Discrete Morse flow for Ricci flow and Porous Media equation

In this paper, we study the discrete Morse flow for the Ricci flow on football, which is the 2-sphere with removed north and south poles and with the metric $g_0$ of constant scalar curvature, and and for Porous media equation on a bounded regular domain in the plane. We show that with a suitable assumption about $g(0)$ we have a weak approximated discrete Morse flow for the approximated Ricci flow and Porous media equation on any time intervals.Comment: 9 page

Stability of cigar soliton

In this paper, we shall use the K\"ahler geometry formulation to study the global behavior of the Ricci flow on $R^2$. The geometric feature of our Ricci flow is that it has finite width. Our aim is to determine the limiting metric (which corresponds an eternal Ricci flow) obtained by L.F.Wu. We can use the classification result of Daskalopoulos-Sesum to give a sufficient condition such that the limiting metric of L.F.Wu is the metric of cigar soliton.Comment: a gap in L.F.Wu's result cited in our paper is filled in our cas

Large Baryon Densities Achievable in High Energy Heavy Ion Collisions Outside the Central Rapidity Region

Nuclei are nearly transparent to each other when they collide at high energy, but the collisions do produce high energy density matter in the central rapidity region where most experimental measurements are made. What happens to the receding nuclear fireballs? We calculate the energy loss of the nuclei using the color glass condensate model. We then use a simple space-time picture of the collision to calculate the baryon and energy densities of the receding fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider we find baryon densities more than ten times that of normal nuclear matter. These results provide initial conditions for subsequent hydrodynamic evolution and could test the equation of state at very high baryon densities.Comment: 35 pages, 29 figures, 5 table

High Baryon Densities Achieveable at RHIC and LHC

In high energy collisions nuclei are practically transparent to each other but produce very hot, nearly baryon-free, matter in the central rapidity region. Where do the baryons go? We calculate the energy loss of the nuclei using the color glass condensate model. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of large nuclei at RHIC and LHC we find baryon densities more than ten times that of atomic nuclei over a large volume which appear at high rapidities. These results can and are being used as initial conditions for subsequent hydrodynamic evolution and could test the equation of state of matter at very high baryon densities.Comment: 4 pages, 6 figures. Proceedings of Quark Matter 201

High Baryon Densities in Heavy Ion Collisions at Energies Attainable at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

In very high energy collisions nuclei are practically transparent to each other but produce very hot, nearly baryon-free, matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei at the highest energy attainable at the Relativistic Heavy Ion Collider, for example, we find baryon densities more than ten times that of atomic nuclei over a large volume.Comment: 5 pages, 7 figures. This version incorporates changes in response to the referee report

Modeling the Infrared Emission from the HR 4796A Disk

We model the spectral energy distribution (SED) from the mid-infrared to submillimeter of the ring-like disk of HR 4796A, the dustiest A-type star. We consider dust made either of coagulated but otherwise unaltered protostellar interstellar grains, or grains that are highly-processed in a protostellar/protoplanetary nebula with silicate dust annealed and carbon dust oxidized. Both types of dust are successful in reproducing the observed SED, provided that the grains are highly fluffy, with a vacuum volume fraction of \~90%. We find no evidence for the existence of a hot ``zodiacal dust'' component a few AU from the star, which was suggested by previous workers to account for the 10 micron-wavelength emission.Comment: published in The Astrophysical Journal, vol. 590, pp. 368--378; 26 pages; 9 figure

Analysis of Fleet Modularity in an Artificial Intelligence-Based Attacker-Defender Game

Because combat environments change over time and technology upgrades are widespread for ground vehicles, a large number of vehicles and equipment become quickly obsolete. A possible solution for the U.S. Army is to develop fleets of modular military vehicles, which are built by interchangeable substantial components also known as modules. One of the typical characteristics of module is their ease of assembly and disassembly through simple means such as plug-in/pull-out actions, which allows for real-time fleet reconfiguration to meet dynamic demands. Moreover, military demands are time-varying and highly stochastic because commanders keep reacting to enemy's actions. To capture these characteristics, we formulated an intelligent agent-based model to imitate decision making process during fleet operation, which combines real-time optimization with artificial intelligence. The agents are capable of inferring enemy's future move based on historical data and optimize dispatch/operation decisions accordingly. We implement our model to simulate an attacker-defender game between two adversarial and intelligent players, representing the commanders from modularized fleet and conventional fleet respectively. Given the same level of combat resources and intelligence, we highlight the tactical advantages of fleet modularity in terms of win rate, unpredictability and suffered damage.Comment: 30 pages, 15 figures, manuscript to be submitted to European Journal of Operational Researc

Inducing Uniform Asymptotic Stability in Non-Autonomous Accelerated Optimization Dynamics via Hybrid Regularization

There have been many recent efforts to study accelerated optimization algorithms from the perspective of dynamical systems. In this paper, we focus on the robustness properties of the time-varying continuous-time version of these dynamics. These properties are critical for the implementation of accelerated algorithms in feedback-based control and optimization architectures. We show that a family of dynamics related to the continuous-time limit of Nesterov's accelerated gradient method can be rendered unstable under arbitrarily small bounded disturbances. Indeed, while solutions of these dynamics may converge to the set of optimizers, in general, this set may not be uniformly asymptotically stable. To induce uniformity, and robustness as a byproduct, we propose a framework where we regularize the dynamics by using resetting mechanisms that are modeled by well-posed hybrid dynamical systems. For these hybrid dynamics, we establish uniform asymptotic stability and robustness properties, as well as convergence rates that are similar to those of the non-hybrid dynamics. We finish by characterizing a family of discretization mechanisms that retain the main stability and robustness properties of the hybrid algorithms.Comment: To appear at the 2019 IEEE Conference on Decision and Contro

Electric Spaser in the Extreme Quantum Limit

We consider theoretically the spaser excited electrically via a nanowire with ballistic quantum conductance. We show that in the extreme quantum regime, i.e., for a single conductance-quantum nanowire, the spaser with the core made of common plasmonic metals, such as silver and gold, is fundamentally possible. For ballistic nanowires with multiple-quanta or non-quantized conductance, the performance of the spaser is enhanced in comparison with the extreme quantum limit. The electrically-pumped spaser is promising as an optical source, nanoamplifier, and digital logic device for optoelectronic information processing with speed ~100 GHz to ~100 THz.Comment: 5 pages, 1 figur

CP Asymmetries in Strange Baryon Decays

While indirect & direct CP violations (CPV) had been established in the decays of strange & beauty mesons, none have been done for baryons. There are different "roads" for finding CP asymmetries in the decays of strange baryons; they are highly non-trivial ones. The HyperCP Collaboration had probed CPV in the decays of single $\Xi$ & $\Lambda$ [Phys.Rev.Lett 93 (2004) 262001]. We talk about future lessons from $e^+e^-$ collisions at BESIII/BEPCII: probing decays of pairs of strange baryons, namely $\Lambda$, $\Sigma$ & $\Xi$. Realistic goals are to learn about non-perturbative QCD. One can hope to find CPV in the decays of strange baryons; one can also dream to find impact of New Dynamics (ND). We point out that a new important era starts with the BESIII/BEPCII data accumulated by the end of 2018.Comment: final version, slight typos correcte