreement between LES and DNS results on the temporal evolution of turbulence kinetic energy ${E(t)}$, kinetic energy spectrum ${E_{u}(k)}$, kinetic energy flux ${Π_u(k)}$. The isosurfaces of velocity magnitude at a given time are similar for DNS and LES. This establishes the suitability of using renormalized viscosity for performing large eddy simulations.

physics.flu-dyn↗

arXiv2018

Statistical features of rapidly rotating decaying turbulence: enstrophy and energy spectra, and coherent structures

In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to $\sim 10^{-3}$, and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes $(\pm1,0,0)$ and $(0,\pm1,0)$ that correspond to the largest columnar structure in the flow. For wavenumbers ($k$) greater than the enstrophy dissipation wavenumber ($k_d$), our phenomenological arguments and numerical study show that the enstrophy flux and spectrum of a horizontal cross-section perpendicular to the axis of rotation are given by $ε_ω\exp(-C(k/k_d)^2)$ and $Cε_ω^{2/3}k^{-1}\exp(-C(k/k_d)^2)$ respectively; for this 2D flow, $ε_ω$ is the enstrophy dissipation rate, and $C$ is a constant. Using these results, we propose a new form for the energy spectrum of rapidly rotating decaying turbulence: $E(k)=Cε_ω^{2/3}k^{-3}\exp(-C(k/k_d)^2)$. This model of the energy spectrum is based on wavenumber-dependent enstrophy flux, and it deviates significantly from power law energy spectrum reported earlier.

physics.flu-dyn↗

arXiv2018

Applicability of Taylor's hypothesis in thermally driven turbulence

In this paper, we show that in the presence of large-scale circulation (LSC), Taylor's hypothesis can be invoked to deduce the energy spectrum in thermal convection using real space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov's spectrum ($k^{-5/3}$). We also record the velocity time series using real space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov's spectrum ($f^{-5/3}$), thus validating Taylor's hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence.

physics.flu-dyn↗

arXiv2018

Complexity of viscous dissipation in turbulent thermal convection

Using direct numerical simulations of turbulent thermal convection for Rayleigh number ($\mathrm{Ra}$) between $10^6$ and $10^8$ and unit Prandtl number, we derive scaling relations for viscous dissipation in the bulk and in the boundary layers. We show that contrary to the general belief, the total viscous dissipation in the bulk is larger, albeit marginally, than that in the boundary layers. The bulk dissipation rate is similar to that in hydrodynamic turbulence with log-normal distribution, but it differs from $(U^3/d)$ by a factor of $\mathrm{Ra}^{-0.18}$. Viscous dissipation in the boundary layers are rarer but more intense with a stretched-exponential distribution.

physics.flu-dyn↗

arXiv2018

Combating Reinforcement Learning's Sisyphean Curse with Intrinsic Fear

Many practical environments contain catastrophic states that an optimal agent would visit infrequently or never. Even on toy problems, Deep Reinforcement Learning (DRL) agents tend to periodically revisit these states upon forgetting their existence under a new policy. We introduce intrinsic fear (IF), a learned reward shaping that guards DRL agents against periodic catastrophes. IF agents possess a fear model trained to predict the probability of imminent catastrophe. This score is then used to penalize the Q-learning objective. Our theoretical analysis bounds the reduction in average return due to learning on the perturbed objective. We also prove robustness to classification errors. As a bonus, IF models tend to learn faster, owing to reward shaping. Experiments demonstrate that intrinsic-fear DQNs solve otherwise pathological environments and improve on several Atari games.

cs.LG↗

arXiv2018

Endoscopic optical coherence tomography with a flexible fiber bundle

We demonstrate in vivo endoscopic optical coherence tomography (OCT) imaging in the forward direction using a flexible fiber bundle. In comparison to current conventional forward looking probe schemes, our approach simplifies the endoscope design by avoiding the integration of any beam steering components in the distal probe end due to 2D scanning of a focused light beam over the proximal fiber bundle surface. We describe the challenges that arise when OCT imaging with a fiber bundle is performed, such as multimoding or cross-coupling. The performance of different fiber bundles with varying parameters such as numerical aperture, core size and core structure was consequently compared and artifacts that degrade the image quality were described in detail. Based on our findings, we propose an optimal fiber bundle design for endoscopic OCT imaging.

physics.med-ph↗

arXiv2017

Semi-supervised Learning with GANs: Manifold Invariance with Improved Inference

Semi-supervised learning methods using Generative Adversarial Networks (GANs) have shown promising empirical success recently. Most of these methods use a shared discriminator/classifier which discriminates real examples from fake while also predicting the class label. Motivated by the ability of the GANs generator to capture the data manifold well, we propose to estimate the tangent space to the data manifold using GANs and employ it to inject invariances into the classifier. In the process, we propose enhancements over existing methods for learning the inverse mapping (i.e., the encoder) which greatly improves in terms of semantic similarity of the reconstructed sample with the input sample. We observe considerable empirical gains in semi-supervised learning over baselines, particularly in the cases when the number of labeled examples is low. We also provide insights into how fake examples influence the semi-supervised learning procedure.

cs.LG↗

arXiv2017

Improved Neural Text Attribute Transfer with Non-parallel Data

Text attribute transfer using non-parallel data requires methods that can perform disentanglement of content and linguistic attributes. In this work, we propose multiple improvements over the existing approaches that enable the encoder-decoder framework to cope with the text attribute transfer from non-parallel data. We perform experiments on the sentiment transfer task using two datasets. For both datasets, our proposed method outperforms a strong baseline in two of the three employed evaluation metrics.

cs.CL↗

arXiv2017

The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.

cs.LG↗

arXiv2017

Sweeping effect and Taylor's hypothesis via correlation function

We performed high-resolution numerical simulations of hydrodynamic turbulence with and without mean velocity ($U_0=0,10$), and demonstrate the sweeping effect. For $U_0=0$, the velocity correlation function, $C({\bf k},τ)$ decays with time due to eddy viscosity, but it also shows fluctuations due to the sweeping effect. For $U_0=10$, $C({\bf k},τ)$ exhibits damped oscillations with the frequency of $U_0 k$ and decay time scale corresponding to the $U_0=0$ case. A closer examination of $\Im[C({\bf k},τ)]$ also demonstrates sweeping effect for $U_0=10$. We also demonstrate that the frequency spectra of the velocity fields measured by real-space probes are respectively $f^{-2}$ and $f^{-5/3}$ for $U_0=0$ and 10; these spectra are related to the Lagrangian and Eulerian space-time correlations.

physics.flu-dyn↗

arXiv2017

SenGen: Sentence Generating Neural Variational Topic Model

We present a new topic model that generates documents by sampling a topic for one whole sentence at a time, and generating the words in the sentence using an RNN decoder that is conditioned on the topic of the sentence. We argue that this novel formalism will help us not only visualize and model the topical discourse structure in a document better, but also potentially lead to more interpretable topics since we can now illustrate topics by sampling representative sentences instead of bag of words or phrases. We present a variational auto-encoder approach for learning in which we use a factorized variational encoder that independently models the posterior over topical mixture vectors of documents using a feed-forward network, and the posterior over topic assignments to sentences using an RNN. Our preliminary experiments on two different datasets indicate early promise, but also expose many challenges that remain to be addressed.

cs.CL↗

arXiv2017

Application of Superhalogens in the Design of Organic Superconductors

Bechgaard salts, (TMTSF)2X (TMTSF = tetramethyl tetraselenafulvalene and X = complex anion), form the most popular series of organic superconductors. In these salts, TMTSF molecules act as super-electron donor and X as acceptor. We computationally examine the electronic structure and properties of X in commonly used (TMTSF)2X (X = NO3, BF4, ClO4, PF6) superconductors and notice that they belong to the class of superhalogens due to their higher vertical detachment energy than halogen anions. This prompted us to choose other superhalogens such as X = BO2, BH4, B2F7, AuF6 and study their (TMTSF)2X complexes. Our findings suggest that these complexes behave more or less similar to those of established (TMTSF)2X superconductors, particularly for X = BO2 and B2F7. We, therefore, believe that the concept of superhalogen can be successfully applied in the design of novel organic superconductors.

physics.chem-ph↗

arXiv2017

Local Group Invariant Representations via Orbit Embeddings

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.

cs.LG↗

arXiv2017

Theory of non-Markovian dynamics in resonance fluorescence spectrum

We present a detailed theoretical study of non-Markovian dynamics in the fluorescence spectrum of a driven semiconductor quantum dot (QD), embedded in a cavity and coupled to a three-dimensional (3D) acoustic phonon reservoir. In particular, we investigate the effect of pure dephasing on one of the side-peaks of the Mollow-triplet spectrum, expressed in terms of the off-diagonal element of the reduced system operator. The QD is modeled as a two-level system with an excited state representing a single exciton, and ground state represents the absence of an exciton. Coupling to the radiative modes of the cavity is treated within usual Born-Markov approximation, whereas dot-phonon coupling is discussed within non-Markovian regime beyond Born approximation. Using an equation-of-motion technique, the dot-phonon coupling is solved exactly and found that the exact result coincides with that of obtained within Born approximation. Furthermore, a Markov approximation is carried out with respect to the phonon interaction and compared with the non- Markovian lineshape for different values of the phonon bath temperature. We have found that coupling to the phonons vanishes for a resonant pump laser. For a non-resonant pump, we have characterzied the effect of dot-laser detuning and temperature of the phonon bath on the lineshape. The sideband undergoes a distinct narrowing and aquires an asymmetric shape with increasing phonon bath temperature. We have explained this behavior using a dressed-state picture of the QD levels.

cond-mat.mes-hall↗

arXiv2017

Surface Ocean Enstrophy, Kinetic Energy Fluxes and Spectra from Satellite Altimetry

Enstrophy, kinetic energy (KE) fluxes and spectra are estimated in different parts of the mid-latitudinal oceans via altimetry data. To begin with, using geostrophic currents derived from sea-surface height anomaly data provided by AVISO, we confirm the presence of a strong inverse flux of surface KE at scales larger than approximately 250 km. We then compute enstrophy fluxes to help develop a clearer picture of the underlying dynamics at smaller scales, i.e., 250 km to 100 km. Here, we observe a robust enstrophy cascading regime, wherein the enstrophy shows a large forward flux and the KE spectra follow an approximate $k^{-3.5}$ power-law. Given the rotational character of the flow, not only is this large scale inverse KE and smaller scale forward enstrophy transfer scenario consistent with expectations from idealized studies of three-dimensional rapidly-rotating and strongly-stratified turbulence, it also agrees with detailed analyses of spectra and fluxes in the upper level midlatitude troposphere. Decomposing the currents into components with greater and less than 100 day variability (referred to as seasonal and eddy, respectively), we find that, in addition to the eddy-eddy contribution, the seasonal-eddy and seasonal-seasonal fluxes play a significant role in the inverse (forward) flux of KE (enstrophy) at scales larger (smaller) than about 250 km. Taken together, we suspect, it is quite possible that, from about 250 km to 100 km, the altimeter is capturing the relatively steep portion of a surface oceanic counterpart of the upper tropospheric Nastrom-Gage spectrum.

physics.ao-ph↗

arXiv2017

Effective lattice model for collective modes in a Fermi liquid with spin-orbit coupling

A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes--chiral spin waves--which are oscillations of magnetization even in the absence of the external magnetic field. We study the chiral spin waves of a two-dimensional FL in the presence of both the Rashba and Dresselhaus types of SOC and also subject to the in-plane magnetic field. We map the system of coupled kinetic equations for the angular harmonics of the occupation number onto an effective one-dimensional tight-binding model, in which the lattice sites correspond to angular-momentum channels. Linear-in-momentum SOC ensures that the effective tight-binding model has only nearest-neighbor hopping on a bipartite lattice. In this language, the continuum of spin-flip particle-hole excitations becomes a conduction band of the lattice model, whereas electron-electron interaction, parameterized by the harmonics of the Landau function, is mapped onto lattice defects of both on-site and bond type. Collective modes correspond to bound states formed by such defects. All the features of the collective-mode spectrum receive natural explanation in the lattice picture as resulting from the competition between on-site and bond defects.

cond-mat.mes-hall↗

arXiv2016

Low temperature dissipation scenarios in palladium nano-mechanical resonators

We study dissipation in Pd nano-mechanical resonators at low temperatures in the linear response regime. Metallic resonators have shown characteristic features of dissipation due to tunneling two level systems (TLS). This system offers a unique tunability of the dissipation scenario by adsorbing hydrogen ($H_2$) which induces a compressive stress. The intrinsic stress is expected to alter TLS behaviour. We find a sub-linear power law $\sim T^{0.4}$ in dissipation. As seen in TLS dissipation scenarios we find a logarithmic increase of frequency characteristic from the lowest temperatures till a characteristic temperature $T_{co}$ is reached. In samples without $H_2$ the $T_{co} \sim 1K$ whereas with $H_2$ it is clearly reduced to $\sim 700 mK$. Based on standard TLS phenomena we attribute this to enhanced phonon-TLS coupling in samples with compressive strain. We also find with $H_2$ there is a saturation in low temperature dissipation which may possibly be due to super-radiant interaction between TLS and phonons. We discuss the data in the scope of TLS phenomena and similar data for other systems.

cond-mat.mes-hall↗