4 AN10 Abstracts
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Conservative High Order Semi-Lagrangian Finite Difference WENO Methods for Advection in Incompressible Flow Jing-Mei Qiu1 and Ch
Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow Jing-Mei Qiu1 and Chi-Wang Shu 2 Abstract In this paper, we propose a semi-Lagrangian finite difference formulation for approximat- ing conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes [4, 21], which approximate the advective form of the equation via direct characteristics tracing, the scheme proposed in this paper approximates the conservative form of the equation. This essential difference makes the proposed scheme naturally conservative for equations with general variable coef- ficients. The proposed conservative semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and to capture sharp inter- faces without introducing spurious oscillations. The scheme is extended to high dimensional problems by Strang splitting. The performance of the proposed schemes is demonstrated by linear advection, rigid body rotation and swirling deformation. As the information is propa- gating along characteristics, the proposed scheme does not have CFL time step restriction of the Eulerian method, allowing for a more efficient numerical realization for many application problems. Keywords: advection in incompressible flow; conservative scheme; semi-Lagrangian meth- ods; WENO reconstruction. 1Department of Mathematical and Computer Science, Colorado School of Mines, Golden, 80401. E-mail: [email protected]. Research supported by NSF grant number 0914852 and Air Force Office of Scientific Research grant number FA9550-09-1-0344. 2Division of Applied Mathematics, Brown University, Providence, 02912. -
Download PDF Call for Papers
2020 IEEE International Symposium on Information Theory Los Angeles, CA, USA |June 21-26, 2020 The Westin Bonaventure Hotel & Suites, Los Angeles Call for Papers Interested authors are encouraged to submit previously unpublished contributions in any area related to information theory, including but not limited to the following topic areas: Topics ➢ Communication and Storage Coding ➢ Distributed Storage ➢ Network Information Theory ➢ Coding Theory ➢ Emerging Applications of IT ➢ Pattern Recognition and ML ➢ Coded and Distributed Computing ➢ Information Theory and Statistics ➢ Privacy in Information Processing ➢ Combinatorics and Information Theory ➢ Information Theory in Biology ➢ Quantum Information Theory ➢ Communication Theory ➢ Information Theory in CS ➢ Shannon Theory ➢ Compressed Sensing and Sparsity ➢ Information Theory in Data Science ➢ Signal Processing ➢ Cryptography and Security ➢ Learning Theory ➢ Source Coding and Data Compression ➢ Detection and Estimation ➢ Network Coding and Applications ➢ Wireless Communication ➢ Deep Learning for Networks ➢ Network Data Analysis Researchers working in emerging fields of information theory or on novel applications of information theory are especially encouraged to submit original findings. The submitted work and the published version are limited to 5 pages in the standard IEEE format, plus an optional extra page containing references only. Information about paper formatting and submission policies can be found on the conference web page, noted below. The paper submission deadline is Sunday, January 12, 2020, at 11:59 PM, Eastern Time (New York, USA). Acceptance notifications will be sent out by Friday, March 27, 2020. We look forward to your participation in ISIT 2020! General Chairs: Salman Avestimehr, Giuseppe Caire, and Babak Hassibi TPC Chairs: Young-Han Kim, Frederique Oggier, Greg Wornell, and Wei Yu https://2020.ieee-isit.org . -
Reason in Motion
Student Works 11-9-2018 Reason in Motion Luke Francis Embry-Riddle Aeronautical University, [email protected] Follow this and additional works at: https://commons.erau.edu/student-works Part of the Philosophy of Science Commons, and the The Sun and the Solar System Commons Scholarly Commons Citation Francis, L. (2018). Reason in Motion. , (). Retrieved from https://commons.erau.edu/student-works/82 This Article is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Student Works by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. Reason in Motion Luke Francis∗ Embry Riddle Aeronautical University Prescott, AZ 86301 (Dated: November 9, 2018) This essay will explain the historical models of the solar system, which was the known universe for most of human history. There is far more to each model than simply positioning different celestial bodies at the center of the system, and the stories of the astronomers who derived the controversial theories are not discussed often enough. The creation of these theories is part of a much broader revolution in scientific thought and marked the start of a series of observational discoveries that would change the the philosophy of science for centuries to come. I. STUDY PURPOSE Model. This was also influenced by metaphysical notions of human importance. In other words, man saw himself Although science and history are seen as two very sep- as the most important and the most divinely endowed arate fields of study, they depend greatly on each other. -
Lecture 1: Introduction
Lecture 1: Introduction E. J. Hinch Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2, we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry. 1 Fluid Mechanical Preliminaries The equations of motion for an incompressible fluid of unit density are (for details and derivation see any text on fluid mechanics, e.g. [1]) @u + (u · r) u = r · S + F (1) @t r · u = 0 (2) where u is the velocity, S is the total stress tensor and F are the body forces. It is customary to divide the total stress into an isotropic part and a deviatoric part as in S = −pI + σ (3) where tr σ = 0. These equations are closed only if we can relate the deviatoric stress to the velocity field (the pressure field satisfies the incompressibility condition). It is common to look for local models where the stress depends only on the local gradients of the flow: σ = σ (E) where E is the rate of strain tensor 1 E = ru + ruT ; (4) 2 the symmetric part of the the velocity gradient tensor. The trace-free requirement on σ and the physical requirement of symmetry σ = σT means that there are only 5 independent components of the deviatoric stress: 3 shear stresses (the off-diagonal elements) and 2 normal stress differences (the diagonal elements constrained to sum to 0). -
Overview of Turbulent Shear Flows
Overview of turbulent shear flows Fabian Waleffe notes by Giulio Mariotti and John Platt revised by FW WHOI GFD Lecture 2 June 21, 2011 A brief review of basic concepts and folklore in shear turbulence. 1 Reynolds decomposition Experimental measurements show that turbulent flows can be decomposed into well-defined averages plus fluctuations, v = v¯ + v0. This is nicely illustrated in the Turbulence film available online at http://web.mit.edu/hml/ncfmf.html that was already mentioned in Lecture 1. In experiments, the average v¯ is often taken to be a time average since it is easier to measure the velocity at the same point for long times, while in theory it is usually an ensemble average | an average over many realizations of the same flow. For numerical simulations and mathematical analysis in simple geometries such as channels and pipes, the average is most easily defined as an average over the homogeneous or periodic directions. Given a velocity field v(x; y; z; t) we define a mean velocity for a shear flow with laminar flow U(y)^x by averaging over the directions (x; z) perpendicular to the shear direction y, 1 Z Lz=2 Z Lx=2 v¯ = lim v(x; y; z; t)dxdz = U(y; t)^x: (1) L ;L !1 x z LxLz −Lz=2 −Lx=2 The mean velocity is in the x direction because of incompressibility and the boundary conditions. In a pipe, the average would be over the streamwise and azimuthal (spanwise) direction and the mean would depend only on the radial distance to the pipe axis, and (possibly) time. -
Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
NfST Nisr National institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 946 Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems Vincent A. Hackley and Chiara F. Ferraris rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Arxiv:2010.10473V2 [Cs.LG] 1 Feb 2021
Proceedings of Machine Learning Research vol 134:1{22, 2021 Regret-optimal control in dynamic environments Gautam Goel [email protected] California Insititute of Technology Babak Hassibi [email protected] California Insititute of Technology Abstract We consider control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which minimizes regret against the best dynamic sequence of control actions selected in hindsight (dynamic regret), instead of the best fixed controller in some specific class of controllers (policy regret). This formulation is attractive when the environ- ment changes over time and no single controller achieves good performance over the entire time horizon. We derive the state-space structure of the regret-optimal controller via a novel reduction to H1 control and present a tight data-dependent bound on its regret in terms of the energy of the disturbance. Our results easily extend to the model-predictive setting where the controller can anticipate future disturbances and to settings where the controller only affects the system dynamics after a fixed delay. We present numerical experiments which show that our regret-optimal controller interpolates between the performance of the H2-optimal and H1-optimal controllers across stochastic and adversarial environments. Keywords: dynamic regret, robust control 1. Introduction The central question in control theory is how to regulate the behavior of an evolving system with state x that is perturbed by a disturbance w by dynamically adjusting a control action u. Traditionally, this question has been studied in two distinct settings: in the H2 setting, we assume that the disturbance w is generated by a stochastic process and seek to select the control u so as to minimize the expected control cost, whereas in the H1 setting we assume the noise is selected adversarially and instead seek to minimize the worst-case control cost. -
PROGRAM and ABSTRACTS
LASERENANUM E´ R I C A II Octavo Encuentro de Analisis´ Numerico´ de Ecuaciones Diferenciales Parciales Departamento de Matem´aticas,Universidad de La Serena La Serena, Chile, Enero 14 - 16, 2015 PROGRAM and ABSTRACTS Contents 1 Introduction 2 2 Wednesday, January 14 3 3 Thursday, January 15 4 4 Friday, January 16 5 5 Abstracts 6 1 1 Introduction The Octavo Encuentro de An´alisisNum´ericode Ecuaciones Diferenciales Parciales has been organized in sequential talks of 45 and 30 minutes length (40 and 25 minutes of presentation, respectively, and 5 minutes for questions and comments). All the talks will be given at Salon´ Multiuso, CETECFI (3th floor), Facultad de Ingenier´ıa, Universi- dad de la Serena. In the following pages we describe the corresponding program. In case of a multi-authored contribution, the speaker is underlined. The organizers acknowledge financial support by: • CONICYT-Chile through Project Anillo ACT 1118 ANANUM, • Departamento de Matem´aticas, Universidad de La Serena, • Centro de Modelamiento Matem´atico(CMM), Universidad de Chile, and • Centro de Investigaci´onen Ingenier´ıaMatem´atica(CI2MA), Universidad de Concepci´on. In addition, we express our recognition and gratitude to all speakers for making La Serena Num´ericaII possible. Organizing Committee Raimund B¨urger Gabriel N. Gatica Ricardo Oyarz´ua H´ectorTorres La Serena, January 2015 2 2 Wednesday, January 14 8.30-9.15 REGISTRATION 9.15-9.30 WELCOME SPEECH [Chairman: N. HEUER] 9.30-10.15 Alexandre Ern, Martin Vohral´ık: Polynomial-degree-robust a posteri- ori estimates in a unified setting. 10.15-10.45 Dante Kalise: High-order semi-Lagrangian schemes for static Hamilton- Jacobi-Bellman equations. -
GENERALIZED DEFORMATION-RATES in SECONDARY FLOWS of VISCOELASTIC FLUIDS BETWEEN ROTATING SPHERES Redacted for Privacy Kbstract Approved: M.N.L
AN ABSTRACT OF THE THESIS OF RONALD NORMAN KNOSHAUG for the MASTER OF ARTS (Name) (Degree) in MATHEMATICS presented on October 10, 1968 (Major) (Date) Title: GENERALIZED DEFORMATION-RATES IN SECONDARY FLOWS OF VISCOELASTIC FLUIDS BETWEEN ROTATING SPHERES Redacted for Privacy kbstract approved: M.N.L. Narasimhan By various experiments, it has been found that the re- sponse of real materials to external forces is, in general, nonlinear in character. In classical continuum mechanics, the use of ordinary measures of strain have forced the constitutive equations to take complex forms and since the orders of these measures are not fixed, many unknown re- sponse coefficients have to be introduced into the consti- tutive equations. In general, there is no basis of choos- ing these coefficients. Seth attempted to resolve this difficulty by introducing generalized measures in continuum mechanics and Narasimhan and Sra extended these measures in such a way as to adequately explain some rheological behav- ior of materials. The constitutive equation of Narasimhan and Sra essentially contains two terms and four rheological constants and, unlike some previous theories, it does not contain any unknown functions of the invariants of kine- matic matrices while at the same time explains many visco- elastic phenomena. In the present investigation, a theorem has been proved establishing certain criteria for fixing the orders of generalized measures suitably so as to predict different types of viscoelastic phenomena, such as dilatancy. We have found during the course of this investigation that the constitutive equation of Narasimhan and Sra does not ade- quately explain such physical phenomena as pseudoplasticity. -
Revolution of Charged Particles in a Central Field of Attraction with Emission of Radiation
ISSN: 2639-0108 Research Article Advances in Theoretical & Computational Physics Revolution of Charged Particles in a Central Field of Attraction with Emission of Radiation Musa D Abdullahi *Corresponding author Musa D Abdullahi, Department of Electrical and Electronics Engineering, Department of Electrical and Electronics Engineering Kaduna Polytechnic, Kaduna, Nigeria. Submitted: 09 Jan 2020; Accepted: 20 Jan 2020; Published: 01 Feb 2020 Abstract A particle of mass nm, carrying the electronic charge -e, revolves in an orbit through angle ψ at distances nr from a center of force of attraction, with angular momenta nL perpendicular to the orbital plane, where n is an integer greater than 0, m the electronic mass and r1 is the radius of the first circular orbit. The equation of motion of the nth orbit of revolution is derived, revealing that an excited particle revolves in an unclosed elliptic orbit, with emission of radiation at the frequency of revolution, before settling down, after many cycles of ψ, in a stable circular orbit. In unipolar revolution, a radiating particle settles in a circular orbit of radius nr1 round a positively charged nucleus. In bipolar revolution, two radiating particles of the same mass nm and charges e and –e, settle in a circular stable orbit of radius ns1 round a common center of mass, where s1 is the radius of the first orbit. Discrete masses nm and angular momenta nL lead to quantization of the orbits outside Bohr’s quantum mechanics. The frequency of radiation in the bipolar revolution is found to be in conformity with the Balmer-Rydberg formula for the spectral lines of radiation from the atom hydrogen gas. -
Linear Estimation in Krein Spaces-- Part II: Applications
34 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 41, NO. 1, JANUARY 1996 stimation in Krein Spaces- art 11: Applications Babak Hassibi, Ali H. Sayed, Member, IEEE, and Thomas Kailath, Fellow, IEEE Abstract-We show that several interesting problems in Rw - by constructing the corresponding Krein-space "stoc filtering, quadratic game theory, and risk sensitive control and problems for which the Kalman-filter solutions can be written estimation follow as special cases of the Krein-space linear esti- down immediately; moreover, the conditions for a minimum mation theory developed in [l]. We show that a11 these problems can be cast into the problem of calculating the stationary point can also be expressed in terms of quantities easily related to the of certain second-order forms, and that by considering the ap- basic Riccati equations of the Kalman filter. This approach also propriate state space models and error Gramians, we can use the explains the many similarities between, say, the H" solutions ~re~n-spa~eestimation theory to calculate the stationary points and ~e classical LQ solutions and in addition marks out their and study their properties. The approach discussed here allows key differences. for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns. The paper is organized as follows. In Section I1 we introduce the H" estimation problem, state the conventional solution, and discuss its similarities with and differences from the I. INTRODUCTION Conventional Kalman filter. In Section I11 we reduce the H" LASSICAL results in linear least-squares estimation and estimation problem to guaranteeing the positivity of a certain Kalman filtering are based on an LZ or HZ criterion indefinite quadratic form. -
Stochastic Mirror Descent on Overparameterized Nonlinear Models: Convergence, Implicit Regularization, and Generalization
Stochastic Mirror Descent on Overparameterized Nonlinear Models: Convergence, Implicit Regularization, and Generalization Navid Azizan1, Sahin Lale2, Babak Hassibi2 1 Department of Computing and Mathematical Sciences 2 Department of Electrical Engineering California Institute of Technology {azizan,alale,hassibi}@caltech.edu Abstract Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors that perfectly interpolate the training data). Therefore, it is important to understand which interpolating solutions we converge to, how they depend on the initialization point and the learning algorithm, and whether they lead to different generalization performances. In this paper, we study these questions for the family of stochastic mirror descent (SMD) algorithms, of which the popular stochastic gradient descent (SGD) is a special case. Our contributions are both theoretical and experimental. On the theory side, we show that in the overparameterized nonlinear setting, if the initialization is close enough to the manifold of global minima (something that comes for free in the highly overparameterized case), SMD with sufficiently small step size converges to a global minimum that is approximately the closest one in Bregman divergence. On the experimental side, our extensive experiments on standard datasets and models, using various initializations, various mirror descents,