Stochastic Lorentz forces on a point charge moving near the conducting plate

The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the method of Feynman-Vernon influence functional. This stochastic approach incorporates not only the stochastic noise manifested from electromagnetic vacuum fluctuations, but also dissipation backreaction on a charge in the form of the retarded Lorentz forces. Since the imposition of the boundary is expected to anisotropically modify the effects of the fields on the evolution of the particle, we consider the motion of a charge undergoing small-amplitude oscillations in the direction either parallel or normal to the plane boundary. Under the dipole approximation for nonrelativistic motion, velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rather different rate, revealing strong anisotropic behavior. They are then asymptotically saturated as a result of the fluctuation-dissipation relation, and the same saturated value is found for the motion in both directions. The observational consequences are discussed. plane boundary. Velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rate given by the relaxation constant, which turns out to be smaller in the parallel case than in the perpendicular one in a similar configuration. Then, they are asymptotically saturated as a result of the fluctuation-dissipation relation. For the electron, the same saturated value is obtained for motion in both directions, and is mainly determined by its oscillatory motion. Possible observational consequences are discussed.Comment: 33 pages, 2 figure

Optimized Broadcast for Deep Learning Workloads on Dense-GPU InfiniBand Clusters: MPI or NCCL?

Dense Multi-GPU systems have recently gained a lot of attention in the HPC arena. Traditionally, MPI runtimes have been primarily designed for clusters with a large number of nodes. However, with the advent of MPI+CUDA applications and CUDA-Aware MPI runtimes like MVAPICH2 and OpenMPI, it has become important to address efficient communication schemes for such dense Multi-GPU nodes. This coupled with new application workloads brought forward by Deep Learning frameworks like Caffe and Microsoft CNTK pose additional design constraints due to very large message communication of GPU buffers during the training phase. In this context, special-purpose libraries like NVIDIA NCCL have been proposed for GPU-based collective communication on dense GPU systems. In this paper, we propose a pipelined chain (ring) design for the MPI_Bcast collective operation along with an enhanced collective tuning framework in MVAPICH2-GDR that enables efficient intra-/inter-node multi-GPU communication. We present an in-depth performance landscape for the proposed MPI_Bcast schemes along with a comparative analysis of NVIDIA NCCL Broadcast and NCCL-based MPI_Bcast. The proposed designs for MVAPICH2-GDR enable up to 14X and 16.6X improvement, compared to NCCL-based solutions, for intra- and inter-node broadcast latency, respectively. In addition, the proposed designs provide up to 7% improvement over NCCL-based solutions for data parallel training of the VGG network on 128 GPUs using Microsoft CNTK.Comment: 8 pages, 3 figure

Brownian motion of a charged particle in electromagnetic fluctuations at finite temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle's equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a suparohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.Comment: accepter by Foundation of Physics, for IARD 6, 200

Acceptability with general orderings

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program termination analysis, but we apply these orderings directly to the logic program and not to the term-rewrite system obtained through some transformation. We define some variants of acceptability, based on general orderings, and show how they are equivalent to LD-termination. We develop a demand driven, constraint-based approach to verify these acceptability-variants. The advantage of the approach over standard acceptability is that in some cases, where complex level mappings are needed, fairly simple orderings may be easily generated. The advantage over transformational approaches is that it avoids the transformation step all together. {\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the Future

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

Extraction of VubV_{ub} from the Decay B→πlνB\to \pi l \nu

We develop the perturbative QCD formalism including Sudakov effects for semi-leptonic $B$ meson decays. We evaluate the differential decay rate of $B\to \pi l \nu$, and find that the perturbative calculation is reliable for the energy fraction of the pion above 0.3. Combining predictions from the soft pion theorems, we extract the value of the matrix element $|V_{ub}|$ which is roughly $2.7\times 10^{-3}$.Comment: 10 pages, CCUTH-94-05, IP-ASTP-13-9

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set