Laurent polynomial moment problem: a case study
Pakovich, F; Zvonkin, A
2009-01-01
In recent years, the so-called polynomial moment problem, motivated by the classical Poincare center-focus problem, was thoroughly studied, and the answers to the main questions have been found. The study of a similar problem for rational functions is still at its very beginning. In this paper, we make certain progress in this direction; namely, we construct an example of a Laurent polynomial for which the solutions of the corresponding moment problem behave in a significantly more complicated way than it would be possible for a polynomial.
Problems in classical mechanics
Katkar, L N
2014-01-01
Problems in classical mechanics presents a lucid treatment of the formulations of Lagrangian, Hamiltonian, and the Principles of Calculus of Variations etc. important for the study of modern physics. The study of classical mechanics prepares students to apply the principles and the mathematical tools to solve real life problems. The book also incorporates and discusses in detail topics such as Central Force Motion, Rigid Body Motion and Canonical Transformations. KEY FEATURES: Around 200 solved examples with complete mathematical theory Around 70 examples given as an exercise to test and develop students understanding The physical interpretation of the Hamiltonian is highlighted
Classic Problems of Probability
Gorroochurn, Prakash
2012-01-01
"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin
A note on noncommutative moment problems
Institute of Scientific and Technical Information of China (English)
MA Xiujuan
2005-01-01
Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.
Fractional Moments on Bandit Problems
B, Ananda Narayanan
2012-01-01
Reinforcement learning addresses the dilemma between exploration to find profitable actions and exploitation to act according to the best observations already made. Bandit problems are one such class of problems in stateless environments that represent this explore/exploit situation. We propose a learning algorithm for bandit problems based on fractional expectation of rewards acquired. The algorithm is theoretically shown to converge on an eta-optimal arm and achieve O(n) sample complexity. Experimental results show the algorithm incurs substantially lower regrets than parameter-optimized eta-greedy and SoftMax approaches and other low sample complexity state-of-the-art techniques.
Collection of problems in classical mechanics
Kotkin, G L; ter Haar, D
1971-01-01
Collection of Problems in Classical Mechanics presents a set of problems and solutions in physics, particularly those involving mechanics. The coverage of the book includes 13 topics relevant to classical mechanics, such as integration of one-dimensional equations of motion; the Hamiltonian equations of motion; and adiabatic invariants. The book will be of great use to physics students studying classical mechanics.
Large Deviations for Random Matricial Moment Problems
Nagel, Jan; Gamboa, Fabrice; Rouault, Alain
2010-01-01
We consider the moment space $\\mathcal{M}_n^{K}$ corresponding to $p \\times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \\rightarrow \\infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\\times p$ matrices. Then we lift a random element of $\\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carth\\'eodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.
The Krein condition for the moment problem
DEFF Research Database (Denmark)
Pedersen, Henrik Laurberg
2005-01-01
In this paper, we describe a class of Wiener functionals that are `indeterminate by their moments', that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover......, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen....
Kholmetskii, A. L.; Missevitch, O. V.; Yarman, T.
2016-09-01
We consider the relativistic transformation of the magnetic dipole moment and disclose its physical meaning, shedding light on the related difficulties in the physical interpretation of classical electrodynamics in material media.
The inverse variational problem in classical mechanics
Lopuszánski, Jan T
1999-01-01
This book provides a concise description of the current status of a fascinating scientific problem - the inverse variational problem in classical mechanics. The essence of this problem is as follows: one is given a set of equations of motion describing a certain classical mechanical system, and the question to be answered is: Do these equations of motion correspond to some Lagrange function as its Euler-Lagrange equations? In general, not for every system of equations of motion does a Lagrange function exist; it can, however, happen that one may modify the given equations of motion in such a w
Using CAS to Solve Classical Mathematics Problems
Burke, Maurice J.; Burroughs, Elizabeth A.
2009-01-01
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
Using CAS to Solve Classical Mathematics Problems
Burke, Maurice J.; Burroughs, Elizabeth A.
2009-01-01
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
The inverse moment problem for convex polytopes
Gravin, Nick; Pasechnik, Dmitrii; Robins, Sinai
2011-01-01
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.
The photon magnetic moment problem revisited
Energy Technology Data Exchange (ETDEWEB)
Perez Rojas, H. [Matematica y Fisica, Departamento de Fisica Teorica, Instituto de Cibernetica, Havana (Cuba); Rodriguez Querts, E. [Matematica y Fisica, Departamento de Fisica Teorica, Instituto de Cibernetica, Havana (Cuba); ICTP, Trieste (Italy)
2014-06-15
The photon magnetic moment for radiation propagating in magnetized vacuum is defined as a pseudotensor quantity, proportional to the external electromagnetic field tensor. After expanding the eigenvalues of the polarization operator in powers of k{sup 2}, we obtain approximate dispersion equations (cubic in k{sup 2}), and analytic solutions for the photon magnetic moment, valid for low momentum and/or large magnetic field. The paramagnetic photon experiences a redshift, with opposite sign to the gravitational one, which differs for parallel and perpendicular polarizations. It is due to the drain of photon transverse momentum and energy by the external field. By defining an effective transverse momentum, the constancy of the speed of light orthogonal to the field is guaranteed. We conclude that the propagation of the photon non-parallel to the magnetic direction behaves as if there is a quantum compression of the vacuum or a warp of space-time in an amount depending on its angle with regard to the field. (orig.)
Explicit Solutions of Moment Problems 1.
1987-07-01
well known,(see e.g. Levin and Miljutin (1978), Kellerer (1984), Kemperman (1983), Haneveld (1985), Rischendorf (1985), Rachev (1984) and references...the marginal problem for different spaces U and criterion functions c are given by Levin and Miljutin (1978), Kellerer (1984), Haneveld (1985...Krein (1962), Karlin and Studden (1966), Hoeffding (1955), Hoeffding and Shrikhande (1956), Basu and Simons (1983), Kemperman (1972,1983), Haneveld (1985
Better relaxations of classical discrete optimization problems.
Energy Technology Data Exchange (ETDEWEB)
Lancia, Giuseppe; Konjevod, Goran; Carr, Robert D.; Parehk, Ojas
2008-08-01
A mathematical program is an optimization problem expressed as an objective function of multiple variables subject to set of constraints. When the optimization problem has specific structure, the problem class usually has a special name. A linear program is the optimization of a linear objective function subject to linear constraints. An integer program is a linear program where some of the variables must take only integer values. A semidefinite program is a linear program where the variables are arranged in a matrix and for all feasible solutions, this matrix must be positive semidefinite. There are general-purpose solvers for each of these classes of mathematical program. There are usually many ways to express a problem as a correct, say, linear program. However, equivalent formulations can have significantly different practical tractability. In this poster, we present new formulations for two classic discrete optimization problems, maximum cut (max cut) and the graphical traveling salesman problem (GTSP), that are significantly stronger, and hence more computationally tractable, than any previous formulations of their class. Both partially answer longstanding open theoretical questions in polyhedral combinatorics.
Inverse Problems in Classical and Quantum Physics
Almasy, Andrea A
2009-01-01
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. In this thesis, als...
The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity
Directory of Open Access Journals (Sweden)
Roman Janjgava
2016-01-01
Full Text Available We consider a two-dimensional system of differential equations of the moment theory of elasticity. The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation. Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed. Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed. The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared. In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one. Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.
Moment theory and some inverse problems in potential theory and heat conduction
Ang, Dang Dinh; Le, Vy Khoi; Trong, Dang Duc
2002-01-01
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.
Inverse problems in classical and quantum physics
Energy Technology Data Exchange (ETDEWEB)
Almasy, A.A.
2007-06-29
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
A Semidefinite Approach for Truncated K-Moment Problem
Helton, J William
2011-01-01
A truncated moment sequence (tms) of degree d is a vector indexed by monomials whose degree is at most d. Let K be a semialgebraic set.The truncated K-moment problem (TKMP) is: when does a tms y admit a positive Borel measure supported? This paper proposes a semidefinite programming (SDP) approach for solving TKMP. When K is compact, we get the following results: whether a tms y of degree d admits a K-measure or notcan be checked via solving a sequence of SDP problems; when y admits no K-measure, a certificate will be given; when y admits a K-measure, a representing measure for y would be obtained from solving the SDP under some necessary and some sufficient conditions. Moreover, we also propose a practical SDP method for finding flat extensions, which in our numerical experiments always finds a finitely atomic representing measure for a tms when it admits one.
Distributionally Robust Joint Chance Constrained Problem under Moment Uncertainty
Directory of Open Access Journals (Sweden)
Ke-wei Ding
2014-01-01
Full Text Available We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.
An evaluation of collision models in the Method of Moments for rarefied gas problems
Emerson, David; Gu, Xiao-Jun
2014-11-01
The Method of Moments offers an attractive approach for solving gaseous transport problems that are beyond the limit of validity of the Navier-Stokes-Fourier equations. Recent work has demonstrated the capability of the regularized 13 and 26 moment equations for solving problems when the Knudsen number, Kn (where Kn is the ratio of the mean free path of a gas to a typical length scale of interest), is in the range 0.1 and 1.0-the so-called transition regime. In comparison to numerical solutions of the Boltzmann equation, the Method of Moments has captured both qualitatively, and quantitatively, results of classical test problems in kinetic theory, e.g. velocity slip in Kramers' problem, temperature jump in Knudsen layers, the Knudsen minimum etc. However, most of these results have been obtained for Maxwell molecules, where molecules repel each other according to an inverse fifth-power rule. Recent work has incorporated more traditional collision models such as BGK, S-model, and ES-BGK, the latter being important for thermal problems where the Prandtl number can vary. We are currently investigating the impact of these collision models on fundamental low-speed problems of particular interest to micro-scale flows that will be discussed and evaluated in the presentation. Engineering and Physical Sciences Research Council under Grant EP/I011927/1 and CCP12.
Symmetric moment problems and a conjecture of Valent
Berg, C.; Szwarc, R.
2017-03-01
In 1998 Valent made conjectures about the order and type of certain indeterminate Stieltjes moment problems associated with birth and death processes which have polynomial birth and death rates of degree {p≥slant 3}. Romanov recently proved that the order is 1/p as conjectured. We prove that the type with respect to the order is related to certain multi-zeta values and that this type belongs to the interval which also contains the conjectured value. This proves that the conjecture about type is asymptotically correct as p\\to∞. The main idea is to obtain estimates for order and type of symmetric indeterminate Hamburger moment problems when the orthonormal polynomials P_n and those of the second kind Q_n satisfy P2n^2(0)∼ c_1n-1/β and Q2n-1^2(0)∼ c2 n-1/α, where 0proof of Romanov's Theorem that the order is 1/p. Bibliography: 19 titles.
Planar dynamical systems selected classical problems
Liu, Yirong; Huang, Wentao
2014-01-01
This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. This book is intended for graduate students, post-doctors and researchers in the area of theories and applications of dynamical systems. For all engineers who are interested the theory of dynamical systems, it is also a reasona
Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics
Schlitt, D. W.
1977-01-01
Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)
The classical Stefan problem basic concepts, modelling and analysis
Gupta, SC
2003-01-01
This volume emphasises studies related toclassical Stefan problems. The term "Stefan problem" isgenerally used for heat transfer problems with phase-changes suchas from the liquid to the solid. Stefan problems have somecharacteristics that are typical of them, but certain problemsarising in fields such as mathematical physics and engineeringalso exhibit characteristics similar to them. The term``classical" distinguishes the formulation of these problems fromtheir weak formulation, in which the solution need not possessclassical derivatives. Under suitable assumptions, a weak solutioncould be as good as a classical solution. In hyperbolic Stefanproblems, the characteristic features of Stefan problems arepresent but unlike in Stefan problems, discontinuous solutions areallowed because of the hyperbolic nature of the heat equation. Thenumerical solutions of inverse Stefan problems, and the analysis ofdirect Stefan problems are so integrated that it is difficult todiscuss one without referring to the other. So no...
A Parameter Property of Classical Solutions of Cauchy Problems
Directory of Open Access Journals (Sweden)
Min He
2014-01-01
Full Text Available This work is concerned with the abstract Cauchy problems that depend on parameters. The goal is to study continuity in the parameters of the classical solutions of the Cauchy problems. The situation considered in this work is when the operator of the Cauchy problem is not densely defined. By applying integrated semigroup theory and the results on continuity in the parameters of C0-semigroup and integrated semigroup, we obtain the results on the existence and continuity in parameters of the classical solutions of the Cauchy problems. The application of the obtained abstract results in a parabolic partial differential equation is discussed in the last section of the paper.
Singularity problem of control moment gyro cluster with vibration isolators
Institute of Scientific and Technical Information of China (English)
Cui Yinghui; Zheng Gangtie
2016-01-01
As powerful torque amplification actuators, control moment gyros (CMGs) are often used in the attitude control of many state-of-the-art high resolution satellites. However, the distur-bance generated by the CMGs can not only reduce the attitude stability of a satellite but also dete-riorate the performance of optic payloads. Currently, CMG vibration isolators are widely used to target this problem. The isolators can affect the singularity of the CMG system as they are placed between the CMGs and the satellite bus and provide additional freedoms to the CMG system due to their flexibility. The formulation of the output torque of a CMG is studied first considering the dynamic imbalance of its spin rotor and then the deformation angle as a result of the isolator’s flex-ibility is calculated. With the additional freedoms, the influence of isolator on the singularity problem is studied and a new steering logic to escape from the singular states is proposed.
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
Vladimirov, Igor G
2012-01-01
We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random fie...
On gravitational waves from classical three body problem
Fiziev, Plamen P
2016-01-01
Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular motions of such systems and to the significance of double and triple collisions. The conclusive role of the collinear solutions is also discussed in short.
How some infinities cause problems in classical physical theories
Atkinson, David; Peijnenburg, Jeanne; Allo, P.; van Kerhove, B.
2014-01-01
In this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How Infinities Cause Problems in Classical Physical Theories’, in the light of two later models concerning colliding balls, of Pérez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegem antic
A NOVEL ALGORITHM FOR SOLVING THE CLASSICAL STEFAN PROBLEM
Directory of Open Access Journals (Sweden)
Zhaochun Wu
2011-01-01
Full Text Available A novel algorithm for solving the classic Stefan problem is proposed in the paper. Instead of front tracking, we preset the moving interface locations and use these location coordinates as the grid points to find out the arrival time of moving interface respectively. Through this approach, the difficulty in mesh generation can be avoided completely. The simulation shows the numerical result is well coincident with the exact solution, implying the new approach performes well in solving this problem.
Analytical mechanics solutions to problems in classical physics
Merches, Ioan
2014-01-01
Fundamentals of Analytical Mechanics Constraints Classification Criteria for Constraints The Fundamental Dynamical Problem for a Constrained Particle System of Particles Subject to Constraints Lagrange Equations of the First KindElementary Displacements Generalities Real, Possible and Virtual Displacements Virtual Work and Connected Principles Principle of Virtual WorkPrinciple of Virtual Velocities Torricelli's Principle Principles of Analytical Mechanics D'alembert's Principle Configuration Space Generalized Forces Hamilton's Principle The Simple Pendulum Problem Classical (Newtonian) Formal
A non-classical class of variational problems
Cruz, Pedro A F; Zinober, Alan S I
2009-01-01
We study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand is a function of the unknown y(T). This is a non-standard CoV problem. In this paper we apply the new costate boundary conditions p(T) in the formulation of the CoV problem. We solve some sample examples in this problem class using the numerical shooting method to solve the resulting TPBVP, and incorporate the free y(T) as an additional unknown. Essentially the same results are obtained using symbolic algebra software.
1000 Solved Problems in Classical Physics An Exercise Book
Kamal, Ahmad A
2011-01-01
This book basically caters to the needs of undergraduate and graduate physics students in classical physics, especially Classical Mechanics and Electricity and Electromagnetism. Lecturers/Tutors may use it as a resource book. The contents of the book are based on the syllabi currently used in the undergraduate courses in the USA, U.K., and other countries. The book consists of 15 chapters, each one beginning with a brief but adequate summary and necessary formulas and Line diagrams followed by a variety of typical problems useful for assignments and exams. Detailed solutions are provided at the end of each chapter.
CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM
Institute of Scientific and Technical Information of China (English)
YIFAHUAI
1996-01-01
This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv+δu/δv=0 on the free boundary. under the natural conditions the existence of classical solution locally in time is proved by making use of the property of Frechet derivative operator and fixed point theorem. For the sake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can be dealt with in a similar way with more complicated calculation.
Modified Classical Graph Algorithms for the DNA Fragment Assembly Problem
Directory of Open Access Journals (Sweden)
Guillermo M. Mallén-Fullerton
2015-09-01
Full Text Available DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently.
Is there a flatness problem in classical cosmology?
Helbig, Phillip
2011-01-01
I briefly review the flatness problem within the context of classical cosmology and examine some of the debate in the literature with regard to its definition and even the question whether it exists. I then present some new calculations for cosmological models which will collapse in the future; together with previous work by others for models which will expand forever, this allows one to examine the flatness problem quantitatively for all cosmological models. This leads to the conclusion that the flatness problem does not exist, not only for the cosmological models corresponding to the currently popular values of lambda_0 and Omega_0 but indeed for all Friedmann-Lema\\^itre models.
Exploring classical Greek construction problems with interactive geometry software
Meskens, Ad
2017-01-01
In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software. The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of GeoGebra the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those student...
Silenko, Alexander J
2014-01-01
The fulfilled derivation of equation of spin precession of a particle possessing magnetic and electric dipole moments uses a fully covariant approach and explicitly separates contributions from classical electrodynamics and from the Thomas effect. The expression of the final equation in terms of the fields in the instantly accompanying frame presents it in a very simple form. The Lorentz transformations of the magnetic and electric dipole moments and the spin are derived from basic equations of classical electrodynamics, namely, from the equation connecting the angular momentum and the magnetic moment and from the Maxwell equations in matter. An antisymmetric four-tensor is constructed from the electric and magnetic dipole moments.
An approximate method for solution to variable moment of inertia problems
Beans, E. W.
1981-01-01
An approximation method is presented for reducing a nonlinear differential equation (for the 'weather vaning' motion of a wind turbine) to an equivalent constant moment of inertia problem. The integrated average of the moment of inertia is determined. Cycle time was found to be the equivalent cycle time if the rotating speed is 4 times greater than the system's minimum natural frequency.
E. Cartan moment of rotation in classical and quantum gravity. Final report
Energy Technology Data Exchange (ETDEWEB)
Kheyfets, A. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics
1994-05-25
The geometric construction of the E. Cartan moment of rotation associated to the spacetime curvature provides a geometric interpretation of the gravitational field sources and describes geometrically how the sources are ``wired`` to the field in standard geometrodynamics. E. Cartan moment of rotation yields an alternate way (as opposed to using variational principles) to obtain Einstein equations. The E. Cartan construction uses in an essential way the soldering structure of the frame bundle underlying the geometry of the gravitational field of general relativity. The geometry of Ashtekar`s connection formulation of gravitation theory is based on a complex-valued self-dual connection that is defined not on the frame bundle of spacetime but, rather, on its complexification. We show how to transfer the construction of the E. Cartan moment of rotation to Ashtekar`s theory of gravity and demonstrate that no spurious equations are produced via this procedure.
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, Alexander
2011-01-01
Robbins' problem of optimal stopping asks one to minimise the expected {\\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\\it value} of the stopped variable under the rule optimal in the sense of the rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, A.V.; Iksanov, A.
2011-01-01
Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, A.V.; Iksanov, A.
2011-01-01
Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much mor
The moment problem and vibrations damping of beams and plates
Energy Technology Data Exchange (ETDEWEB)
Atamuratov, Andrey G. [Pepsico Holding LTD, Leningrad Avenue, 72/4, 125315 Moscow (Russian Federation); Mikhailov, Igor E. [Dorodnicyn Computing Centre of RAS, Vavilov str., 40, 119333 Moscow (Russian Federation); Muravey, Leonid A. [Russian State Technological University, Orshanskaya str., 3, 121552 Moscow (Russian Federation)
2016-06-08
Beams and plates are the elements of different complex mechanical structures, for example, pipelines and aerospace platforms. That is why the problem of damping of their vibrations caused by unwanted perturbations is actual task.
Energy Technology Data Exchange (ETDEWEB)
Silenko, Alexander J. [Belarusian State University, Research Institute for Nuclear Problems, Minsk (Belarus); Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation)
2017-05-15
A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are obtained for an arbitrary initial polarization. These formulas are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance with allowance for both rotating fields. A general quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is shown. Quasimagnetic resonances for particles and nuclei moving in noncontinuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasimagnetic resonances in storage ring electric-dipole-moment experiments are investigated in detail. The exact formulas for the effect caused by the electric dipole moment are derived. The difference between the resonance effects conditioned by the rf electric-field flipper and the rf Wien filter is found and is calculated for the first time. The existence of this difference is crucial for the establishment of a consent between analytical derivations and computer simulations and for checking spin tracking programs. The main systematical errors are considered. (orig.)
On the Rankin-Selberg problem: higher power moments of the Riesz mean error term
Institute of Scientific and Technical Information of China (English)
2008-01-01
LetΔ1（x;φ） be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ1（x;φ） and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic’s large value arguments and other techniques.
Classical Machian Resolution of the Spacetime Reconstruction Problem
Anderson, Edward
2013-01-01
Following from a question of Wheeler, why does the Hamiltonian constraint ${\\cal H}$ of GR have the particular form it does? A first answer, by Hojman, Kucha\\v{r} and Teitelboim is that using embeddability into spacetime as a principle gives the form of ${\\cal H}$. The present paper culminates a second Machian answer -- initially by Barbour, Foster and \\'{o} Murchadha -- in which space but not spacetime are assumed. Thus this answer is additionally a classical-level resolution of the spacetime reconstruction problem. In this approach, mere consistency imposed by the Dirac procedure whittles down a general ansatz to one of four alternatives: Lorentzian, Galilean, Carrollian relativity and constant mean curvature slicing. These arise together as the different ways to kill off a 4-factor obstruction term. It is novel for such an alternative to arise from principles of dynamics considerations (in contrast with the historical form of the dichotomy between universal local Galilean or Lorentzian relativity). It is f...
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
Jung, C; Torres, J M
2005-01-01
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
Jung, C.; Seligman, T. H.; Torres, J. M.
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.
Bin-picking new approaches for a classical problem
Buchholz, Dirk
2016-01-01
This book is devoted to one of the most famous examples of automation handling tasks – the “bin-picking” problem. To pick up objects, scrambled in a box is an easy task for humans, but its automation is very complex. In this book three different approaches to solve the bin-picking problem are described, showing how modern sensors can be used for efficient bin-picking as well as how classic sensor concepts can be applied for novel bin-picking techniques. 3D point clouds are firstly used as basis, employing the known Random Sample Matching algorithm paired with a very efficient depth map based collision avoidance mechanism resulting in a very robust bin-picking approach. Reducing the complexity of the sensor data, all computations are then done on depth maps. This allows the use of 2D image analysis techniques to fulfill the tasks and results in real time data analysis. Combined with force/torque and acceleration sensors, a near time optimal bin-picking system emerges. Lastly, surface normal maps are empl...
Galapon, E A
2001-01-01
We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically we seek to define and motivate a solution to the quantum-classical correspondence problem independent from quantization and discuss the general insufficiency of prescriptive quantization, particularly the Weyl quantization. We demonstrate our points by constructing time of arrival operators without quantization and from these recover their classical counterparts.
Truncated matricial moment problems on a finite interval: the operator approach
Zagorodnyuk, Sergey M
2009-01-01
In this paper we obtain a description of all solutions of truncated matricial moment problems on a finite interval in a general case (no conditions besides solvability are assumed). We use the basic results of M.G. Krein and I.E. Ovcharenko about generalized sc-resolvents of Hermitian contractions.
Tackling the sign problem with a moment expansion and application to Heavy dense QCD
Garron, Nicolas
2016-01-01
Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications, HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which depends on the value of the chemical potential, which makes this theory ideal to test the reach of new algorithms. We use the LLR approach to obtain the probability distribution of the phase of the fermion determinant. Our goal is the calculation of the phase factor expectation value, which appears as Fourier transform of this probability distribution. We here propose a new and systematic moment expansion for this phase factor. We compare the answer from the moment expansion order by order with the exact answer. We find that this expansion converge quickly and works very well in the strong sign problem region.
Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation
Institute of Scientific and Technical Information of China (English)
MA YUN-YUN; MA FU-MING
2012-01-01
In this paper,we consider the reconstruction of the wave field in a bounded domain.By choosing a special family of functions,the Cauchy problem can be transformed into a Fourier moment problem.This problem is ill-posed.We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary.We also give the convergence analysis and error estimate of the numerical algorithm.Finally,we present some numerical examples to show the effectiveness of this method.
Classical Zero-Point Radiation and Relativity: The Problem of Atomic Collapse Revisited
Boyer, Timothy H.
2015-01-01
The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point radiation, and 2) the importance of special relativity. In classes in modern physics today, the problem of atomic collapse is still mentioned in the historical context of the early 20th century. However, the classical problem of atomic collapse is currently bein...
Problems in classical and quantum mechanics extracting the underlying concepts
Kelley, J Daniel
2017-01-01
This book is a collection of problems intended to aid students in their graduate courses in physics and in preparing for the PhD qualifying exam. Thus, the included problems are of the type that could be on a qualifying exam or are problems that are meant to elucidate a principle that is important for the exam. Unlike other compilations of problems, the problems in this text are placed in the broader context of the subject. The goal of the book is to develop the problem solving skills of the reader to insure a complete understanding of the physics. Problems and solutions are presented in detail, and, additionally, their significance is discussed within the context of the physical principle(s) that they illustrate. The solution of the problem is only the beginning of the learning process--it is in manipulating the solution and changing the parameters that a great deal of insight can be gleaned. This technique is referred to by the authors as "massaging the problem," and it is a technique that the authors have ...
Revisiting a classic: the Parker-Moffatt problem
Pezzi, O; Servidio, S; Valentini, F; Vasconez, C L; Yang, Y; Malara, F; Matthaeus, W H; Veltri, P
2016-01-01
The interaction of two colliding Alfv\\'en wave packets is here described by means of magnetohydrodynamics (MHD) and hybrid kinetic numerical simulations. The MHD evolution revisits the theoretical insights described by Moffatt, Parker, Kraichnan, Chandrasekhar and Els\\"asser in which the oppositely propagating large amplitude wave packets interact for a finite time, initiating turbulence. However, the extension to include compressive and kinetic effects, while maintaining the gross characteristics of the simpler classic formulation, also reveals intriguing features which go beyond the pure MHD treatment.
Revisiting a Classic: The Parker–Moffatt Problem
Pezzi, O.; Parashar, T. N.; Servidio, S.; Valentini, F.; Vásconez, C. L.; Yang, Y.; Malara, F.; Matthaeus, W. H.; Veltri, P.
2017-01-01
The interaction of two colliding Alfvén wave packets is described here by means of magnetohydrodynamics (MHD) and hybrid kinetic numerical simulations. The MHD evolution revisits the theoretical insights described by Moffatt, Parker, Kraichnan, Chandrasekhar, and Elsässer in which the oppositely propagating large-amplitude wave packets interact for a finite time, initiating turbulence. However, the extension to include compressive and kinetic effects, while maintaining the gross characteristics of the simpler classic formulation, also reveals intriguing features that go beyond the pure MHD treatment.
Handy, C R; Okbagabir, S; Yarahmad, T
2003-01-01
For one-dimensional Schroedinger quantum systems, the correlation expression S(x, tau, a) ident to PSI*(x - tau/2/a)PSI(x + tau/2) satisfies a fourth-order linear differential equation with regard to x. This generalizes the result previously derived by Handy (2001 J. Phys. A: Math. Gen. 34 L271), and Handy and Wang (2001 J. Phys. A: Math. Gen. 34 8297), with regard to S(x, 0, 1). We are then able to incorporate this within a generalized Wigner transform representation, through the use of scalets (Handy C R and Brooks H A 2001 J. Phys. A: Math. Gen. 34 3577). Energy quantization is achieved through a moment problem positivity analysis (focusing on the moments of the probability density, vertical bar PSI vertical bar sup 2) at a=1, tau=0. The wavefunction, PSI, is then generated through a multiscale analysis proceeding from the unity scale, extended into the zero scale limit. The power moments, mu sub p =integral dx x sup p PSI(x), can be generated through a similar procedure. We present the general formalism a...
Problems in classical potential theory with applications to mathematical physics
Lundberg, Erik
In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters. Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem). Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain. Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.
Classical and Quantum Two-Body Problem in General Relativity
Maheshwari, Amar; Todorov, Ivan
2016-01-01
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different `Schwarzschild radii'. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.
New Algebraic Approaches to Classical Boundary Layer Problems
Institute of Scientific and Technical Information of China (English)
Xiao Ping XU
2011-01-01
Classical non-steady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer theory of fluid dynamics. In this paper, we introduce various schemes with multiple parameter functions to solve these equations and obtain many families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations are used to simplify our arguments. The technique of moving frame is applied in the three-dimensional case in order to capture the rotational properties of the fluid. In particular, we obtain a family of solutions singular on any moving surface, which may be used to study turbulence. Many other solutions are analytic related to trigonometric and hyperbolic functions, which reflect various wave characteristics of the fluid. Our solutions may also help engineers to develop more effective algorithms to find physical numeric solutions to practical models.
A question on the spectra of algebras of symmetric functions on L_∞ related to the moment problem
Directory of Open Access Journals (Sweden)
T. V. Vasylyshyn
2012-11-01
Full Text Available We consider a question on description of the set of characters of the algebra of bounded type symmetric analytic functions on L ∞ [0;1] and establish some connection with the trigonometric moment problem.
A question on the spectra of algebras of symmetric functions on L_∞ related to the moment problem
T. V. Vasylyshyn; A. V. Zagorodnyuk
2013-01-01
We consider a question on description of the set of characters of the algebra of bounded type symmetric analytic functions on L ∞ [0;1] and establish some connection with the trigonometric moment problem.
Ng, Jonathan; Hakim, Ammar; Bhattacharjee, Amitava; Stanier, Adam; Daughton, William; Wang, Liang; Germaschewski, Kai
2015-01-01
As modeling of collisionless magnetic reconnection in most space plasmas with realistic parameters is beyond the capability of today's simulations, due to the separation between global and kinetic length scales, it is important to establish scaling relations in model problems so as to extrapolate to realistic scales. Recently, large scale particle-in-cell (PIC) simulations of island coalescence have shown that the time averaged reconnection rate decreases with system size, while fluid systems at such large scales in the Hall regime have not been studied. Here we perform the complementary resistive MHD, Hall MHD and two fluid simulations using a ten-moment model with the same geometry. In contrast to the standard Harris sheet reconnection problem, Hall MHD is insufficient to capture the physics of the reconnection region. Additionally, motivated by the results of a recent set of hybrid simulations which show the importance of ion kinetics in this geometry, we evaluate the efficacy of the ten-moment model in re...
Energy Technology Data Exchange (ETDEWEB)
Ng, Jonathan; Huang, Yi-Min; Hakim, Ammar; Bhattacharjee, A. [Center for Heliophysics, Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Stanier, Adam; Daughton, William [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Wang, Liang; Germaschewski, Kai [Space Science Center and Physics Department, University of New Hampshire, Durham, New Hampshire 03824 (United States)
2015-11-15
As modeling of collisionless magnetic reconnection in most space plasmas with realistic parameters is beyond the capability of today's simulations, due to the separation between global and kinetic length scales, it is important to establish scaling relations in model problems so as to extrapolate to realistic scales. Recently, large scale particle-in-cell simulations of island coalescence have shown that the time averaged reconnection rate decreases with system size, while fluid systems at such large scales in the Hall regime have not been studied. Here, we perform the complementary resistive magnetohydrodynamic (MHD), Hall MHD, and two fluid simulations using a ten-moment model with the same geometry. In contrast to the standard Harris sheet reconnection problem, Hall MHD is insufficient to capture the physics of the reconnection region. Additionally, motivated by the results of a recent set of hybrid simulations which show the importance of ion kinetics in this geometry, we evaluate the efficacy of the ten-moment model in reproducing such results.
Classical Zero-Point Radiation and Relativity: The Problem of Atomic Collapse Revisited
Boyer, Timothy H.
2016-07-01
The physicists of the early twentieth century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: (1) the presence of classical electromagnetic zero-point radiation, and (2) the importance of special relativity. In classes in modern physics today, the problem of atomic collapse is still mentioned in the historical context of the early twentieth century. However, the classical problem of atomic collapse is currently being treated in the presence of classical zero-point radiation where the problem has been transformed. The presence of classical zero-point radiation indeed keeps the electron from falling into the Coulomb potential center. However, the old collapse problem has been replaced by a new problem where the zero-point radiation may give too much energy to the electron so as to cause "self-ionization." Special relativity may play a role in understanding this modern variation on the atomic collapse problem, just as relativity has proved crucial for a classical understanding of blackbody radiation.
On Semi-classical Degravitation and the Cosmological Constant Problems
Patil, Subodh P
2010-01-01
In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein's equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d'Alembertian. If the functional form of the resulting Newton's `constant' is such that it annihilates very long wavelength sources, but reduces to $1/M^2_{pl}$ ($M_{pl}$ being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm-- a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce no...
Classical Zero-Point Radiation and Relativity: The Problem of Atomic Collapse Revisited
Boyer, Timothy H
2015-01-01
The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point radiation, and 2) the importance of special relativity. In classes in modern physics today, the problem of atomic collapse is still mentioned in the historical context of the early 20th century. However, the classical problem of atomic collapse is currently being treated in the presence of classical zero-point radiation where the problem has been transformed. The presence of classical zero-point radiation indeed keeps the electron from falling into the Coulomb potential center. However, the old collapse problem has been replaced by a new problem where the zero-point radiation may give too much energy to the electron so as to cause self-ionization. Special relativity may play a role in understanding this modern variation on the atomic collapse problem, just as relativity has prov...
Optimization in First Semester Calculus: A Look at a Classic Problem
LaRue, Renee; Infante, Nicole Engelke
2015-01-01
Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…
From the classical self-force problem to the foundations of quantum mechanics and beyond
2012-01-01
Classical electrodynamics and general relativity are successful non-theories: Plagued by the self-force problem, both are ill defined yet extremely practical. The paradox of a `practical non theory' is resolved in the current paper by showing that the experimentally valid content of classical electrodynamics can be extracted from a set of axioms, or constitutive relations, circumventing the ill-definedness of the self-force. A concrete realization of these constitutive relations by a well def...
de Villiers, Michael
2017-01-01
This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…
de Villiers, Michael
2017-01-01
This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
Radiation reaction of multipole moments
Kazinski, P. O.
2007-08-01
A Poincaré-invariant description is proposed for the effective dynamics of a localized system of charged particles in classical electrodynamics in terms of the intrinsic multipole moments of the system. A relativistic-invariant definition for the intrinsic multipole moments of a system of charged particles is given. A new generally covariant action functional for a relativistic perfect fluid is proposed. In the case of relativistic charged dust, it is proven that the description of the problem of radiation reaction of multipole moments by the model of particles is equivalent to the description of this problem by a hydrodynamic model. An effective model is obtained for a pointlike neutral system of charged particles that possesses an intrinsic dipole moment, and the free dynamics of this system is described. The bound momentum of a point dipole is found.
Well-posedness for the Classical Stefan Problem and the Zero Surface Tension Limit
Hadžić, Mahir; Shkoller, Steve
2016-11-01
We develop a framework for a unified treatment of well-posedness for the Stefan problem with or without surface tension. In the absence of surface tension, we establish well-posedness in Sobolev spaces for the classical Stefan problem. We introduce a new velocity variable which extends the velocity of the moving free-boundary into the interior domain. The equation satisfied by this velocity is used for the analysis in place of the heat equation satisfied by the temperature. Solutions to the classical Stefan problem are then constructed as the limit of solutions to a carefully chosen sequence of approximations to the velocity equation, in which the moving free-boundary is regularized and the boundary condition is modified in a such a way as to preserve the basic nonlinear structure of the original problem. With our methodology, we simultaneously find the required stability condition for well-posedness and obtain new estimates for the regularity of the moving free-boundary. Finally, we prove that solutions of the Stefan problem with positive surface tension {σ} converge to solutions of the classical Stefan problem as {σ to 0}.
Sweat, Noah W; Bates, Larry W; Hendricks, Peter S
2016-01-01
Developing methods for improving creativity is of broad interest. Classic psychedelics may enhance creativity; however, the underlying mechanisms of action are unknown. This study was designed to assess whether a relationship exists between naturalistic classic psychedelic use and heightened creative problem-solving ability and if so, whether this is mediated by lifetime mystical experience. Participants (N = 68) completed a survey battery assessing lifetime mystical experience and circumstances surrounding the most memorable experience. They were then administered a functional fixedness task in which faster completion times indicate greater creative problem-solving ability. Participants reporting classic psychedelic use concurrent with mystical experience (n = 11) exhibited significantly faster times on the functional fixedness task (Cohen's d = -.87; large effect) and significantly greater lifetime mystical experience (Cohen's d = .93; large effect) than participants not reporting classic psychedelic use concurrent with mystical experience. However, lifetime mystical experience was unrelated to completion times on the functional fixedness task (standardized β = -.06), and was therefore not a significant mediator. Classic psychedelic use may increase creativity independent of its effects on mystical experience. Maximizing the likelihood of mystical experience may need not be a goal of psychedelic interventions designed to boost creativity.
Excursions in classical analysis pathways to advanced problem solving and undergraduate research
Chen, Hongwei
2010-01-01
Excursions in Classical Analysis introduces undergraduate students to advanced problem solving and undergraduate research in two ways. Firstly, it provides a colourful tour of classical analysis which places a wide variety of problems in their historical context. Secondly, it helps students gain an understanding of mathematical discovery and proof. In demonstrating a variety of possible solutions to the same sample exercise, the reader will come to see how the connections between apparently inapplicable areas of mathematics can be exploited in problem-solving. This book will serve as excellent preparation for participation in mathematics competitions, as a valuable resource for undergraduate mathematics reading courses and seminars and as a supplement text in a course on analysis. It can also be used in independent study, since the chapters are free-standing.
Sri Ranga, A.
1984-01-01
Just as the denominator polynomials of a J-fraction are orthogonal polynomials with respect to some moment functional, the denominator polynomials of an M-fraction are shown to satisfy a skew orthogonality relation with respect to a stronger moment functional. Many of the properties of the numerators and denominators of an M- fraction are also studied using this pseudo orthogonality relation of the denominator polynomials. Properties of the zeros of the denominator polyno...
Danek, Amory H.; Wiley, Jennifer; Öllinger, Michael
2016-01-01
Insightful problem solving is a vital part of human thinking, yet very difficult to grasp. Traditionally, insight has been investigated by using a set of established "insight tasks," assuming that insight has taken place if these problems are solved. Instead of assuming that insight takes place during every solution of the 9 Dot, 8 Coin,…
The classical Doppler effect as a rendezvous problem; 3D case
Di Rocco, Hector Omar
2016-01-01
En este trabajo se deriva la fórmula para el corrimiento Doppler como si tratásemos un problema de encuentro, unificando todos los posibles movimientos relativos entre la fuente y el observador We derive the classical Doppler shift formula as a rendezvous problem, unifying all possible relative movements between the source and the observer Fil: Di Rocco, Hector Omar. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Instituto de Fisica Arroyo...
Classical Universe emerging from quantum cosmology without horizon and flatness problems
Fathi, M; Moniz, P V
2016-01-01
We apply the complex de Broglie-Bohm formulation of quantum mechanics [1] to a spatially closed homogeneous and isotropic early Universe whose matter content are radiation and dust perfect fluids. We then show that an expanding classical Universe can emerge from an oscillating (with complex scale factor) quantum Universe without singularity. Furthermore, the Universe obtained in this process has no horizon or flatness problems.
Energy Technology Data Exchange (ETDEWEB)
Lakhno, V. D., E-mail: lak@impb.psn.ru [Russian Academy of Sciences, Institute of Mathematical Problems of Biology (Russian Federation)
2013-06-15
A physical interpretation of translation-invariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipolaron energy E({eta}) with E(0) = -0.440636{alpha}{sup 2}, where {alpha} is a constant of electron-phonon coupling, {eta} is a parameter of ion binding.
New insights into classical solutions of the local instability of the sandwich panels problem
Pozorska, Jolanta; Pozorski, Zbigniew
2016-06-01
The paper concerns the problem of local instability of thin facings of a sandwich panel. The classic analytical solutions are compared and examined. The Airy stress function is applied in the case of the state of plane stress and the state of plane strain. Wrinkling stress values are presented. The differences between the results obtained using the differential equations method and energy method are discussed. The relations between core strain energies are presented.
Acker, A.
Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.
SNO results and neutrino magnetic moment solution to the solar neutrino problem
Indian Academy of Sciences (India)
Debasish Majumdar
2002-01-01
We have analysed the solar neutrino data obtained from chlorine, gallium and Super-Kamiokande (SK) experiments (1258 days) and also the new results that came from Sudbury Neutrino Observatory (SNO) charge current (CC) and elastic scattering (ES) experiments considering that the solar neutrino deﬁcit is due to the interaction of neutrino transition magnetic moment with the solar magnetic ﬁeld. We have also analysed the moments of the spectrum of scattered electrons at SK. Another new feature in the analysis is that for the global analysis, we have replaced the spectrum by its centroid.
Problems using ratios of galaxy shape moments in requirements for weak lensing surveys
Israel, H.; Kitching, T. D.; Massey, R.; Cropper, M.
2017-01-01
Context. The shapes of galaxies are typically quantified by ratios of their quadrupole moments. Knowledge of these ratios (i.e. their measured standard deviation) is commonly used to assess the efficiency of weak gravitational lensing surveys. For faint galaxies, observational noise can make the denominator close to zero, so the ratios become ill-defined. Aims: Since the requirements cannot be formally tested for faint galaxies, we explore two complementary mitigation strategies. In many weak lensing contexts, the most problematic sources can be removed by a cut in measured size. This first technique is applied frequently. As our second strategy, we propose requirements directly on the quadrupole moments rather than their ratio. Methods: As an example of the first strategy, we have investigated how a size cut affects the required precision of the charge transfer inefficiency model for two shape measurement settings. For the second strategy, we analysed the joint likelihood distribution of the image quadrupole moments measured from simulated galaxies, and propagate their (correlated) uncertainties into ellipticities. Results: Using a size cut, we find slightly wider tolerance margins for the charge transfer inefficiency parameters compared to the full size distribution. However, subtle biases in the data analysis chain may be introduced. These can be avoided using the second strategy. To optimally exploit a Stage-IV dark energy survey, we find that the mean and standard deviation of a population of galaxies' quadrupole moments must to be known to better than 1.4 × 10-3 arcsec2, or the Stokes parameters to 1.9 × 10-3 arcsec2. Conclusions: Cuts in measured size remove sources that otherwise make ellipticity statistics of weak lensing galaxy samples diverge. However, size cuts bias the source population non-trivially. Assessing weak lensing data quality directly on the quadrupole moments instead mitigates the need for size cuts. Such testable requirements can form
Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
Oltean, Marius; Bonetti, Luca; Spallicci, Alessandro D. A. M.; Sopuerta, Carlos F.
2016-09-01
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the nonexistence of entropy in the latter sense. We explicate, clarify, and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the noncompactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy production.
Linear problem of the shock wave disturbance in a non-classical case
Semenko, Evgeny V.
2017-06-01
A linear problem of the shock wave disturbance for a special (non-classical) case, where both pre-shock and post-shock flows are subsonic, is considered. The phase transition for the van der Waals gas is an example of this problem. Isentropic solutions are constructed. In addition, the stability of the problem is investigated and the known result is approved: the only neutral stability case occurs here. A strictly algebraic representation of the solution in the plane of the Fourier transform is obtained. This representation allows the solution to be studied both analytically and numerically. In this way, any solution can be decomposed into a sum of acoustic and vorticity waves and into a sum of initial (generated by initial perturbations), transmitted (through the shock) and reflected (from the shock) waves. Thus, the wave incidence/refraction/reflection is investigated. A principal difference of the refraction/reflection from the classical case is found, namely, the waves generated by initial pre-shock perturbations not only pass through the shock (i.e., generate post-shock transmitted waves) but also are reflected from it (i.e., generate pre-shock reflected waves). In turn, the waves generated by the initial post-shock perturbation are not only reflected from the shock (generate post-shock reflected waves) but also pass through it (generate pre-shock transmitted waves).
An Approach to Some Non-Classical Eigenvalue Problems of Structural Dynamics
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Sandi Horea
2015-12-01
Full Text Available Two main shortcomings of common formulations, encountered in the literature concerning the linear problems of structural dynamics are revealed: the implicit, not discussed, postulation, of the use of Kelvin – Voigt constitutive laws (which is often infirmed by experience and the calculation difficulties involved by the attempts to use other constitutive laws. In order to overcome these two categories of shortcomings, the use of the bilateral Laplace – Carson transformation is adopted. Instead of the dependence on time, t, of a certain function f (t, the dependence of its image f# (p on the complex parameter p = χ + iω (ω: circular frequency will occur. This leads to the formulation of associated non-classical eigenvalue problems. The basic relations satisfied by the eigenvalues λr#(p and the eigenvectors vr#(p of dynamic systems are examined (among other, the property of orthogonality of eigenvectors is replaced by the property of pseudo-orthogonality. The case of points p = p’, where multiple eigenvalues occur and where, as a rule, chains of principal vectors are to be considered, is discussed. An illustrative case, concerning a non-classical eigenvalue problem, is presented. Plots of variation along the ω axis, for the real and imaginary components of eigenvalues and eigenvectors, are presented. A brief final discussion closes the paper.
Classical universe emerging from quantum cosmology without horizon and flatness problems
Energy Technology Data Exchange (ETDEWEB)
Fathi, M.; Jalalzadeh, S. [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of); Moniz, P.V. [Centro de Matematica e Aplicacoes-UBI, Covilha (Portugal); Universidade da Beira Interior, Departmento de Fisica, Covilha (Portugal)
2016-10-15
We apply the complex de Broglie-Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007), Gozzi (Phys Lett B 165: 351, 1985), Bhalla et al. (Am J Phys 65: 1187, 1997) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems. (orig.)
A Heuristic and complete planner for the classical mover`s problem
Energy Technology Data Exchange (ETDEWEB)
Hwang, Yong K.; Chen, Pang C.
1995-03-01
We present a motion planner for the classical mover`s problem in three dimensions that is both resolution-complete and efficient in that it has performance commensurate with task difficulty. It is based on the SANDROS search strategy, which uses a hierarchical, multi-resolution representation of the configuration space along with a generate-and-test paradigm for solution paths. This planner can control the trade-offs between the computation resource and algorithmic completeness/solution path quality, and thus can fully utilize the available computing power. It is useful for navigation of mobile robots, submarines and spacecraft, or part motion feasibility in assembly planning.
Zhu, Jian; Wu, Qing-Ding; Wang, Ping; Li, Ke-Lin; Lei, Ming-Jing; Zhang, Wei-Li
2013-11-01
In order to fully understand adsorption nature of Cu2+, Zn2+, Pb2+, Cd2+, Mn2+, Fe3+ onto natural diatomite, and to find problems of classical isothermal adsorption models' application in liquid/solid system, a series of isothermal adsorption tests were conducted. As results indicate, the most suitable isotherm models for describing adsorption of Pb2+, Cd2+, Cu2+, Zn2+, Mn2+, Fe3+ onto natural diatomite are Tenkin, Tenkin, Langmuir, Tenkin, Freundlich and Freundlich, respectively, the adsorption of each ion onto natural diatomite is mainly a physical process, and the adsorption reaction is favorable. It also can be found that, when using classical isothermal adsorption models to fit the experimental data in liquid/solid system, the equilibrium adsorption amount q(e) is not a single function of ion equilibrium concentration c(e), while is a function of two variables, namely c(e) and the adsorbent concentration W0, q(e) only depends on c(e)/W(0). Results also show that the classical isothermal adsorption models have a significant adsorbent effect, and their parameter values are unstable, the simulation values of parameter differ greatly from the measured values, which is unhelpful for practical use. The tests prove that four-adsorption-components model can be used for describing adsorption behavior of single ion in nature diatomite-liquid system, its parameters k and q(m) have constant values, which is favorable for practical quantitative calculation in a given system.
Nassar, Antonio B; Miret-Artés, Salvador
2013-10-11
This Letter proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the dividing line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant that should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8×10(-15) m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i.e., τ(Bmax)=10(-26) s.
Disheveled Arnold’s cat and the problem of quantum-classic correspondence
Kuznetsov, S. P.
2000-03-01
Quantum Arnold’s cat map is studied for a case of perfect square inverse Planck’s constant, N = M2. The classic limit is analyzed on a subset of numbers N increasing as 4 k. The quantum problem in this case allows exact reduction to the classic cat map defined on a discrete lattice of size M × M and supplemented by evolution of a phase variable. A link between the classic periodic orbits and spectrum of eigenvalues of the quantum evolution operator is outlined. For M growing as 2 k genetic analysis is developed for periodic orbits, and they are classified by means of a tree-like graph. A phase shift, accumulated over a period of the orbits, evolves from level to level of the graph according to a certain rule, governed by non-periodic binary code. Representation of a localized Gaussian wave packet in a basis of eigenvectors of the evolution operator gives rise to a probability measure distributed on a unit circle, where the eigenvalues are located. This measure looks like spectrum of a finite-time sample of a stationary random process (periodogram): (1) majority of the eigenstates have intensities of comparable order of magnitude, (2) the spectral distribution is of locally random-like nature, i.e. statistical variance of the amplitudes has the same order as the amplitudes themselves. This combination of properties in very straightforward manner follows from chaotic nature of the classic map and is conjectured to be the most fundamental attribute of quantum chaos.
Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán
2016-07-01
We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation
Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain
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Wojciech Czernous
2014-01-01
Full Text Available We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain \\(\\Omega\\ with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of \\(\\partial\\Omega\\ with the property that if a characteristic trajectory has a point therein, then its every earlier point lies there as well. With local assumptions on coefficients and on the free term, we prove existence and Lipschitz dependence on data of classical solutions on \\((0,c\\times\\Omega\\ to the initial boundary value problem, for small \\(c\\. Regularity of solutions matches this domain, and the proof uses the Banach fixed-point theorem. Our general model of functional dependence covers problems with deviating arguments and integro-differential equations.
Comparison of classical and conductivity zones methods for solving EIT inverse problem
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I. O. Sushko
2012-10-01
Full Text Available Comparison of classical iteration imagine reconstruction method and conductivity zones method properties in EIT from the point of view of calculation organization, expecting precision and computational cost of imagine receiving is carried out. Reasonably small transfer resistances sensitivity to surface conductivity changes of separate finite element is shown. Small sensitivity is appeared for finite elements, which are situated in the central part of phantom, and also for finite elements, which are situated in the phantom outline. Small sensitivity is the cause of derivative matrix bad conditionality, that is aggravated with big matrix order. It led to quantity instability by solving of inverse problem (reconstruction problem. Conductivity zones method allows to avoid some difficulties: leads to derivative matrix order reduction, increasing of sensitivity and matrix conditionality. Transfer resistances and derivatives values for uniform phantom and for phantoms with different inhomogeneities for assessment are proposed.
On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type
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Gülden Gün Polat
2014-01-01
Full Text Available In this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y and g(y functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ-symmetry method, we analyze λ-symmetries for the case that λ-function is in the form of λ(x,y,y′=λ1(x,yy′+λ2(x,y. Finally, a classification problem for the conservation forms and invariant solutions are considered.
Using Graphics Processing Units to solve the classical N-body problem in physics and astrophysics
Spera, Mario
2014-01-01
Graphics Processing Units (GPUs) can speed up the numerical solution of various problems in astrophysics including the dynamical evolution of stellar systems; the performance gain can be more than a factor 100 compared to using a Central Processing Unit only. In this work I describe some strategies to speed up the classical N-body problem using GPUs. I show some features of the N-body code HiGPUs as template code. In this context, I also give some hints on the parallel implementation of a regularization method and I introduce the code HiGPUs-R. Although the main application of this work concerns astrophysics, some of the presented techniques are of general validity and can be applied to other branches of physics such as electrodynamics and QCD.
Spectral moments of polycyclic aromatic hydrocarbons. Solution of a kinetic problem.
Marković, Svetlana; Marković, Zoran; Engelbrecht, Johan P; McCrindle, Robert I
2002-01-01
The relationship between the rate of supercritical fluid extraction of polycyclic aromatic hydrocarbons (PAHs) from coal-tar pitch and some topological invariants are examined. The aim is to explain the appearance of a minimum value on the activation energy/molar mass curve of the PAHs. Rate constants are approximated using spectral moment expansion. It is shown that the size of the PAHs determines more than 95% of the extraction rate. Activation energy for the extraction of the PAHs was found to increase with increasing molar mass. The appearance of a minimum value on the activation energy/molar mass curve is the consequence of experimental difficulties resulting from the tendency of lower members of the PAHs to sublime.
Quinn, J. D.; Reed, P. M.; Keller, K.
2015-12-01
Recent multi-objective extensions of the classical shallow lake problem are useful for exploring the conceptual and computational challenges that emerge when managing irreversible water quality tipping points. Building on this work, we explore a four objective version of the lake problem where a hypothetical town derives economic benefits from polluting a nearby lake, but at the risk of irreversibly tipping the lake into a permanently polluted state. The trophic state of the lake exhibits non-linear threshold dynamics; below some critical phosphorus (P) threshold it is healthy and oligotrophic, but above this threshold it is irreversibly eutrophic. The town must decide how much P to discharge each year, a decision complicated by uncertainty in the natural P inflow to the lake. The shallow lake problem provides a conceptually rich set of dynamics, low computational demands, and a high level of mathematical difficulty. These properties maximize its value for benchmarking the relative merits and limitations of emerging decision support frameworks, such as Direct Policy Search (DPS). Here, we explore the use of DPS as a formal means of developing robust environmental pollution control rules that effectively account for deeply uncertain system states and conflicting objectives. The DPS reformulation of the shallow lake problem shows promise in formalizing pollution control triggers and signposts, while dramatically reducing the computational complexity of the multi-objective pollution control problem. More broadly, the insights from the DPS variant of the shallow lake problem formulated in this study bridge emerging work related to socio-ecological systems management, tipping points, robust decision making, and robust control.
Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
Oltean, Marius; Spallicci, Alessandro D A M; Sopuerta, Carlos F
2016-01-01
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy producti...
The convergence problem for dissipative autonomous systems classical methods and recent advances
Haraux, Alain
2015-01-01
The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywh...
Motion in classical field theories and the foundations of the self-force problem
Harte, Abraham I
2014-01-01
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally ...
Common problems in using, modifying, and reporting on classic measurement instruments.
Daltroy, L H
1997-12-01
Users of classic summated scales can clear up some common quandaries by considering the underlying assumptions that a scale's items represent a random sample drawn from an infinite pool of items representing a unidimensional domain. Scale reliability is higher with more items and a higher average correlation among items. Standards of reliability need to be higher when decisions about treatment are to be based on scores, because confidence intervals around individual scores expand quickly below alpha = 0.95. Scales that are longer than needed may sometimes be shortened, using a formula to determine the approximate number of questions that will yield the desired reliability. Reliability may be improved by addition of new items or expansion of response sets for existing items. Such alterations of scales should always be corroborated with new data. The use of coefficient alpha for scales with severely limited domains, such as self-care knowledge, is rarely useful or appropriate psychometrically, and can be misleading. Standard item selection procedures in classic scales maximize reliability at the scale center and overestimate change at the center and underestimate it at the ends; there are both classic and modern techniques to improve scale construction in this regard. The omission of specific items (such as symptoms) on many scales is often immaterial to the reliability of the scale and to the usefulness of the summary score; this is because each item is well correlated with other scale items, so that information about the underlying domain from any single item is redundant. Finally, despite the attractiveness of disease-specific scales, generic scales often do as well, even in arthritis populations, and have the added benefit of allowing comparisons with a wider range of disease and cultural groups. The development, modification, and use of classic summated scales can be complex in practice, calling on both statistical skills and content area judgment, but at heart
Včelař, František; Pátíková, Zuzana
2017-07-01
For the case of classical Tarski's theorem on fixed points of isotone maps we show that embedding of this statement into fuzzy logical environment leads to surprising results, which cannot be easily seen and awaited in classical logical environment.
Hao, Jie; Zhu, Jiang; Zhang, Peng; Xin, Si-Yuan; Qi, Dan-Dan; Hu, Ni-Juan; Lin, Chi; Wang, Pei; Zhao, Min-Yi; Hu, Shang-Qing; Wu, Gui-Wen
2015-04-01
In our previous paper, we analyzed "Deqi" in book Huangdi Neijing (The Yellow Emperor's Internal Classic) and Nanjing (Canon of Difficult Medical Problems) from "Zhishen"(Treating mentality) and Tiaoqi (Regulating qi). In the present paper, the authors discuss the connotations of "Deqi" and related events in the later ages of the abovementioned two classic books to the later stage of the Qing Dynasty when involves about 20 classical works as Zhenjiu Dacheng ( The Great Compendium of Acupuncture and Moxibustion), Zhenjing Zhinan (Guide to the classics of Acupuncture), Zhenjiu Daquan (A Complete Works of Acupuncture and Moxibustion) etc. from 1) close association between "Deqi" and patients' mental activity; 2) how to wait for arrival of qi if the needling does not induce "Deqi" for the time being; 3) how to identify "qi-arrival" and then, performing suitable manipulations; 4) Deqi and shallow- or deep-needling; 5) putting more emphasis on patients' feeling and reactions, rather than the practitioners perception beneath the needle which is described in book Huangdi Neijing; and 6) not withdrawing the acupuncture needles if qi does not arrive. Generally, in the later ages, the connotations of Deqi are enriched greatly.
Excitation of ship waves by a submerged object: new solution to the classical problem
Arzhannikov, Anrei V
2016-01-01
We have proposed a new method for solving the problem of ship waves excited on the surface of a non-viscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.
Directory of Open Access Journals (Sweden)
E. E. Grigorenko
2012-09-01
Full Text Available The problem of identification of the interface region between the lobe and the Plasma Sheet (PS – the Plasma Sheet Boundary Layer (PSBL – using ion moments and magnetic field data often arises in works devoted to statistical studies of various PSBL phenomena. Our experience in the identification of this region based on the analysis of ion velocity distribution functions demonstrated that plasma parameters, such as the ion density and bulk velocity, the plasma beta or the dynamic pressure vary widely depending on the state of magnetotail activity. For example, while field-aligned beams of accelerated ions are often observed propagating along the lobeward edge of the PSBL there are times when no signatures of these beams could be observed. In the last case, a spacecraft moving from the lobe region to the PS registers almost isotropic PS-like ion velocity distribution. Such events may be classified as observations of the outer PS region. In this paper, we attempt to identify ion parameter ranges or their combinations that result in a clear distinction between the lobe, the PSBL and the adjacent PS or the outer PS regions. For this we used 100 crossings of the lobe-PSBL-PS regions by Cluster spacecraft (s/c made in different periods of magnetotail activity. By eye inspection of the ion distribution functions we first identify and separate the lobe, the PSBL and the adjacent PS or outer PS regions and then perform a statistical study of plasma and magnetic field parameters in these regions. We found that the best results in the identification of the lobe-PSBL boundary are reached when one uses plasma moments, namely the ion bulk velocity and density calculated not for the entire energy range, but for the energies higher than 2 keV. In addition, we demonstrate that in many cases the plasma beta fails to correctly identify and separate the PSBL and the adjacent PS or the outer PS regions.
Moment-to-Moment Emotions during Reading
Graesser, Arthur C.; D'Mello, Sidney
2012-01-01
Moment-to-moment emotions are affective states that dynamically change during reading and potentially influence comprehension. Researchers have recently identified these emotions and the emotion trajectories in reading, tutoring, and problem solving. The primary learning-centered emotions are boredom, frustration, confusion, flow (engagement),…
The problem of psychophysical agency in the classical Sāṃkhya and Yoga perspective
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Marzenna JAKUBCZAK
2015-06-01
Full Text Available The paper discusses the issue of psychophysical agency in the context of Indian philosophy, focusing on the oldest preserved texts of the classical tradition of Sāṃkhya-Yoga. The author raises three major questions: What is action in terms of Sāṃkhyakārikā (ca. fifth century CE and Yogasūtra (ca. third century CE? Whose action is it, or what makes one an agent? What is a right and morally good action? The first part of the paper reconsiders a general idea of action — including actions that are deliberately done and those that ‘merely’ happen — identified by Patañjali and Ῑśvarakṛṣṇa as a permanent change or transformation (pariṇāma determined by the universal principle of causation (satkārya. Then, a threefold categorization of actions according to their causes is presented, i.e. internal agency (ādhyātmika, external agency (ādhibhautika and ‘divine’ agency (ādhidaivika. The second part of the paper undertakes the problem of the agent’s autonomy and the doer’s psychophysical integrity. The main issues that are exposed in this context include the relationship between an agent and the agent’s capacity for perception and cognition, as well as the crucial Sāṃkhya-Yoga distinction between ‘a doer’ and ‘the self ’. The agent’s self-awareness and his or her moral self-esteem are also briefly examined. Moreover, the efficiency of action in present and future is discussed (i.e. karman, karmāśaya, saṃskāra, vāsanā, along with the criteria of a right act accomplished through meditative insight (samādhi and moral discipline (yama.
Quantization of the Maxwell fish-eye problem and the quantum-classical correspondence
Makowski, A. J.; Górska, K. J.
2009-05-01
The so-called fish-eye model, originally investigated by Maxwell in geometrical optics, is studied both in the classical as well as in the quantum formulations. The best agreement between the two approaches is achieved by using a suitably constructed coherent state, which is of the SU(2) type. The perfect quantum-classical correspondence is obtained in the sense that classical rays go exactly over maxima of the corresponding quantum probability distributions. The distributions are made of linear combinations of the E=0 bound states of the considered model.
Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
Kol, Barak
2009-01-01
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the non-relativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a non-linear classical field theory coupled to point-like sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain non-linear world-line vertices, and we classify all the possible topologies of irreducible ...
Energy Technology Data Exchange (ETDEWEB)
Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V. [National Academy of Sciences of the Republic of Armenia, Institute for Informatics and Automation Problems (Armenia)
2017-03-15
We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.
Sazonov, Vas. V.; Sazonov, V. V.
2011-04-01
A new mathematical model of the uncontrolled rotational motion of the Foton satellite is presented. The model is based on the Euler dynamic equations of rigid body motion and takes into account the action upon the satellite of four external mechanical moments: gravitational, restoring aerodynamic, moment with constant components in the satellite-fixed coordinate system, and moment arising due to interaction of the Earth's magnetic field with the satellite's proper magnetic moment. To calculate the aerodynamic moment a special geometrical model of the outer satellite shell is used. Detailed form of the formulas giving above-mentioned moments in the equations of satellite motion is agreed with the form of the considered motion. Model testing is performed by determining with its help the rotational motion of the Foton M-2 satellite (it was in orbit from May 31, 2005 to June 16, 2005) using the data of the onboard measurements of the Earth's magnetic field strength. The use of the new model has led to a relatively small improvement in the accuracy of the motion determination, but allowed us to obtain physically real estimates of some parameters.
Torubarova, Tatyana V.
2016-01-01
Classic modern European philosophy explicate, reflect; leaving own history in fundamental metaphysical position, where the existence is understood as conscience. This position is representative in the process of historic development, transition of philosophical thought from R. Dekart to G. Hegel. It appears exactly the field of key metaphysical…
Dressing the post-Newtonian two-body problem and classical effective field theory
Kol, Barak; Smolkin, Michael
2009-12-01
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling post-Newtonian (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain nonlinear worldline vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a nonrelativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.
Space languages: Solving the classic scheduling problem in Ada and Lisp
Davis, Stephen; Hays, Dan; Wolfsberger, John W.
1988-01-01
The comparison of programming languages is best seen while evaluating similar systems. The strengths and weaknesses of both languages were investigated as the scheduler was being implemented. Some features used in both languages shall be object-oriented paradigms, parallel programming, search and production heuristics, and other classical artificial intelligence implementations.
Moment inference from tomograms
Day-Lewis, F. D.; Chen, Y.; Singha, K.
2007-01-01
Time-lapse geophysical tomography can provide valuable qualitative insights into hydrologic transport phenomena associated with aquifer dynamics, tracer experiments, and engineered remediation. Increasingly, tomograms are used to infer the spatial and/or temporal moments of solute plumes; these moments provide quantitative information about transport processes (e.g., advection, dispersion, and rate-limited mass transfer) and controlling parameters (e.g., permeability, dispersivity, and rate coefficients). The reliability of moments calculated from tomograms is, however, poorly understood because classic approaches to image appraisal (e.g., the model resolution matrix) are not directly applicable to moment inference. Here, we present a semi-analytical approach to construct a moment resolution matrix based on (1) the classic model resolution matrix and (2) image reconstruction from orthogonal moments. Numerical results for radar and electrical-resistivity imaging of solute plumes demonstrate that moment values calculated from tomograms depend strongly on plume location within the tomogram, survey geometry, regularization criteria, and measurement error. Copyright 2007 by the American Geophysical Union.
Institute of Scientific and Technical Information of China (English)
2000-01-01
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.
Niemi, Antti
2011-06-03
We perform finite element analysis of the so called Girkmann problem in structural mechanics. The problem involves an axially symmetric spherical shell stiffened with a foot ring and is approached (1) by using the axisymmetric formulation of linear elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used in the second approach. We study the convergence behaviour of the different numerical models and show that accurate stress resultants can be obtained with both models by using effective post-processing formulas. © Springer-Verlag London Limited 2011.
Taxonomic Review of Classical and Current Literature on the Perennial American Family Forest Problem
Directory of Open Access Journals (Sweden)
Thomas J. Straka
2011-08-01
Full Text Available One of the fundamental issues in American forest policy has been the small forest ownership problem. Early in the twentieth century, it was called the farm forestry problem, later, the nonindustrial private forest problem, and today, the family forest problem. Family forest owners are thought to manage their lands in a suboptimal manner resulting in low forest productivity relative to other ownership groups. This can lead to future timber supply problems. The exact nature of the problem, especially its social and economic basis, was a common subject of early forestry research studies. This article includes many of the major nonindustrial private forest or family forest studies, from early to current, and classifies them both by themes used by other authors and categories that relate to major research areas in the current literature. A major focus of this literature deals with promoting management on family forest holdings and possible land management incentives and disincentives. Natural trends in family forest ownership, like parcelization, also impact upon forest management opportunities. By developing a taxonomy that classifies these studies by research objective, methodology, owner motivation, and problem definition, this article serves to organize the family forest literature in a manner that provides a temporal framework for better understanding the historical motivation for and development of family forest research in the United States.
Computational complexity of classical problems for hereditary clique-helly graphs
Flavia Bonomo; Guillermo Durán
2004-01-01
A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of them can be deduced easily by known results. We prove that the clique-covering problem remains NP-comp...
Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.
Gannon, Gerald E.; Martelli, Mario U.
2001-01-01
Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)
Solved problems in classical mechanics analytical and numerical solutions with comments
de Lange, O L
2010-01-01
Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...
Paul R. Reed; Carol J. Cumber
2000-01-01
In October, 1996 Private Moments, an adult novelty store, opened for business in Huntsville, Texas. Huntsville had no ordinances in place to prevent the opening of this type of business. In fact, the local Small Business Development Center provided guidance and assistance to Edward Delagarza, the founder and owner of Private Moments. Many of the Huntsville citizens, unhappy with the opening of Private Moments, approached the City Council requesting that it be closed immediately and asked for ...
Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem
Diacu, Florin
2016-11-01
We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of new classes of orbits. In particular, we find some families of isosceles triangles, which occur in elliptic space.
Acker, A.
We give an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity μ >0 is embedded in a closed irrotational flow inside a closed, convex vessel in ℜ 2. The unknown boundary of the vortex core is a closed curve Γ along which (v+)^2-(v^-)^2=Λ , where v+ and v- denote, respectively, the exterior and interior flow-speeds along Γ and Λ is a given constant. Our existence results all apply to the natural multidimensional mathematical generalization of the above problem. The present existence theorems are the only ones available for the Prandtl-Batchelor problem for Λ >0, because (a) the author's prior existence treatment was restricted to the case where Λ <0, and because (b) there is no analytical existence theory available for this problem in the non-convex case, regardless of the sign of Λ .
Quantum learning of classical stochastic processes: The completely positive realization problem
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Monràs, Alex [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Winter, Andreas [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys, 23, 08010 Barcelona (Spain)
2016-01-15
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine
Torrielli, Alessandro
2016-08-01
We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand-Levitan-Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.
Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
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R. J. Moitsheki
2012-01-01
Full Text Available We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure
LaFave, Tim
2014-01-01
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\\le 100$ electrons into discrete geometries of neighboring $N-1$ systems. These non-uniformities yield electron energy pairs, intra-subshell pattern similarities with empirical ionization energy, and a salient pattern that coincides with size-normalized empirical ionization energies. Spatial symmetry limitations on discrete charges constrained to a spherical volume are conjectured as underlying physical mechanisms responsible for shell-filling patterns in atomic electronic structure and the Periodic Law.
Energy Technology Data Exchange (ETDEWEB)
Bottcher, C.; Strayer, M.R. [Oak Ridge National Lab., TN (United States); Werby, M.F. [Naval Research Lab. Detachment, Stennis Space Center, MS (United States)
1993-10-01
The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWE`s. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can by obtained in matrix form be expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways to long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented.
The problem of the motion of bodies a historical view of the development of classical mechanics
Capecchi, Danilo
2014-01-01
This book focuses on the way in which the problem of the motion of bodies has been viewed and approached over the course of human history. It is not another traditional history of mechanics but rather aims to enable the reader to fully understand the deeper ideas that inspired men, first in attempting to understand the mechanisms of motion and then in formulating theories with predictive as well as explanatory value. Given this objective, certain parts of the history of mechanics are neglected, such as fluid mechanics, statics, and astronomy after Newton. On the other hand, due attention is paid, for example, to the history of thermodynamics, which has its own particular point of view on motion. Inspired in part by historical epistemology, the book examines the various views and theories of a given historical period (synchronic analysis) and then makes comparisons between different periods (diachronic analysis). In each period, one or two of the most meaningful contributions are selected for particular attent...
Rivera, R.; Villarroel, D.
1997-11-01
An exactly solvable two-body problem dealing with the Lorentz-Dirac equation is constructed in this paper. It corresponds to the motion of two identical charges rotating at opposite ends of a diameter, in a fixed circle, at constant angular velocity. The external electromagnetic field that allows this motion consists of a tangential time-independent electric field with a fixed value over the orbit circle, and a homogeneous time-independent magnetic field that points orthogonally to the orbit plane. Because of the geometrical symmetries of the charges' motion, in this case it is possible to obtain the rate of radiation emitted by the charges directly from the equation of motion. The rate of radiation is also calculated by studying the energy flux across a sphere of a very large radius, using the far retarded fields of the charges. Both calculations lead to the same result, in agreement with energy conservation.
Stability of the classical type of relative equilibria of a rigid body in the J2 problem
Wang, Yue
2013-01-01
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variationa...
A Study of Three Intrinsic Problems of the Classic Discrete Element Method Using Flat-Joint Model
Wu, Shunchuan; Xu, Xueliang
2016-05-01
Discrete element methods have been proven to offer a new avenue for obtaining the mechanics of geo-materials. The standard bonded-particle model (BPM), a classic discrete element method, has been applied to a wide range of problems related to rock and soil. However, three intrinsic problems are associated with using the standard BPM: (1) an unrealistically low unconfined compressive strength to tensile strength (UCS/TS) ratio, (2) an excessively low internal friction angle, and (3) a linear strength envelope, i.e., a low Hoek-Brown (HB) strength parameter m i . After summarizing the underlying reasons of these problems through analyzing previous researchers' work, flat-joint model (FJM) is used to calibrate Jinping marble and is found to closely match its macro-properties. A parametric study is carried out to systematically evaluate the micro-parameters' effect on these three macro-properties. The results indicate that (1) the UCS/TS ratio increases with the increasing average coordination number (CN) and bond cohesion to tensile strength ratio, but it first decreases and then increases with the increasing crack density (CD); (2) the HB strength parameter m i has positive relationships to the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle, but a negative relationship to the average coordination number (CN); (3) the internal friction angle increases as the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle increase; (4) the residual friction angle has little effect on these three macro-properties and mainly influences post-peak behavior. Finally, a new calibration procedure is developed, which not only addresses these three problems, but also considers the post-peak behavior.
Institute of Scientific and Technical Information of China (English)
吴化璋; 乔云
2005-01-01
An intrinsic one-to-one correspondence between solutions to the multiple Nevanlinna-Pick interpolation problems in five function classes and solutions to their associated standard/nonstandard truncated power moment problems is established.The method is based on the so-called Hankel vector approach.%建立了在五个函数类中Nevanlinna-Pick插值问题的解与相关的幂矩量问题的解之间明确的一一对应关系,所用的方法是Hankel向量方法.
Knoll, Yehonatan
2011-01-01
In a recent paper by the present author ("Scale covariant physics: a 'quantum deformation' of classical electrodynamics", J. Phys. A 2010), using a novel mathematical construction, the formalism of extended charge dynamics (ECD) was presented. In that Lorentz and scale covariant framework, charges are represented by localized conserved currents, while the electromagnetic field is the classical Maxwellian field. Despite this seemingly classical setting, and the reduction of ECD to classical electrodynamics in the latter's domain of validity, it is shown in the present paper that ensembles of ECD solutions could, in principle, reproduce the statistical predictions of quantum mechanics. Exclusively quantum mechanical concepts, such as interference, violations of Bell's inequalities, spin and even photons (despite the use of a classical EM field), all emerge as mere statistical manifestations of the self interaction of ECD charges. Moreover, ECD is not merely an interpretation of relativistic quantum mechanics, b...
Ou, Yaobin
2017-01-01
The vacuum free boundary problem of one-dimensional non-isentropic compressible Navier-Stokes equations with large initial data is investigated in this paper. The fluid is initially assumed to occupy a finite interval and connect to the vacuum continuously at the free boundary, which is often considered in the gas-vacuum interface problem. Using the method of Lagrangian particle path, we derive some point-wise estimates and weighted spatial and time energy estimates for the classical solutions. Then the global existence and uniqueness of classical solutions are shown, and the expanding speed for the free boundary is proved to be finite. The main difficulty of this problem is the degeneracy of the system near the free boundary. Previous results are only for the solutions with low regularity (cf. [G. Q. Chen and M. Kratka, Commun. Partial Differ. Equations. 27 907-943 (2002)]).
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
Henner, Victor; Belozerova, Tatyana
2015-01-01
Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used but the validity of reduction of a quantum problem to a classical problem should be justified. In this paper we formulate the correspondence principle, which shows that the classical equations of motion for a system of dipole interacting spins have identical form with the quantum equations. The classical simulations based on the correspondence principle for spin systems provide a practical tool to study different macroscopic spin physics phenomena. Three classical magnetic resonance problems in solids are considered as examples - free induction decay (FID), spin echo and the Pake doublet.
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Chubykalo, Andrew; Espinoza, Augusto; Flores, Rolando Alvarado; Rodriguez, Alejandro Gutierrez [Universidad Autonoma de Zacatecas (Mexico). Unidad Academica de Fisica
2011-07-01
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called V-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light C and the other one (irrotational) with an arbitrary finite velocity V (including a velocity more than C). We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously. We provide a theoretical rationale (within the framework of classical electrodynamics) of a series of well-known recent experiments, which detected superluminal signals. Finally, we affirm that applying the Helmholtz theorem to classical electrodynamics allows to conclude that in classical electrodynamics so called instantaneous action at a distance with the infinite velocity of interaction can take place as well as (within the framework of the v-gauge-theory) the superluminal action with a finite velocity of interaction. (author)
Quantum computing classical physics.
Meyer, David A
2002-03-15
In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.
Directory of Open Access Journals (Sweden)
Adriana C. Briozzo
2006-02-01
Full Text Available We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.
Directory of Open Access Journals (Sweden)
Urbański Piotr
2015-11-01
Full Text Available The present article is a close reading of the libretto of the first opera (drama musicale staged in the Netherlands, in Brussels in 1650. The main point of interest is Ascanio Amalteo’s transformation or even breakaway from the classical tradition (esp. Homer and Ovid to create a work with its own message, quite distant from classical texts but, paradoxically, approaching moral and psychological categories in Neo-Stoic mode. Perhaps it is not by chance that a parallel piece, Calderon’s second play on Circe (after the fiesta entitled El mayor encanto, amor, 1635, i.e. the auto sacramentale entitled Los encantos de la culpa (ca. 1650, is also a significant transformation of the motive done in the spirit of the Counter-Reformation. Both plays are the last allegorical interpretations of Circe myth and for the next two-hundred years the last important literary works about Ulysses.
Liubarskiĭ, G Iu
2006-01-01
The sequence of classic paradigms in taxonomy that partly replaced each other and partly co-exist is given as follows: the theory of "organ and organism similarity", the naturalistic theory, the descriptive theory, and the phylogenetic theory. The naturalistic classics accepted the notion of "the plan of creation". The rejection of appealing to this plan brought forth certain problems in the formulation of the purpose of taxonomy; these problems were differently solved by the descriptive and the phylogenetic classic traditions. The difficulties of the current paradigms arising from the loss of a "strong purpose", a problem to be solved by taxonomists that is to be clear and interesting to a wide range of non-professionals. The paradox of formalization led to the losing of content of the methods due to their formalization. To attract attention to taxonomy, a new "image of the results" of its work that would be interesting to the non-professionals is necessary. The co-existence of different methods of reseach applied to different groups of facts leads to the loss of integrity of the research. It is not only that the taxon becomes a hypothesis and such hypotheses multiply. The comparison of these hypotheses is problematic, because each of them is supported by its own independent scope of facts. Because of the existence of a fundamental meronotaxonomic discrepancy, taxonomic systems based on different groups of characters appear to be incomparable, being rather systems of characters than systems of taxa. Systems of characters are not directly comparable with each other; they can be compared only through appealing to taxa, but taxa themselves exist only in the form of a number of hypotheses. Consequently, each separate taxonomic approach creates its own nature, its own subject of research. Therefore, it is necessary to describe the subject of research correctly (and indicate the purpose of research), as well as to distinguish clearly between results achieved through
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Gonzalez Gonzalez, A.; Rubayo Soneira, J.; Portuondo Campa, E.
2001-07-01
In this work the use of numerical methods in the solution of physics academic problems is discussed, particularly those on classical mechanics. Frequently the solution of academic problems is limited to finding a differential equation which is left unsolved for having no analytical solution. However, by means of numerical methods we can solve these equations and enrich the physical analysis of the problem. This approach also makes the academic process a little closer to modern physical research, where numerical methods have increasingly been used in almost every field. In the present paper we discuss a classical mechanics problem using these methods. We start from both Newton's and Lagrange's formulations and apply different numerical algorithms in the solution of the obtained equations. During last academic semester, recently concluded, we tested the ideas of this work with students of Nuclear Physics career of the Higher Institute of Nuclear Sciences and technologies, at Havana, cuba. The results were encouraging. (Author) 7 refs.
Davis, J.C.
2000-01-01
Geologists may feel that geological data are not amenable to statistical analysis, or at best require specialized approaches such as nonparametric statistics and geostatistics. However, there are many circumstances, particularly in systematic studies conducted for environmental or regulatory purposes, where traditional parametric statistical procedures can be beneficial. An example is the application of analysis of variance to data collected in an annual program of measuring groundwater levels in Kansas. Influences such as well conditions, operator effects, and use of the water can be assessed and wells that yield less reliable measurements can be identified. Such statistical studies have resulted in yearly improvements in the quality and reliability of the collected hydrologic data. Similar benefits may be achieved in other geological studies by the appropriate use of classical statistical tools.
Learning for Classical Planning
Chrpa, Lukáš
2009-01-01
This thesis is mainly about classical planning for articial intelligence (AI). In planning, we deal with searching for a sequence of actions that changes the environment from a given initial state to a goal state. Planning problems in general are ones of the hardest problems not only in the area of AI, but in the whole computer science. Even though classical planning problems do not consider many aspects from the real world, their complexity reaches EXPSPACE-completeness. Nevertheless, there ...
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Nelson Maculan
2003-01-01
Full Text Available We present integer linear models with a polynomial number of variables and constraints for combinatorial optimization problems in graphs: optimum elementary cycles, optimum elementary paths and optimum tree problems.Apresentamos modelos lineares inteiros com um número polinomial de variáveis e restrições para problemas de otimização combinatória em grafos: ciclos elementares ótimos, caminhos elementares ótimos e problemas em árvores ótimas.
Qin, Hong
2016-10-01
Many of the classical particle-field systems in (neutral and nonneutral) plasma physics and accelerator physics become unstable when the system parameters vary. How do these instabilities happen? It turns out, very interestingly, that all conservative systems become unstable by the same mechanism, i.e, the resonance between a positive- and a negative-action modes. And this is the only route that a stable system can become unstable. In this talk, I will use several examples in plasma physics and accelerator physics with finite and infinite degrees of freedom to illustrate the basic physical picture and the rigorous theoretical structure of the process. The features at the transition between stable and unstable regions in the parameter space are the fundamental characteristics of the underlying real Hamiltonian system and complex G-Hamiltonian system. The resonance between a positive- and a negative-action modes at the transition is the Krein collision well-known to mathematicians. Research supported by the U.S. Department of Energy (DE-AC02-09CH11466).
Calogero, Francesco
2001-01-01
This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
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Mark S. Hoddle
2014-12-01
Full Text Available Advances in scientific disciplines that support classical biological control have provided “new tools” that could have important applications for biocontrol programs for some long-established invasive arthropod pests. We suggest that these previously unavailable tools should be used in biological control programs targeting “legacy pests”, even if they have been targets of previously unsuccessful biocontrol projects. Examples of “new tools” include molecular analyses to verify species identities and likely geographic area of origin, climate matching and ecological niche modeling, preservation of natural enemy genetic diversity in quarantine, the use of theory from invasion biology to maximize establishment likelihoods for natural enemies, and improved understanding of the interactions between natural enemy and target pest microbiomes. This review suggests that opportunities exist for revisiting old pest problems and funding research programs using “new tools” for developing biological control programs for “legacy pests” could provide permanent suppression of some seemingly intractable pest problems. As a case study, we use citricola scale, Coccus pseudomagnoliarum, an invasive legacy pest of California citrus, to demonstrate the potential of new tools to support a new classical biological control program targeting this insect.
Hoddle, Mark S; Warner, Keith; Steggall, John; Jetter, Karen M
2014-12-23
Advances in scientific disciplines that support classical biological control have provided "new tools" that could have important applications for biocontrol programs for some long-established invasive arthropod pests. We suggest that these previously unavailable tools should be used in biological control programs targeting "legacy pests", even if they have been targets of previously unsuccessful biocontrol projects. Examples of "new tools" include molecular analyses to verify species identities and likely geographic area of origin, climate matching and ecological niche modeling, preservation of natural enemy genetic diversity in quarantine, the use of theory from invasion biology to maximize establishment likelihoods for natural enemies, and improved understanding of the interactions between natural enemy and target pest microbiomes. This review suggests that opportunities exist for revisiting old pest problems and funding research programs using "new tools" for developing biological control programs for "legacy pests" could provide permanent suppression of some seemingly intractable pest problems. As a case study, we use citricola scale, Coccus pseudomagnoliarum, an invasive legacy pest of California citrus, to demonstrate the potential of new tools to support a new classical biological control program targeting this insect.
What classicality? Decoherence and Bohr's classical concepts
Schlosshauer, Maximilian
2010-01-01
Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum and signifies a break with the Copenhagen interpretation-for example, that classical concepts do not need to be assumed but can be derived? In this paper we'll try to shine some light down the murky waters where formalism and philosophy cohabitate. To begin, we'll clarify the notion of classicality in the decoherence description. We'll then discuss Bohr's and Heisenberg's take on the quantum-classical problem and reflect on different meanings of the terms "classicality" and "classical concepts" in the writings of Bohr and his followers. This analysis will allow us to put forward some tentative suggestions for how we may better understand the relation between decoherence-induced classical...
DEFF Research Database (Denmark)
Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter
1995-01-01
The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...
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Costella, J.P.; McKellar, B.H.J.; Rawlinson, A.A.
1997-03-01
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain. (authors). 13 refs., 1 tab.
Costella, J P; Rawlinson, A A; Costella, John P.; Kellar, Bruce H. J. Mc; Rawlinson, Andrew A.
1997-01-01
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain.
Mineev, V. P.
2009-01-01
The roton excitation in the superfluid He-4 does not possess a stationary dipole moment. However, a roton has an instantaneous dipole moment, such that at any given moment one can find it in the state either with positive or with negative dipole moment projection on its momentum direction. The instantaneous value of electric dipole moment of roton excitation is evaluated. The result is in reasonable agreement with recent experimental observation of the splitting of microwave resonance absorpt...
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Italo Paolini
2008-12-01
Full Text Available It is known that the transition from the inpatient to the outpatient setting is a critical time. Evidence suggests that contact between patients and providers (i.e., physicians, nurse practitioners, and physician assistants during this interval may be crucial for appropriate treatment modifications and recognition of errors in treatment. Ambulatory follow-up provides opportunities for clinical assessment, patient education, and medication review, which may in turn improve outcomes. However, little is known about the appropriate timing and type of follow-up that is necessary following hospitalization for AMI. In Italian System of Heath contact between general pratictioner and specialists, after dicharge, is critical moment for management of chronic pharmacological and non pharmacological therapy. If professional approaches are not integrated can reduce patients compliance and effectiveness of therapies themselves. Good management of chronic cardiovascular disease requires attention to stenghtening the continuity of information and management of patients.
Clayman, Dee L.
1995-01-01
Appraises several databases devoted to classical literature. Thesaurus Linguae Graecae (TLG) contains the entire extant corpus of ancient Greek literature, including works on lexicography and historiography, extending into the 15th century. Other works awaiting completion are the Database of Classical Bibliography and a CD-ROM pictorial dictionary…
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Radiation reaction for multipole moments
Kazinski, P O
2006-01-01
We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.
Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
Barreto, Yadira; Verjovsky, Alberto
2013-01-01
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
Classical Trajectories and Quantum Spectra
Mielnik, Bogdan; Reyes, Marco A.
1996-01-01
A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.
Decoupling light and matter: permanent dipole moment induced collapse of Rabi oscillations
Baranov, Denis G; Krasnok, Alexander E
2016-01-01
Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two-level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects...
Muscle moment-arms: a key element in muscle-force estimation.
Ingram, David; Engelhardt, Christoph; Farron, Alain; Terrier, Alexandre; Müllhaupt, Philippe
2015-01-01
A clear and rigorous definition of muscle moment-arms in the context of musculoskeletal systems modelling is presented, using classical mechanics and screw theory. The definition provides an alternative to the tendon excursion method, which can lead to incorrect moment-arms if used inappropriately due to its dependency on the choice of joint coordinates. The definition of moment-arms, and the presented construction method, apply to musculoskeletal models in which the bones are modelled as rigid bodies, the joints are modelled as ideal mechanical joints and the muscles are modelled as massless, frictionless cables wrapping over the bony protrusions, approximated using geometric surfaces. In this context, the definition is independent of any coordinate choice. It is then used to solve a muscle-force estimation problem for a simple 2D conceptual model and compared with an incorrect application of the tendon excursion method. The relative errors between the two solutions vary between 0% and 100%.
Lectures on Classical Integrability
Torrielli, Alessandro
2016-01-01
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schroedinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel'fand-Levitan-Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.
Posterior moments computed by mixed integration
H.K. van Dijk (Herman); T. Kloek (Teun); C.G.E. Boender
1985-01-01
textabstractA flexible numerical integration method is proposed for the computation of moments of a multivariate posterior density with different tail properties in different directions. The method (called mixed integration) amounts to a combination of classical numerical integration and Monte Carlo
Harmonic moment dynamics in Laplacian growth.
Leshchiner, Alexander; Thrasher, Matthew; Mineev-Weinstein, Mark B; Swinney, Harry L
2010-01-01
Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem [S. Richardson, J. Fluid Mech. 56, 609 (1972)], so that all moments except the lowest one (the area of the bubble) are conserved in time. In our experiments, we directly determine the harmonic moments and show that for nonzero surface tension, all moments (except the lowest one) decay in time rather than exhibiting the divergences of other representations. Further, we derive an expression that relates the derivative of the k(th) harmonic moment M(k) to measurable quantities (surface tension, viscosity, the distance between the plates, and a line integral over the contour encompassing the growing bubble). The laboratory observations are in good accord with the expression we derive for dM(k)/dt , which is proportional to the surface tension; thus in the zero surface tension limit, the moments (above k=0) are all conserved, in accord with Richardson's theory. In addition, from the measurements of the time evolution of the harmonic moments we obtain a value for the surface tension that is within 20% of the accepted value. In conclusion, our analysis and laboratory observations demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust.
Some problems of classical electrodynamics
Ginzburg, I. F.
2011-12-01
In this lecture, I discuss issues that usually escape attention of students in electrodynamics. These are the questions of (1) what the photon observed in nature "looks like," (2) how an interference pattern arises from a source containing a lot of incoherently emitting atoms, and (3) how light "slows down" in a medium. Answers to these questions, if discussed at all, are scattered over various textbooks. Here, I follow our textbook [1].
Semi-classical Electrodynamics
Lestone, John
2016-03-01
Quantum electrodynamics is complex and its associated mathematics can appear overwhelming for those not trained in this field. We describe semi-classical approaches that can be used to obtain a more intuitive physical feel for several QED processes including electro-statics, Compton scattering, pair annihilation, the anomalous magnetic moment, and the Lamb shift, that could be taught easily to undergraduate students. Any physicist who brings their laptop to the talk will be able to build spread sheets in less than 10 minutes to calculate g/2 =1.001160 and a Lamb shift of 1057 MHz.
Alekseenko, Alexander; Euler, Craig
2016-05-01
We propose a Bhatnagar-Gross-Krook (BGK) kinetic model in which the collision frequency is a linear combination of polynomials in the velocity variable. The coefficients of the linear combination are determined so as to enforce proper relaxation rates for a selected group of moments. The relaxation rates are obtained by a direct numerical evaluation of the full Boltzmann collision operator. The model is conservative by construction. Simulations of the problem of spatially homogeneous relaxation of hard spheres gas show improvement in accuracy of controlled moments as compared to solutions obtained by the classical BGK, ellipsoidal-statistical BGK and the Shakhov models in cases of strong deviations from continuum.
Classical mechanics with Maxima
Timberlake, Todd Keene
2016-01-01
This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software.
Expert judgement combination using moment methods
Energy Technology Data Exchange (ETDEWEB)
Wisse, Bram [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom); TNO Defence, Security and Safety, The Hague (Netherlands)], E-mail: bram.wisse@strath.ac.uk; Bedford, Tim [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom)], E-mail: tim.bedford@strath.ac.uk; Quigley, John [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom)], E-mail: j.quigley@strath.ac.uk
2008-05-15
Moment methods have been employed in decision analysis, partly to avoid the computational burden that decision models involving continuous probability distributions can suffer from. In the Bayes linear (BL) methodology prior judgements about uncertain quantities are specified using expectation (rather than probability) as the fundamental notion. BL provides a strong foundation for moment methods, rooted in work of De Finetti and Goldstein. The main objective of this paper is to discuss in what way expert assessments of moments can be combined, in a non-Bayesian way, to construct a prior assessment. We show that the linear pool can be justified in an analogous but technically different way to linear pools for probability assessments, and that this linear pool has a very convenient property: a linear pool of experts' assessments of moments is coherent if each of the experts has given coherent assessments. To determine the weights of the linear pool we give a method of performance based weighting analogous to Cooke's classical model and explore its properties. Finally, we compare its performance with the classical model on data gathered in applications of the classical model.
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Balantekin, A. B.
2006-01-01
Current experimental and observational limits on the neutrino magnetic moment are reviewed. Implications of the recent results from the solar and reactor neutrino experiments for the value of the neutrino magnetic moment are discussed. It is shown that spin-flavor precession in the Sun is suppressed.
African Journals Online (AJOL)
Court of Law because there has emerged the professional called the lawyer who must speak .... The literary interview is a discourse that occupies the borderland .... rewriting should be understood as any changing of the pristine primal text into .... a moment of rewriting the Self But the resistance is also a moment of rewriting.
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...... algebras and of simple algebraic groups. The first section contains some background on equivariant cohomology....
Zamick, Larry
2012-01-01
We note that for a system of 2 nucleons in a stretched case (J=J1+J2) the magnetic moment of the combined system is the sum of the magnetic moments of the 2 constituents. In general there is no additive rule for g factors.
Energy Technology Data Exchange (ETDEWEB)
Michael Ramsey-Musolf; Wick Haxton; Ching-Pang Liu
2002-03-29
Nuclear anapole moments are parity-odd, time-reversal-even E1 moments of the electromagnetic current operator. Although the existence of this moment was recognized theoretically soon after the discovery of parity nonconservation (PNC), its experimental isolation was achieved only recently, when a new level of precision was reached in a measurement of the hyperfine dependence of atomic PNC in 133Cs. An important anapole moment bound in 205Tl also exists. In this paper, we present the details of the first calculation of these anapole moments in the framework commonly used in other studies of hadronic PNC, a meson exchange potential that includes long-range pion exchange and enough degrees of freedom to describe the five independent S-P amplitudes induced by short-range interactions. The resulting contributions of pi-, rho-, and omega-exchange to the single-nucleon anapole moment, to parity admixtures in the nuclear ground state, and to PNC exchange currents are evaluated, using configuration-mixed shell-model wave functions. The experimental anapole moment constraints on the PNC meson-nucleon coupling constants are derived and compared with those from other tests of the hadronic weak interaction. While the bounds obtained from the anapole moment results are consistent with the broad ''reasonable ranges'' defined by theory, they are not in good agreement with the constraints from the other experiments. We explore possible explanations for the discrepancy and comment on the potential importance of new experiments.
Gallavotti, Giovanni
2012-01-01
This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066
Randomness: Quantum versus classical
Khrennikov, Andrei
2016-05-01
Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).
Boundary effects in welded steel moment connections
Lee, Kyoung-Hyeog
Unprecedented widespread failure of welded moment connections in steel frames caused by the 1994 Northridge and the 1995 Kobe earthquakes have alarmed the engineering communities throughout the world. Welded moment connections in steel frames have been traditionally designed by using the classical beam theory which leads to assumptions that the flanges transfer moment while the web connection primarily resists the shear force. However, this study shows that the magnitude and direction of the principal stresses in the connection region are better approximated by using truss analogy rather than the classical beam theory. Accordingly, both the bending moment and the shear force are transferred across the connection near the beam flanges through diagonal strut action. Thus, the beam flange region of the traditionally designed connection is overloaded. This conclusion explains, to a large extent, the recently observed steel moment connection failures. In this study, detailed finite element analyses were carried out for a representative beam-to-column subassemblage with fully welded connection. The stress distribution in the beam web and flanges in the vicinity of the connection were closely studied. The factors responsible for stress redistribution and concentration were identified by using fundamental principles of mechanics. It was concluded that peak resultant stresses can exceed the values used in simple design calculations by large margins. Using the finite element analysis results and the truss analogy to establish a realistic load path in the connection, a practical and more rational analysis and design procedure was developed. The proposed design procedure and the new connection details were successfully validated through cyclic load testing of a nearly full size specimen. The truss model represented the force transmission around the beam-to-column moment connection region very well. Results of the finite element analyses and the laboratory testing showed
Exact collisional moments for plasma fluid theories
Pfefferlé, D.; Hirvijoki, E.; Lingam, M.
2017-04-01
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.
Energy Technology Data Exchange (ETDEWEB)
Chang, D. (Northwestern Univ., Evanston, IL (USA). Dept. of Physics and Astronomy Fermi National Accelerator Lab., Batavia, IL (USA)); Senjanovic, G. (Zagreb Univ. (Yugoslavia). Dept. of Theoretical Physics)
1990-01-01
We review attempts to achieve a large neutrino magnetic moment ({mu}{sub {nu}} {le} 10{sup {minus}11}{mu}{sub B}), while keeping neutrino light or massless. The application to the solar neutrino puzzle is discussed. 24 refs.
DEFF Research Database (Denmark)
Swann, Andrew Francis; Madsen, Thomas Bruun
2012-01-01
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose secon......-torus symmetry in terms of tri-symplectic geometry of four-manifolds. (C) 2012 Elsevier Inc. All rights reserved....
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Dynamical systems in classical mechanics
Kozlov, V V
1995-01-01
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include… the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics
Bayesian analysis in moment inequality models
Liao, Yuan; 10.1214/09-AOS714
2010-01-01
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any $\\delta$-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region. We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.
Randomness: quantum versus classical
Khrennikov, Andrei
2015-01-01
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is elaboration of a consistent and commonly accepted interpretation of quantum state. Closely related problem is clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. The second part of this review is devoted to the information interpretation of quantum mechanics (QM) in the spirit of Zeilinger and Brukner (and QBism of Fuchs et al.) and physics in general (e.g., Wheeler's "it from bit") as well as digital philosophy of Chaitin (with historical coupling to ideas of Leibnitz). Finally, w...
Classical approach in quantum physics
Solov'ev, Evgeni A
2010-01-01
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\\acute{\\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semicla...
Neo-classical economics, institutional economics and improved fisheries management
van der Burg, Tsjalle
2000-01-01
According to neo-classical economists, taxes and individual transferable quotas (ITQs) are the most efficient measures for dealing with the problem of overfishing. Institutional economists, however, criticise neo-classical economists for neglecting political problems, enforcement problems and transa
Neo-classical economics, institutional economics and improved fisheries management
Burg, van der Tsjalle
2000-01-01
According to neo-classical economists, taxes and individual transferable quotas (ITQs) are the most efficient measures for dealing with the problem of overfishing. Institutional economists, however, criticise neo-classical economists for neglecting political problems, enforcement problems and transa
Greenwood, Donald T
1997-01-01
Graduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d'Alembert's principle and the idea of virtual work, Hamilton's equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends.
Pieters, Jurgen
2001-01-01
'Moments of Negotiation' offers the first book-length and indepth analysis of the New Historicist reading method, which the American Shakespeare-scolar Stephen Greenblatt introduced at the beginning of the 1980s. Ever since, Greenblatt has been hailed as the prime representative of this movement,
Higgins, Chris
2014-01-01
In "The Humanist Moment," Chris Higgins sets out to recover a tenable, living humanism, rejecting both the version vilified by the anti-humanists and the one sentimentalized by the reactionary nostalgists. Rescuing humanism from such polemics is only the first step, as we find at least nine rival, contemporary definitions of humanism.…
Pieters, Jurgen
2001-01-01
'Moments of Negotiation' offers the first book-length and indepth analysis of the New Historicist reading method, which the American Shakespeare-scolar Stephen Greenblatt introduced at the beginning of the 1980s. Ever since, Greenblatt has been hailed as the prime representative of this movement, wh
Classroom Ready Teaching Moments
Whalen, D. Joel; Coker, Kesha K.
2017-01-01
This article features thumbnail descriptions of 26 "Teaching Moments" presented at the Society for Marketing Advances 2016 Annual Conference. A wide variety of marketing education interventions are presented, from games that teach marketing fundamentals and enhance faculty effectiveness when counseling students, to visualizing data, and…
The computation of first order moments on junction trees
Djuric, Milos B; Stankovic, Miomir S
2012-01-01
We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this way, the problem is solved using the memory space of an order of the junction tree edge-set cardinality. After that, we consider two algorithms, Lauritzen-Nilsson algorithm, and Mau\\'a et al. algorithm, which computes the first order moments as the normalization problem in junction tree, using the memory space of an order of the junction tree leaf-set cardinality.
Strong Coupling and Classicalization
Dvali, Gia
2016-01-01
Classicalization is a phenomenon in which a theory prevents itself from entering into a strong-coupling regime, by redistributing the energy among many weakly-interacting soft quanta. In this way, the scattering process of some initial hard quanta splits into a large number of soft elementary processes. In short, the theory trades the strong coupling for a high-multiplicity of quanta. At very high energies, the outcome of such a scattering experiment is a production of soft states of high occupation number that are approximately classical. It is evident that black hole creation in particle collision at super-Planckian energies is a result of classicalization, but there is no a priory reason why this phenomenon must be limited to gravity. If the hierarchy problem is solved by classicalization, the LHC has a chance of detecting a tower of new resonances. The lowest-lying resonances must appear right at the strong coupling scale in form of short-lived elementary particles. The heavier members of the tower must b...
The approach of moments for polynomial equations
M. Laurent (Monique); P. Rostalski
2012-01-01
htmlabstractIn this chapter we present the moment based approach for computing all real solutions of a given system of polynomial equations. This approach builds upon a lifting method for constructing semidefinite relaxations of several nonconvex optimization problems, using sums of squares of
Energy Technology Data Exchange (ETDEWEB)
Peaucelle, Ch
2001-10-01
High-power linear accelerators are needed as driver for several projects (spallation neutron sources, hybrid system). This interest brings us to the question of dynamics of high intensity particle beam. Inside intense beam, particles are under non linear forces mainly due to space charge effects. In order to have less heavy and more realistic tools than classical simulation methods (particle-particle interactions, particle-core model), we consider a description of the evolution of a particle density from its statistical parameters, its moments. In a first part, a detailed analysis of the moment problems is shown in a simplified but non restrictive case. To begin with, we develop an original study based on orthogonal polynomial properties which allows us to consider one-dimension density moments. We can see that we obtain information about density from only few moments. Such an investigation is essential for a better understanding of moment significance. Then, we apply this description to two-dimension phase space, so that we can precisely estimate where particles are in this phase space. Finally, we enumerate difficulties met and deduce the limits of this method. The second part of this thesis, more experimental, presents the measurements of the beam characteristics of the accelerator GENEPI as a part of hybrid reactor program. Moreover, we show how these specifications yields to beam calibration and validation of theoretical calculations used to design GENEPI. (author)
Solar rotation gravitational moments
Directory of Open Access Journals (Sweden)
A. Ajabshirizadeh
2005-09-01
Full Text Available Gravitational multipole moments of the Sun are still poorly known. Theoretically, the difficulty is mainly due to the differential rotation for which the velocity rate varies both on the surface and with the depth. From an observational point of view, the multipole moments cannot be directly measured. However, recent progresses have been made proving the existence of a strong radial differential rotation in a thin layer near the solar surface (the leptocline. Applying the theory of rotating stars, we will first compute values of J2 and J4 taking into account the radial gradient of rotation, then we will compare these values with the existing ones, giving a more complete review. We will explain some astrophysical outcomes, mainly on the relativistic Post Newtonian parameters. Finally we will conclude by indicating how space experiments (balloon SDS flights, Golf NG, Beppi-Colombo, Gaia... will be essential to unambiguously determine these parameters.
Redefining the political moment
Directory of Open Access Journals (Sweden)
James Arvanitakis
2011-07-01
Full Text Available On 16 February 2003, more than half a million people gathered in Sydney, Australia, as part of a global anti-war protest aimed at stopping the impending invasion of Iraq by the then US Administration. It is difficult to estimate how many millions marched on the coordinated protest, but it was by far the largest mobilization of a generation. Walking and chanting on the streets of Sydney that day, it seemed that a political moment was upon us. In a culture that rarely embraces large scale activism, millions around Australian demanded to be heard. The message was clear: if you do not hear us, we would be willing to bring down a government. The invasion went ahead, however, with the then Australian government, under the leadership of John Howard, being one of the loudest and staunchest supporters of the Bush Administrations drive to war. Within 18 months, anti-war activists struggled to have a few hundred participants take part in anti-Iraq war rallies, and the Howard Government was comfortably re-elected for another term. The political moment had come and gone, with both social commentators and many members of the public looking for a reason. While the conservative media was often the focus of analysis, this paper argues that in a time of late capitalism, the political moment is hollowed out by ‘Politics’ itself. That is to say, that formal political processes (or ‘Politics’ undermine the political practices that people participate in everyday (or ‘politics’. Drawing on an ongoing research project focusing on democracy and young people, I discuss how the concept of ’politics‘ has been destabilised and subsequently, the political moment has been displaced. This displacement has led to a re-definition of ‘political action’ and, I argue, the emergence of a different type of everyday politics.
Electrodynamics classical inconsistencies
De Souza, M M
1995-01-01
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world line but that gives a non null contribution on its world line. The self-field stress tensor of a point classical electron is integrable, there is no causality violation and no conflict with energy conservation in its equation of motion, and there is no need of any kind of renormalization nor of any change in the Maxwell's theory for this. (This is part of the paper hep-th/9510160, stripped , for simplicity, of its non-Minkowskian geometrization of causality and of its discussion about the physical meaning of the Maxwell-Faraday concept of field).
Computation in Classical Mechanics
Timberlake, Todd
2007-01-01
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.
Moment-to-moment dynamics of ADHD behaviour
Directory of Open Access Journals (Sweden)
Aase Heidi
2005-08-01
Full Text Available Abstract Background The behaviour of children with Attention-Deficit / Hyperactivity Disorder is often described as highly variable, in addition to being hyperactive, impulsive and inattentive. One reason might be that they do not acquire complete and functional sequences of behaviour. The dynamic developmental theory of ADHD proposes that reinforcement and extinction processes are inefficient because of hypofunctioning dopamine systems, resulting in a narrower time window for associating antecedent stimuli and behaviour with its consequences. One effect of this may be that the learning of behavioural sequences is delayed, and that only short behavioural sequences are acquired in ADHD. The present study investigated acquisition of response sequences in the behaviour of children with ADHD. Methods Fifteen boys with ADHD and thirteen boys without, all aged between 6–9 yr, completed a computerized task presented as a game with two squares on the screen. One square was associated with reinforcement. The task required responses by the computer mouse under reinforcement contingencies of variable interval schedules. Reinforcers were cartoon pictures and small trinkets. Measures related to response location (spatial dimension and to response timing (temporal dimension were analyzed by autocorrelations of consecutive responses across five lags. Acquired response sequences were defined as predictable responding shown by high explained variance. Results Children with ADHD acquired shorter response sequences than comparison children on the measures related to response location. None of the groups showed any predictability in response timing. Response sequencing on the measure related to the discriminative stimulus was highly related to parent scores on a rating scale for ADHD symptoms. Conclusion The findings suggest that children with ADHD have problems with learning long sequences of behaviour, particularly related to response location. Problems with
Moments, positive polynomials and their applications
Lasserre, Jean Bernard
2009-01-01
Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones,
Directory of Open Access Journals (Sweden)
Yekini Shehu
2010-01-01
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.
Moment searching algorithm for bioluminescence tomography
Institute of Scientific and Technical Information of China (English)
Ludong Jin; Yan Wu; Jie Tian; Heyu Huang; Xiaochao Qu
2009-01-01
To avoid the ill-posedness in the inverse problem of bioluminescence tomography, a moment searching algorithm fusing the finite element method (FEM) with the moment concept in theoretical mechanics is developed. In the algorithm, the source's information is mapped to the surface photon flux density by FEM, and the source's position is modified with the feedback through the algorithm of barycenter searching, which makes full use of the position information of the photon flux density on surface. The position is modified in every iterative step and will finally converge to the real source's value theoretically.
Seven Steps Towards the Classical World
Allori, Valia; Dürr, Detlef; Goldstein, Shelly; Zanghí, Nino
2001-01-01
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard Quantum Mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit be...
Distributions on unbounded moment spaces and random moment sequences
Nagel, Jan
2010-01-01
In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vectors correspond to the moments of the Marchenko-Pastur distribution and Wigner's semi-circle law.
Nuclear Schiff moment and soft vibrational modes
Zelevinsky, Vladimir; Auerbach, Naftali
2008-01-01
The atomic electric dipole moment (EDM) currently searched by a number of experimental groups requires that both parity and time-reversal invariance be violated. According to current theoretical understanding, the EDM is induced by the nuclear Schiff moment. The enhancement of the Schiff moment by the combination of static quadrupole and octupole deformation was predicted earlier. Here we study a further idea of the possible enhancement in the absence of static deformation but in a nuclear system with soft collective vibrations of two types. Both analytical approximation and numerical solution of the simplified problem confirm the presence of the enhancement. We discuss related aspects of nuclear structure which should be studied beyond mean-field and random phase approximations.
Feehan, Paul M. N.
2017-09-01
We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of
Paul Callaghan luminous moments
Callaghan, Paul
2013-01-01
Acknowledged internationally for his ground-breaking scientific research in the field of magnetic resonance, Sir Paul Callaghan was a scientist and visionary with a rare gift for promoting science to a wide audience. He was named New Zealander of the Year in 2011. His death in early 2012 robbed New Zealand of an inspirational leader. Paul Callaghan: Luminous Moments brings together some of his most significant writing. Whether he describes his childhood in Wanganui, reflects on discovering the beauty of science, sets out New Zealand's future potential or discusses the experience of fa
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C1 solution with small and decaying initial data.
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Directory of Open Access Journals (Sweden)
Marc eWittmann
2011-10-01
Full Text Available It has been suggested that perception and action can be understood as evolving in temporal epochs or sequential processing units. Successive events are fused into units forming a unitary experience or ‘psychological present’. Studies have identified several temporal integration levels on different time scales which are fundamental for our understanding of behaviour and subjective experience. In recent literature concerning the philosophy and neuroscience of consciousness these separate temporal processing levels are not always precisely distinguished. Therefore, empirical evidence from psychophysics and neuropsychology on these distinct temporal processing levels is presented and discussed within philosophical conceptualizations of time experience. On an elementary level, one can identify a functional moment, a basic temporal building block of perception in the range of milliseconds that defines simultaneity and succession. Below a certain threshold temporal order is not perceived, individual events are processed as co-temporal. On a second level, an experienced moment, which is based on temporal integration of up to a few seconds, has been reported in many qualitatively different experiments in perception and action. It has been suggested that this segmental processing mechanism creates temporal windows that provide a logistical basis for conscious representation and the experience of nowness. On a third level of integration, continuity of experience is enabled by working-memory in the range of multiple seconds allowing the maintenance of cognitive operations and emotional feelings, leading to mental presence, a temporal window of an individual’s experienced presence.
SELECTION MOMENTS AND GENERALIZED METHOD OF MOMENTS FOR HETEROSKEDASTIC MODELS
Directory of Open Access Journals (Sweden)
Constantin ANGHELACHE
2016-06-01
Full Text Available In this paper, the authors describe the selection methods for moments and the application of the generalized moments method for the heteroskedastic models. The utility of GMM estimators is found in the study of the financial market models. The selection criteria for moments are applied for the efficient estimation of GMM for univariate time series with martingale difference errors, similar to those studied so far by Kuersteiner.
Mandrà, Salvatore; Zhu, Zheng; Wang, Wenlong; Perdomo-Ortiz, Alejandro; Katzgraber, Helmut G.
2016-08-01
To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc. [V. S. Denchev et al., Phys. Rev. X 6, 031015 (2016), 10.1103/PhysRevX.6.031015] proposed a weak-strong cluster model tailored to have tall and narrow energy barriers separating local minima, with the aim to highlight the value of finite-range tunneling. More precisely, results from quantum Monte Carlo simulations as well as the D-Wave 2X quantum annealer scale considerably better than state-of-the-art simulated annealing simulations. Moreover, the D-Wave 2X quantum annealer is ˜108 times faster than simulated annealing on conventional computer hardware for problems with approximately 103 variables. Here, an overview of different sequential, nontailored, as well as specialized tailored algorithms on the Google instances is given. We show that the quantum speedup is limited to sequential approaches and study the typical complexity of the benchmark problems using insights from the study of spin glasses.
Energy-Sensitive and "Classical-like" Distances Between Quantum States
Dodonov, V V; Man'ko, V I; Wünsche, A
1998-01-01
We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.
Electron Spin or "Classically Non-Describable Two-Valuedness"
Giulini, Domenico
2007-01-01
In December 1924 Wolfgang Pauli proposed the idea of an inner degree of freedom of the electron, which he insisted should be thought of as genuinely quantum mechanical in nature. Shortly thereafter Ralph Kronig and, independently, Samuel Goudsmit and George Uhlenbeck took up a less radical stance by suggesting that this degree of freedom somehow corresponded to an inner rotational motion, though it was unclear from the very beginning how literal one was actually supposed to take this picture, since it was immediately recognised (already by Goudsmit and Uhlenbeck) that it would very likely lead to serious problems with Special Relativity if the model were to reproduce the electron's values for mass, charge, angular momentum, and magnetic moment. However, probably due to the then overwhelming impression that classical concepts were generally insufficient for the proper description of microscopic phenomena, a more detailed reasoning was never given. In this contribution I shall investigate in some detail what th...
Magnetic moment nonconservation in magnetohydrodynamic turbulence models.
Dalena, S; Greco, A; Rappazzo, A F; Mace, R L; Matthaeus, W H
2012-07-01
The fundamental assumptions of the adiabatic theory do not apply in the presence of sharp field gradients or in the presence of well-developed magnetohydrodynamic turbulence. For this reason, in such conditions the magnetic moment μ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width Δμ (defined as the half peak-to-peak difference in the particle magnetic moments) and the bounce frequency ω(b). We perform test-particle simulations to investigate magnetic moment behavior when resonance overlapping occurs and during the interaction of a ring-beam particle distribution with a broadband slab spectrum. We find that the changes of magnetic moment and changes of pitch angle are related when the level of magnetic fluctuations is low, δB/B(0) = (10(-3),10(-2)), where B(0) is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function f(α). This is a transient regime during which magnetic moment distribution f(μ) exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance grows linearly in time as in normal diffusion. With strong fluctuations f(α) becomes completely isotropic, spatial diffusion sets in, and the f(μ) behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
Population in the classic economics
Directory of Open Access Journals (Sweden)
Adnan Doğruyol
2013-02-01
Full Text Available Growth subject in economics is an important factor of development. Classic economics ecole indicates the population as main variable which tender of growth. On the other hand T. R. Malthus is known as economist who regards population as a problem and brings up it among the classical economists. However, Adam Smith is an intellectual who discussed population problem earlier on the classic economics theory. According to Adam Smith one of the main factors that realise the growth is labour. In addition to population made it established. The aim of this study is analyzing the mental relationship between Malthus whose name has been identified with relation between population-growth and Smith who discussed this subject first time but put it off on process of theorisation.
Moment Distributions of Phase Type
DEFF Research Database (Denmark)
Bladt, Mogens; Nielsen, Bo Friis
-type distributions. We construct representations for moment distributions based on a general matrix-exponential distribution which turns out to be a generalization of the moment distributions based on exponential distributions. For moment distributions based on phase{type distributions we find an appropriate...... alternative representation in terms of sub{intensity matrices. Finally we are able to nd explicit expressions for both the Lorenz curve and the Gini index....
Regularized Moment Equations and Shock Waves for Rarefied Granular Gas
Reddy, Lakshminarayana; Alam, Meheboob
2016-11-01
It is well-known that the shock structures predicted by extended hydrodynamic models are more accurate than the standard Navier-Stokes model in the rarefied regime, but they fail to predict continuous shock structures when the Mach number exceeds a critical value. Regularization or parabolization is one method to obtain smooth shock profiles at all Mach numbers. Following a Chapman-Enskog-like method, we have derived the "regularized" version 10-moment equations ("R10" moment equations) for inelastic hard-spheres. In order to show the advantage of R10 moment equations over standard 10-moment equations, the R10 moment equations have been employed to solve the Riemann problem of plane shock waves for both molecular and granular gases. The numerical results are compared between the 10-moment and R10-moment models and it is found that the 10-moment model fails to produce continuous shock structures beyond an upstream Mach number of 1 . 34 , while the R10-moment model predicts smooth shock profiles beyond the upstream Mach number of 1 . 34 . The density and granular temperature profiles are found to be asymmetric, with their maxima occurring within the shock-layer.
Institute of Scientific and Technical Information of China (English)
李胜利
2012-01-01
Judging internal and external orbital type of complexes by magnetic moment is a kind ofcommom titles in inorganic chemistry. At first, the number of unpaired electrons should be judged by magnetic moment, then based on the arrangement principle of extranuclear electrons, internal and external orbital type of complexes may be deduced, combined with the position of central atom （ion） in element periodic table.%通过磁矩判断配合物内外轨型是一类无机化学中的常见题目。首先通过磁矩推断出未成对电子数，然后根据核外电子的排布原则，结合中心原子（离子）在元素周期表中的位置，推断出配合物的内外轨型。
Minimum signals in classical physics
Institute of Scientific and Technical Information of China (English)
邓文基; 许基桓; 刘平
2003-01-01
The bandwidth theorem for Fourier analysis on any time-dependent classical signal is shown using the operator approach to quantum mechanics. Following discussions about squeezed states in quantum optics, the problem of minimum signals presented by a single quantity and its squeezing is proposed. It is generally proved that all such minimum signals, squeezed or not, must be real Gaussian functions of time.
Sociale problemer og sociale afvigelser - sociologisk set
DEFF Research Database (Denmark)
Henriksen, Lars Skov
2002-01-01
The arcticle presents central classical sociological theories of social problems and social deviance.......The arcticle presents central classical sociological theories of social problems and social deviance....
Classical approach in atomic physics
Solov'ev, E. A.
2011-12-01
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of a hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom discovered with the help of Poincaré section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treated as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well.
Classical approach in atomic physics
Energy Technology Data Exchange (ETDEWEB)
Solov' ev, E.A. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2011-12-15
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of a hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom discovered with the help of Poincare section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treated as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormalization group symmetry, criterion of accuracy and so on are reviewed as well. (author)
Mechanical Systems, Classical Models
Teodorescu, Petre P
2009-01-01
This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...
Grassmannization of classical models
Pollet, Lode; Prokof'ev, Nikolay V; Svistunov, Boris V
2016-01-01
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick's theorem, and (ii) the Dyson's collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (and correlations) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. A proof-of-principle implement...
Classical and quantum cosmology
Calcagni, Gianluca
2017-01-01
This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography...
Institute of Scientific and Technical Information of China (English)
黄海燕; 姚秀美; 朱海燕; 陈亚江
2016-01-01
Based on the Hamilton principle,a numerical algorithm associated with Lagrange multiplier method for the classical motion path problem is proposed. Different from traditional variational method,the present algorithm transforms the classical motion path problem into the conditional extremum problem with respect to the motion equation. By utilizing this algorithm,numerical solutions to motion path problems in one-dimensional gravitation potential and one-dimensional elastic potential are obtained and compared with the corresponding analytical results,respectively. Such two examples can be used as practical and interesting teaching cases for the relevant curriculums,e.g. Mechanics in college physics,Hamilton principle in theoretical mechanics and numerical calculation in computational mathematics. These examples are helpful for students to understand the Hamilton principle more deeply,and improve the ability of applying the knowledge in the fields of physics,mathematics, and computer science.%基于哈密顿原理，提出经典运动路径问题的拉格朗日乘数数值算法。与传统的变分方法不同，该算法将经典运动路径问题改写为关于路径方程的条件极值问题。利用该算法得到了一维重力势中的运动路径和一维弹性势中的运动路径的数值解，并与各自的解析解作了比较分析。这2个例子可以作为大学物理力学、理论力学哈密顿原理以及计算数学数值计算等相关课程内容实用教学案例，其有助于学生更深刻地理解哈密顿原理，提高综合应用物理、数学、计算机科学等知识的能力。
Fluid moments of the Landau collision operator
Hirvijoki, Eero; Pfefferlé, David; Comisso, Luca; Candy, Jeff; Bhattacharjee, Amitava
2016-01-01
One important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multi-dimensional Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to weakly collisional and strong flow regimes.
2002-01-01
Experiment IS358 uses the intense and pure beams of copper isotopes provided by the ISOLDE RILIS (resonance ionization laser ion source). The isotopes are implanted and oriented in the low temperature nuclear orientation set-up NICOLE. Magnetic moments are measured by $\\beta$-NMR. Copper (Z=29), with a single proton above the proton-magic nickel isotopes provides an ideal testground for precise shell model calculations of magnetic moments and their experimental verification. In the course of our experiments we already determined the magnetic moments of $^{67}$Ni, $^{67}$Cu, $^{68g}$Cu, $^{69}$Cu and $^{71}$Cu which provide important information on the magicity of the N=40 subshell closure. In 2001 we plan to conclude our systematic investigations by measuring the magnetic moment of the neutron-deficient isotope $^{59}$Cu. This will pave the way for a subsequent study of the magnetic moment of $^{57}$Cu with a complementary method.
Evaluating the TD model of classical conditioning.
Ludvig, Elliot A; Sutton, Richard S; Kehoe, E James
2012-09-01
The temporal-difference (TD) algorithm from reinforcement learning provides a simple method for incrementally learning predictions of upcoming events. Applied to classical conditioning, TD models suppose that animals learn a real-time prediction of the unconditioned stimulus (US) on the basis of all available conditioned stimuli (CSs). In the TD model, similar to other error-correction models, learning is driven by prediction errors--the difference between the change in US prediction and the actual US. With the TD model, however, learning occurs continuously from moment to moment and is not artificially constrained to occur in trials. Accordingly, a key feature of any TD model is the assumption about the representation of a CS on a moment-to-moment basis. Here, we evaluate the performance of the TD model with a heretofore unexplored range of classical conditioning tasks. To do so, we consider three stimulus representations that vary in their degree of temporal generalization and evaluate how the representation influences the performance of the TD model on these conditioning tasks.
Sytematics of dynamic moment of inertia in super-deformed bands in Mass ~150 region
Roy, S
2016-01-01
An empirical semi-classical model have been proposed to investigate the nature of dynamic moment-of-inertia , of the super-deformed (SD) bands in nuclei of mass 150 region. The model incorporates an additional frequency dependent distortion, to the dynamic moment-of-inertia term akin to a vibrational component to explain the extreme spin structure of these bands. Using this model two separate components to the dynamic moment of inertia, $\\Im^{(2)}$ have been identified for the SD band structure for the mass 150 region. Three distinct nature of the moment-of-inertia, also have been identified using the two parameter model.
Classical mechanics without determinism
Nikolic, H.
2005-01-01
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical interpretation is sufficient to predict all measurable results of classical mechanics. In the classical case, the wave function that satisfies a linear equation is positive, which is the main source of the fundamental difference between classical and quantum...
Three Moments in Jewish Philosophy
Directory of Open Access Journals (Sweden)
Stefan Goltzberg
2012-04-01
Full Text Available I would like to thank the following people for having proofread my text: Noémie Benchimol, Shemuel Lampronti and Georges-Elia Sarfati. The purpose of this article is to offer a new periodization of Jewish philosophy and to reflect on the definition of Jewish philosophy. It will therefore deal with the characteristic style of each Jewish philosophy rather than with their content. I shall identify three moments in the history of Jewish philosophy: the Arab moment, the German moment, and the an...
Adaptive Integral Method for Higher Order Method of Moments
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter
2008-01-01
The adaptive integral method (AIM) is combined with the higher order method of moments (MoM) to solve integral equations. The technique takes advantage of the low computational complexity and memory requirements of the AIM and the reduced number of unknowns and higher order convergence of higher...... order basis functions. The classical AIM is appropriately modified to allow larger discretization elements and, consequently, higher basis function expansion orders. Numerical examples based on the higher order hierarchical Legendre basis functions show the advantages of the proposed technique over...... the classical AIM based on low-order basis functions in terms of memory and computational time....
Classical Fields and the Quantum Concept
De Souza, M M
1996-01-01
We do a critical review of the Faraday-Maxwell concept of classical field and of its quantization process. With the hindsight knowledge of the essentially quantum character of the interactions, we use a naive classical model of field, based on exchange of classical massless particles, for a comparative and qualitative analysis of the physical content of the Coulomb's and Gauss's laws. It enlightens the physical meaning of a field singularity and of a static field. One can understand the problems on quantizing a classical field but not the hope of quantizing the gravitational field right from General Relativity.
Seven Steps Towards the Classical World
Allori, V; Goldstein, S; Zanghì, N; Allori, Valia; Goldstein, Shelly; Zangh\\'{\\i}, Nino
2001-01-01
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard Quantum Mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?
Face recognition using Krawtchouk moment
Indian Academy of Sciences (India)
J Sheeba Rani; D Devaraj
2012-08-01
Feature extraction is one of the important tasks in face recognition. Moments are widely used feature extractor due to their superior discriminatory power and geometrical invariance. Moments generally capture the global features of the image. This paper proposes Krawtchouk moment for feature extraction in face recognition system, which has the ability to extract local features from any region of interest. Krawtchouk moment is used to extract both local features and global features of the face. The extracted features are fused using summed normalized distance strategy. Nearest neighbour classiﬁer is employed to classify the faces. The proposed method is tested using ORL and Yale databases. Experimental results show that the proposed method is able to recognize images correctly, even if the images are corrupted with noise and possess change in facial expression and tilt.
Institute of Scientific and Technical Information of China (English)
Audrey
2008-01-01
@@ Chinese people would never for-get the moment-14:28, on May 12, 2008, as the 8.0-magnitude earthquake shook the whole of Sichuan; at that moment the world's at-tention was focused on the southwest of China - the homeland of the Giant Panda. This rare yet catastrophic natural disaster has resulted in the heavy loss of lives and property throughout the region.
Entanglement in Classical Optics
Ghose, Partha
2013-01-01
The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.
"Classical-ish": Negotiating the boundary between classical and quantum particles
Dreyfus, Benjamin W; Gupta, Ayush; Elby, Andrew
2015-01-01
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we examine video of a focus group completing a tutorial about the "particle in a box." In reasoning about the properties of a quantum particle, the students bring in elements of a classical particle ontology, evidenced by students' language and gestures. This reasoning, however, is modulated by metacognitive moments when the group explicitly considers whether classical intuitions apply to the quantum system. The students find some cases where they can usefully apply classical ideas to quantum physics, and others where they explicitly contrast classical and quantum mechanics. Negotiating this boundary with metacognitive awareness is part of the process of building quantum intuitions. Our data suggest that (some) students bring productive intellectual resources to this negotiation.
Computing moment-to-moment BOLD activation for real-time neurofeedback.
Hinds, Oliver; Ghosh, Satrajit; Thompson, Todd W; Yoo, Julie J; Whitfield-Gabrieli, Susan; Triantafyllou, Christina; Gabrieli, John D E
2011-01-01
Estimating moment-to-moment changes in blood oxygenation level dependent (BOLD) activation levels from functional magnetic resonance imaging (fMRI) data has applications for learned regulation of regional activation, brain state monitoring, and brain-machine interfaces. In each of these contexts, accurate estimation of the BOLD signal in as little time as possible is desired. This is a challenging problem due to the low signal-to-noise ratio of fMRI data. Previous methods for real-time fMRI analysis have either sacrificed the ability to compute moment-to-moment activation changes by averaging several acquisitions into a single activation estimate or have sacrificed accuracy by failing to account for prominent sources of noise in the fMRI signal. Here we present a new method for computing the amount of activation present in a single fMRI acquisition that separates moment-to-moment changes in the fMRI signal intensity attributable to neural sources from those due to noise, resulting in a feedback signal more reflective of neural activation. This method computes an incremental general linear model fit to the fMRI time series, which is used to calculate the expected signal intensity at each new acquisition. The difference between the measured intensity and the expected intensity is scaled by the variance of the estimator in order to transform this residual difference into a statistic. Both synthetic and real data were used to validate this method and compare it to the only other published real-time fMRI method. Copyright © 2010 Elsevier Inc. All rights reserved.
Moments of probable seas: statistical dynamics of Planet Ocean
Holloway, Greg
The ocean is too big. From the scale of planetary radius to scales of turbulent microstructure, the range of length scales is 109. Likewise for time scales. Classical geophysical fluid dynamics does not have an apparatus for dealing with such complexity, while `brute force' computing on the most powerful supercomputers, extant or presently foreseen, barely scratches this complexity. Yet the everywhere-swirling-churning ocean interacts unpredictably in climate history and climate future - against which we attempt to devise planetary stewardship. Can we better take into account the unpredictability of oceans to improve upon present ocean/climate forecasting? What to do? First, recognize that our goal is to comprehend probabilities of possible oceans. Questions we would ask are posed as moments (expectations). Then the dynamical goal is clear: we seek equations of motion of moments of probable oceans. Classical fluid mechanics offers part of the answer but fails to recognize statistical dynamical aspects (missing the arrow of time as past==>future). At probabilities of oceans, the missing physics emerges: moments are forced by gradients of entropy with respect to moments. Time regains its arrow, and first (simplest) approximations to entropy-gradient forces enhance the fidelity of ocean theories and practical models.
Quantum Models of Classical World
Directory of Open Access Journals (Sweden)
Petr Hájíček
2013-02-01
Full Text Available This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.
Inquiry-Based Science: Turning Teachable Moments into Learnable Moments
Haug, Berit S.
2014-02-01
This study examines how an inquiry-based approach to teaching and learning creates teachable moments that can foster conceptual understanding in students, and how teachers capitalize upon these moments. Six elementary school teachers were videotaped as they implemented an integrated inquiry-based science and literacy curriculum in their classrooms. In this curriculum, science inquiry implies that students search for evidence in order to make and revise explanations based on the evidence found and through critical and logical thinking. Furthermore, the curriculum material is designed to address science key concepts multiple times through multiple modalities (do it, say it, read it, write it). Two types of teachable moments were identified: planned and spontaneous. Results suggest that the consolidation phases of inquiry, when students reinforce new knowledge and connect their empirical findings to theory, can be considered as planned teachable moments. These are phases of inquiry during which the teacher should expect, and be prepared for, student utterances that create opportunities to further student learning. Spontaneous teachable moments are instances when the teacher must choose to either follow the pace of the curriculum or adapt to the students' need. One implication of the study is that more teacher support is required in terms of how to plan for and effectively utilize the consolidation phases of inquiry.
Performance of Object Classification Using Zernike Moment
Institute of Scientific and Technical Information of China (English)
Ariffuddin Joret; Mohammad Faiz Liew Abdullah; Muhammad Suhaimi Sulong; Asmarashid Ponniran; Siti Zuraidah Zainudin
2014-01-01
Moments have been used in all sorts of object classification systems based on image. There are lots of moments studied by many researchers in the area of object classification and one of the most preference moments is the Zernike moment. In this paper, the performance of object classification using the Zernike moment has been explored. The classifier based on neural networks has been used in this study. The results indicate the best performance in identifying the aggregate is at 91.4% with a ten orders of the Zernike moment. This encouraging result has shown that the Zernike moment is a suitable moment to be used as a feature of object classification systems.
Further analysis of the connected moments expansion
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo; Rodriguez, Martin [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M, E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar, E-mail: martinalexander.rv@gmail.com [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2011-12-16
By means of simple quantum-mechanical models we show that under certain conditions the main assumptions of the connected moments expansion (CMX) are no longer valid. In particular, we consider two-level systems: the harmonic oscillator and the pure quartic oscillator. Although derived from such simple models, we think that the results of this investigation may be of utility in future applications of the approach to realistic problems. We show that a straightforward analysis of the CMX exponential parameters may provide a clear indication of the success of the approach. (paper)
A Study of Moment Based Features on Handwritten Digit Recognition
Directory of Open Access Journals (Sweden)
Pawan Kumar Singh
2016-01-01
Full Text Available Handwritten digit recognition plays a significant role in many user authentication applications in the modern world. As the handwritten digits are not of the same size, thickness, style, and orientation, therefore, these challenges are to be faced to resolve this problem. A lot of work has been done for various non-Indic scripts particularly, in case of Roman, but, in case of Indic scripts, the research is limited. This paper presents a script invariant handwritten digit recognition system for identifying digits written in five popular scripts of Indian subcontinent, namely, Indo-Arabic, Bangla, Devanagari, Roman, and Telugu. A 130-element feature set which is basically a combination of six different types of moments, namely, geometric moment, moment invariant, affine moment invariant, Legendre moment, Zernike moment, and complex moment, has been estimated for each digit sample. Finally, the technique is evaluated on CMATER and MNIST databases using multiple classifiers and, after performing statistical significance tests, it is observed that Multilayer Perceptron (MLP classifier outperforms the others. Satisfactory recognition accuracies are attained for all the five mentioned scripts.
Lectures on classical differential geometry
Struik, Dirk J
1988-01-01
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ
Mathematical model of a moment-less arch.
Lewis, W J
2016-06-01
This paper presents a mathematical model for predicting the geometrical shapes of rigid, two-pin, moment-less arches of constant cross section. The advancement of this work lies in the inclusion of arch self-weight and the ability to produce moment-less arch forms for any span/rise ratio, and any ratio of uniformly distributed load per unit span, w, to uniformly distributed arch weight per unit arch length, q. The model is used to derive the shapes of two classical 'moment-less' arch forms: parabolic and catenary, prior to demonstrating a general case, not restricted by the unrealistic load assumptions (absence of q, in the case of a parabolic form, or no w, in the case of a catenary arch). Using the same value of span/rise ratio, and w/q>1, the behaviour of the moment-less and parabolic arches under permanent loading, (w+q), is analysed. Results show the former to be developing much lower stresses than its parabolic rival, even when there are relatively small differences in the two geometries; for a medium span/rise ratio of 4 and w/q=2, differences in the parabolic and moment-less arch geometries would, in practical terms, be viewed as insignificant, but the stresses in them are different.
Aniello, P.; Ciaglia, F. M.; Di Cosmo, F.; Marmo, G.; Pérez-Pardo, J. M.
2016-10-01
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator T with a suitable real-valued function T on the space of physical states. The proper characterization of the function T relies on a particular relation with the dynamical evolution of the system rather than with the infinitesimal generator of the dynamics (Hamiltonian). We first consider the case of classical hamiltonian mechanics, where observables are functions on phase space and the tools of differential geometry can be applied. The idea is then extended to the case of the unitary evolution of pure states of finite-level quantum systems by means of the geometric formulation of quantum mechanics. It is found that T is a function on the space of pure states which is not associated with any self-adjoint operator. The link between T and the dynamical evolution is interpreted as defining a simultaneity relation for the states of the system with respect to the dynamical evolution itself. It turns out that different dynamical evolutions lead to different notions of simultaneity, i.e., the notion of simultaneity is a dynamical notion.
Grassmannization of classical models
Pollet, Lode; Kiselev, Mikhail N.; Prokof'ev, Nikolay V.; Svistunov, Boris V.
2016-11-01
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick’s theorem, and (ii) Dyson’s collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (as well as all correlation functions) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. Our work paves the way for studying lattice gauge theories by treating bosonic and fermionic degrees of freedom on equal footing.
Classical, Semi-classical and Quantum Noise
Poor, H; Scully, Marlan
2012-01-01
David Middleton was a towering figure of 20th Century engineering and science and one of the founders of statistical communication theory. During the second World War, the young David Middleton, working with Van Fleck, devised the notion of the matched filter, which is the most basic method used for detecting signals in noise. Over the intervening six decades, the contributions of Middleton have become classics. This collection of essays by leading scientists, engineers and colleagues of David are in his honor and reflect the wide influence that he has had on many fields. Also included is the introduction by Middleton to his forthcoming book, which gives a wonderful view of the field of communication, its history and his own views on the field that he developed over the past 60 years. Focusing on classical noise modeling and applications, Classical, Semi-Classical and Quantum Noise includes coverage of statistical communication theory, non-stationary noise, molecular footprints, noise suppression, Quantum e...
Characterizing flow fluctuations with moments
Energy Technology Data Exchange (ETDEWEB)
Bhalerao, Rajeev S. [Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005 (India); Ollitrault, Jean-Yves, E-mail: jean-yves.ollitrault@cea.fr [CNRS, URA2306, IPhT, Institut de physique théorique de Saclay, F-91191 Gif-sur-Yvette (France); Pal, Subrata [Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 (India)
2015-03-06
We present a complete set of multiparticle correlation observables for ultrarelativistic heavy-ion collisions. These include moments of the distribution of the anisotropic flow in a single harmonic and also mixed moments, which contain the information on correlations between event planes of different harmonics. We explain how all these moments can be measured using just two symmetric subevents separated by a rapidity gap. This presents a multi-pronged probe of the physics of flow fluctuations. For instance, it allows to test the hypothesis that event-plane correlations are generated by non-linear hydrodynamic response. We illustrate the method with simulations of events in A MultiPhase Transport (AMPT) model.
Characterizing flow fluctuations with moments
Directory of Open Access Journals (Sweden)
Rajeev S. Bhalerao
2015-03-01
Full Text Available We present a complete set of multiparticle correlation observables for ultrarelativistic heavy-ion collisions. These include moments of the distribution of the anisotropic flow in a single harmonic and also mixed moments, which contain the information on correlations between event planes of different harmonics. We explain how all these moments can be measured using just two symmetric subevents separated by a rapidity gap. This presents a multi-pronged probe of the physics of flow fluctuations. For instance, it allows to test the hypothesis that event-plane correlations are generated by non-linear hydrodynamic response. We illustrate the method with simulations of events in A MultiPhase Transport (AMPT model.
Pannone, Marilena
2012-08-01
This paper shows how an exact analytical solution for the transient-state spatial moments of the cross-sectional average tracer concentration in large open channel flows can be derived from the depth-averaged advection-diffusion equation resorting to the method of Green's functions, without any simplifying assumption about the regularity of the actual concentration field, the smallness of the fluctuations, or the large space-time scale of variation of the average concentration gradient (justifying the a priori localization of the problem), which were the basis of the classic Taylor dispersion theory. The results reveal that in agreement with the findings by Aris (1956) and later by others for flows within a conduit, there are an initial centroid displacement and a variance deficit dependent on the specific position and dimension of the initial injection. The second central moment asymptotically tends to the linearly increasing function predictable on the basis of Taylor's classic theory, and the skewness, which is constantly zero for the cross-sectionally uniform injection, in the case of nonuniform initial distributions tends to slowly vanish after having reached a maximum. Thus, the persistent asymmetry exhibited by the field concentration data, as well as the retardations and the accelerations in the peak trajectory, can be justified without making any a priori assumption about the physical mechanism underlying their appearance, like transient storage phenomena, just by rigorously solving the governing equation for the cross-sectional average concentration in the presence of nonuniform, asymmetrically located solute injections.
Stochastic analysis of complex reaction networks using binomial moment equations.
Barzel, Baruch; Biham, Ofer
2012-09-01
The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Energy Technology Data Exchange (ETDEWEB)
Gursel, H.Y.
1983-01-01
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. Novikov, Vernon D. Sandberg and A.A. Starobinsky. In these papers the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole is described. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. It is concluded that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with multipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne. The first one shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second proves a conjecture by Kip S. Thorne: In the limit of ''slow'' motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. This conjecture is proved by giving an algorithm for generating rigidly rotating solutions of Einstein's equation from nonrotating, static solutions.
Neutron star moments of inertia
Ravenhall, D. G.; Pethick, C. J.
1994-01-01
An approximation for the moment of inertia of a neutron star in terms of only its mass and radius is presented, and insight into it is obtained by examining the behavior of the relativistic structural equations. The approximation is accurate to approximately 10% for a variety of nuclear equations of state, for all except very low mass stars. It is combined with information about the neutron-star crust to obtain a simple expression (again in terms only of mass and radius) for the fractional moment of inertia of the crust.
Method of moments in electromagnetics
Gibson, Walton C
2007-01-01
Responding to the need for a clear, up-to-date introduction to the field, The Method of Moments in Electromagnetics explores surface integral equations in electromagnetics and presents their numerical solution using the method of moments (MOM) technique. It provides the numerical implementation aspects at a nuts-and-bolts level while discussing integral equations and electromagnetic theory at a higher level. The author covers a range of topics in this area, from the initial underpinnings of the MOM to its current applications. He first reviews the frequency-domain electromagnetic theory and t
Improved moment scaling estimation for multifractal signals
Directory of Open Access Journals (Sweden)
D. Veneziano
2009-11-01
Full Text Available A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q of moments of different order q from data. Conventional estimators use the empirical moments μ^_{r}^{q}=⟨ | ε_{r}(τ|^{q}⟩ of wavelet coefficients ε_{r}(τ, where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages, whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtains K^(q as the slope of log( μ^_{r}^{q} against log(r over a range of r. Negative moments are sensitive to measurement noise and quantization. For them, one typically uses only the local maxima of | ε_{r}(τ| (modulus maxima methods. For the positive moments, we modify the standard estimator K^(q to significantly reduce its variance at the expense of a modest increase in the bias. This is done by separately estimating K(q from sub-records and averaging the results. For the negative moments, we show that the standard modulus maxima estimator is biased and, in the case of additive noise or quantization, is not applicable with wavelets of order 1 or higher. For these cases we propose alternative estimators. We also consider the fitting of parametric models of K(q and show how, by splitting the record into sub-records as indicated above, the accuracy of standard methods can be significantly improved.
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
Ahlfeld, R.; Belkouchi, B.; Montomoli, F.
2016-09-01
A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10
Divergences in classical theories at non-zero temperature
dr Aarts, G.A.P.T.; Nauta, B.J.; van Weert, C.G.
2000-01-01
The classical approximation provides a non-perturbative approach to time-dependent problems in finite temperature field theory. We study the divergences in hot classical field theory perturbatively. At one-loop, we show that the linear divergences are completely determined by the classical
Classical Corrections in String Cosmology
Brustein, Ram; Brustein, Ram; Madden, Richard
1999-01-01
An important element in a model of non-singular string cosmology is a phase in which classical corrections saturate the growth of curvature in a deSitter-like phase with a linearly growing dilaton (an `algebraic fixed point'). As the form of the classical corrections is not well known, here we look for evidence, based on a suggested symmetry of the action, scale factor duality and on conformal field theory considerations, that they can produce this saturation. It has previously been observed that imposing scale factor duality on the $O(\\alpha')$ corrections is not compatible with fixed point behavior. Here we present arguments that these problems persist to all orders in $\\alpha'$. We also present evidence for the form of a solution to the equations of motion using conformal perturbation theory, examine its implications for the form of the effective action and find novel fixed point structure.
Classical corrections in string cosmology
Brustein, Ram; Madden, Richard
1999-07-01
An important element in a model of non-singular string cosmology is a phase in which classical corrections saturate the growth of curvature in a deSitter-like phase with a linearly growing dilaton (an `algebraic fixed point'). As the form of the classical corrections is not well known, here we look for evidence, based on a suggested symmetry of the action, scale factor duality and on conformal field theory considerations, that they can produce this saturation. It has previously been observed that imposing scale factor duality on the O(alpha') corrections is not compatible with fixed point behavior. Here we present arguments that these problems persist to all orders in alpha'. We also present evidence for the form of a solution to the equations of motion using conformal perturbation theory, examine its implications for the form of the effective action and find novel fixed point structure.
Updating neutrino magnetic moment constraints
Canas, B C; Parada, A; Tortola, M; Valle, J W F
2015-01-01
In this paper we provide an updated analysis of the neutrino magnetic moments (NMMs), discussing both the constraints on the magnitudes of the three transition moments Lambda_i as well as the role of the CP violating phases present both in the mixing matrix and in the NMM matrix. The scattering of solar neutrinos off electrons in Borexino provides the most stringent restrictions, due to its robust statistics and the low energies observed, below 1 MeV. Our new limit on the effective neutrino magnetic moment which follows from the most recent Borexino data is 3.1 x 10^-11 mu_B at 90% C.L. This corresponds to the individual transition magnetic moment constraints: |Lambda_1| < 5.6 x10^-11 mu_B, |Lambda_2| < 4.0 x 10^-11 mu_B, and |Lambda_3| < 3.1 x 10^-11 mu_B (90% C.L.), irrespective of any complex phase. Indeed, the incoherent admixture of neutrino mass eigenstates present in the solar flux makes Borexino insensitive to the Majorana phases present in the NMM matrix. For this reason we also provide a gl...
Searching for electric dipole moments
Jungmann, Klaus
2013-01-01
Searches for a permanent Electric Dipole Moment (EDM) of a fundamental particle provide a wide window for the discovery of potential New Physics. Within todays Standard Model in particle physics the well established violation of CP symmetry gives rise to EDMs which are several orders of magnitude be
Measuring the Moment of Inertia
Lehmberg, George L.
1978-01-01
Two physics experiments are described, One, involving a laboratory cart accelerated along a level surface, examines the concept of inertial mass in translation and the other, using a solid cylinder, measures the moment of inertia of a wheel. Equations and illustrations are included. (MA)
Moment of Inertia by Differentiation
Rizcallah, Joseph A.
2015-01-01
The calculation of the moment of inertia of an extended body, as presented in standard introductory-level textbooks, involves the evaluation of a definite integral--an operation often not fully mastered by beginners, let alone the conceptual difficulties it presents, even to the advanced student, in understanding and setting up the integral in the…
Particle electric dipole-moments
Energy Technology Data Exchange (ETDEWEB)
Pendlebury, J.M. [Sussex Univ., Brighton (United Kingdom)
1997-04-01
The incentive to detect particle electric dipole-moments, as a window on time-reversal violation, remains undiminished. Efforts to improve the measurements for the neutron, the electron and some nuclei are still making rapid progress as more powerful experimental methods are brought to bear. A new measurement for the neutron at ILL is presented. (author). 7 refs.
Anomalous magnetic moment of anyons
Gat, G; Gat, Gil; Ray, Rashmi
1994-01-01
The anomalous magnetic moment of anyons is calculated to leading order in a 1/N expansion. It is shown that the gyromagnetic ratio g remains 2 to the leading order in 1/N. This result strongly supports that obtained in \\cite{poly}, namely that g=2 is in fact exact.
Quiet Moment around the Campfire
Centers for Disease Control (CDC) Podcasts
2014-06-18
Byron Breedlove reads his essay, "Quiet Moment around the Campfire," about the art of Frederic Remington and the transmission of pathogens as frontiers expand. Created: 6/18/2014 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 6/19/2014.
Moment Distributions of Phase Type
DEFF Research Database (Denmark)
Bladt, Mogens; Nielsen, Bo Friis
2011-01-01
Moment distributions of phase-type and matrix-exponential distributions are shown to remain within their respective classes. We provide a probabilistic phase-type representation for the former case and an alternative representation, with an analytically appealing form, for the latter. First order...
Updating neutrino magnetic moment constraints
Directory of Open Access Journals (Sweden)
B.C. Cañas
2016-02-01
Full Text Available In this paper we provide an updated analysis of the neutrino magnetic moments (NMMs, discussing both the constraints on the magnitudes of the three transition moments Λi and the role of the CP violating phases present both in the mixing matrix and in the NMM matrix. The scattering of solar neutrinos off electrons in Borexino provides the most stringent restrictions, due to its robust statistics and the low energies observed, below 1 MeV. Our new limit on the effective neutrino magnetic moment which follows from the most recent Borexino data is 3.1×10−11μB at 90% C.L. This corresponds to the individual transition magnetic moment constraints: |Λ1|≤5.6×10−11μB, |Λ2|≤4.0×10−11μB, and |Λ3|≤3.1×10−11μB (90% C.L., irrespective of any complex phase. Indeed, the incoherent admixture of neutrino mass eigenstates present in the solar flux makes Borexino insensitive to the Majorana phases present in the NMM matrix. For this reason we also provide a global analysis including the case of reactor and accelerator neutrino sources, presenting the resulting constraints for different values of the relevant CP phases. Improved reactor and accelerator neutrino experiments will be needed in order to underpin the full profile of the neutrino electromagnetic properties.
Unteachable Moments and Pedagogical Relationships
Wang, Hongyu
2016-01-01
This paper discusses how Julia Kristeva's theory can inform our understanding of unteachable moments. It proposes a pedagogical relationship that can contain breakdowns of meanings and work toward breakthroughs to new awareness, particularly related to social justice pedagogy in teacher education. First, one example from the author's own teaching…
Classical algebra its nature, origins, and uses
Cooke, Roger L
2008-01-01
This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more,...
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Effective potential for moment-method simulation of quantum devices
Kriman, A. M.; Zhou, J.-R.; Kluksdahl, N. C.; Choi, H. H.; Ferry, D. K.
1989-12-01
In the simulation of submicron devices, complete quantum descriptions can be extremely computationally intensive, and reduced descriptions are desirable. One such description utilizes a few low-order moments of the momentum distribution that are defined by the Wigner function. Two major difficulties occur in applying this moment method: (i) An independent calculation is required to find quantum mechanically accurate initial conditions. (ii) For a system in a mixed state, the hierarchy of time evolution equations for the moments does not close. We describe an approach to solve these problems. The initial distribution is determined in equilibrium by means of a new effective potential, chosen for its ability to treat the sharp potential features which occur in heterostructures. It accurately describes barrier penetration and repulsion, as well as quantum broadening of the momentum distribution. The moment equation hierarchy is closed at the level of the second-moment time evolution equation, using a closure that is exact for a shifted Fermi distribution. Band-bending is included by simultaneous self-consistent determination of all the moments.
Davidson and classical pragmatism
Directory of Open Access Journals (Sweden)
Paula Rossi
2007-06-01
Full Text Available In this paper I wish to trace some connections between Donald Davidson's work (1917-2003 and two major representatives of the classical pragmatist movement: Charles S. Peirce (1839-1914 and William James (1842-1910. I will start with a basic characterization of classical pragmatism; then, I shall examine certain conceptions in Peirce's and James' pragmatism, in order to establish affinities with Davidson´s thought. Finally, and bearing in mind the previous con-nections, I will reflect briefly on the relevance –often unrecognized- of classical pragmatist ideas in the context of contemporary philosophi-cal discussions.
Fermions from classical statistics
2010-01-01
We describe fermions in terms of a classical statistical ensemble. The states $\\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities $p_\\tau$ amounts to a rotation of the wave function $q_\\tau(t)=\\pm \\sqrt{p_\\tau(t)}$, we infer the unitary time evolution of a quantum system of fe...
Classical theory of electric and magnetic fields
Good, Roland H
1971-01-01
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
Classical dynamics of particles and systems
Marion, Jerry B
1965-01-01
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handl
On the Classical Limit of Quantum Mechanics
Allori, V; Allori, Valia; Zangh\\`{\\i}, Nino
2001-01-01
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\\h \\to 0$ asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
A Classical Introduction to Galois Theory
Newman, Stephen C
2012-01-01
This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematic
The Significances of the Translating of Chinese Classics
Institute of Scientific and Technical Information of China (English)
FU Feng
2014-01-01
The translating of Chinese classics plays an important role in the field of Chinese translation. Therefore, after reviewing the development of the translation of Chinese classics in China, this paper mainly explores the two major significances of the translating of Chinese classics. Despite some problems that exist, however, with corresponding measures, the translating of Chi-nese classics will absolutely have a bright future ahead in the field of China.
The dipole moment of the spin density as a local indicator for phase transitions
Schmitz, D.; Schmitz-Antoniak, C.; Warland, A.; Darbandi, M.; Haldar, S.; Bhandary, S.; Eriksson, O.; Sanyal, B.; Wende, H.
2014-07-01
The intra-atomic magnetic dipole moment - frequently called term - plays an important role in the determination of spin magnetic moments by x-ray absorption spectroscopy for systems with nonspherical spin density distributions. In this work, we present the dipole moment as a sensitive monitor to changes in the electronic structure in the vicinity of a phase transiton. In particular, we studied the dipole moment at the Fe2+ and Fe3+ sites of magnetite as an indicator for the Verwey transition by a combination of x-ray magnetic circular dichroism and density functional theory. Our experimental results prove that there exists a local change in the electronic structure at temperatures above the Verwey transition correlated to the known spin reorientation. Furthermore, it is shown that measurement of the dipole moment is a powerful tool to observe this transition in small magnetite nanoparticles for which it is usually screened by blocking effects in classical magnetometry.
The dipole moment of the spin density as a local indicator for phase transitions.
Schmitz, D; Schmitz-Antoniak, C; Warland, A; Darbandi, M; Haldar, S; Bhandary, S; Eriksson, O; Sanyal, B; Wende, H
2014-07-21
The intra-atomic magnetic dipole moment - frequently called ⟨Tz⟩ term - plays an important role in the determination of spin magnetic moments by x-ray absorption spectroscopy for systems with nonspherical spin density distributions. In this work, we present the dipole moment as a sensitive monitor to changes in the electronic structure in the vicinity of a phase transiton. In particular, we studied the dipole moment at the Fe(2+) and Fe(3+) sites of magnetite as an indicator for the Verwey transition by a combination of x-ray magnetic circular dichroism and density functional theory. Our experimental results prove that there exists a local change in the electronic structure at temperatures above the Verwey transition correlated to the known spin reorientation. Furthermore, it is shown that measurement of the dipole moment is a powerful tool to observe this transition in small magnetite nanoparticles for which it is usually screened by blocking effects in classical magnetometry.
NUMERICAL INVERSION OF MULTIDIMENSIONAL LAPLACE TRANSFORMS USING MOMENT METHODS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper develops a numerical method to invert multi-dimensional Laplace transforms. By a variable transform, Laplace transforms are converted to multi-dimensional Hausdorff moment problems so that the numerical solution can be achieved. Stability estimation is also obtained. Numerical simulations show the efficiency and practicality of the method.
Resonances and dipole moments in dielectric, magnetic, and magnetodielectric cylinders
DEFF Research Database (Denmark)
Dirksen, A.; Arslanagic, Samel; Breinbjerg, Olav
2011-01-01
An eigenfunction solution to the problem of plane wave scattering by dielectric, magnetic, and magnetodielectric cylinders is used for a systematic investigation of their resonances. An overview of the resonances with electric and magnetic dipole moments, needed in, e.g., the synthesis...... of metamaterials, is given with an emphasis on their strength, bandwidth, and isolation....
Advanced classical field theory
Giachetta, Giovanni; Sardanashvily, Gennadi
2009-01-01
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory
2007-01-01
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physic...
On Noncommutative Classical Mechanics
Djemai, A E F
2003-01-01
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \\cite{1}. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quantum Mechanics) and its possible relation with UV/IR mixing.
Kisil, Vladimir V.
2000-01-01
We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \\emph{do not} use any kind of semiclassic approximation or limiting procedures for $\\hbar \\to 0$. Harmonic oscillator considered within the approach. Keywords: Classic and quantum mechanics, Hamilton and Heisenberg equations, Poisson brackets, commutator, Heisenberg group.
Classical trajectories and quantum tunneling
Ivlev, B I
2003-01-01
The problem of inter-band tunneling in a semiconductor (Zener breakdown) in a nonstationary and homogeneous electric field is solved exactly. Using the exact analytical solution, the approximation based on classical trajectories is studied. A new mechanism of enhanced tunneling through static non-one-dimensional barriers is proposed in addition to well known normal tunneling solely described by a trajectory in imaginary time. Under certain conditions on the barrier shape and the particle energy, the probability of enhanced tunneling is not exponentially small even for non-transparent barriers, in contrast to the case of normal tunneling.
2006-01-01
One of the first events reconstructed in the Muon Drift Tubes, the Hadron Calorimeter and elements of the Silicon Tracker (TK) at 3 Tesla. The atmosphere in the CMS control rooms was electric. Everbody was at the helm for the first full-scale testing of the experiment. This was a crunch moment for the entire collaboration. On Tuesday, 22 August the magnet attained almost its nominal power of 4 Tesla! At the same moment, in a tiny improvised control room, the physicists were keyed up to test the entire detector system for the first time. The first cosmic ray tracks appeared on their screens in the week of 15 August. The tests are set to continue for several weeks more until the first CMS components are lowered into their final positions in the cavern.
Institute of Scientific and Technical Information of China (English)
周恒; 张涵信
2012-01-01
Turbulence has always been viewed as a century lasting difficult problem in classic physics, hence it is also viewed as a very important basic scientific problem. In this paper, starting from a brief review of the history of turbulence research, we analyze why there seems is a gap separating researches on homogeneous isotropic turbulence and researches on real turbulence, why the former did not make substantial contribution to solving problems of real turbulence, while the latter should be the main focus of the further basic research of turbulence, and how the real turbulence problem can be solved gradually. In conclusions, we list several points worth attention in the turbulence research.%一直以来,湍流都被认为是经典物理留下的世纪难题,因而也被认为是一个重大的基础科学问题.本文简单回顾湍流研究历史,分析了均匀各向同性湍流的研究和真实湍流的研究间为何存在鸿沟.为何前者不能解决真实湍流问题,而后者则是今后应重点开展的湍流基础研究,和如何逐步解决真实的湍流问题.在结论中提出了今后湍流研究中值得注意的几个方面.
Quantitative characterization of non-classic polarization of cations on clay aggregate stability.
Directory of Open Access Journals (Sweden)
Feinan Hu
Full Text Available Soil particle interactions are strongly influenced by the concentration, valence and ion species and the pH of the bulk solution, which will also affect aggregate stability and particle transport. In this study, we investigated clay aggregate stability in the presence of different alkali ions (Li+, Na+, K+, and Cs+ at concentrations from10-5 to 10-1 mol L-1. Strong specific ion effects on clay aggregate stability were observed, and showed the order Cs+>K+>Na+>Li+. We found that it was not the effects of ion size, hydration, and dispersion forces in the cation-surface interactions but strong non-classic polarization of adsorbed cations that resulted in these specific effects. In this study, the non-classic dipole moments of each cation species resulting from the non-classic polarization were estimated. By comparing non-classic dipole moments with classic values, the observed dipole moments of adsorbed cations were up to 104 times larger than the classic values for the same cation. The observed non-classic dipole moments sharply increased with decreasing electrolyte concentration. We conclude that strong non-classic polarization could significantly suppress the thickness of the diffuse layer, thereby weakening the electric field near the clay surface and resulting in improved clay aggregate stability. Even though we only demonstrated specific ion effects on aggregate stability with several alkali ions, our results indicate that these effects could be universally important in soil aggregate stability.
From geodesics of the multipole solutions to the perturbed Kepler problem
Hernandez-Pastora, J L; 10.1103/PhysRevD.82.104001
2010-01-01
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the Monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2$^4$-pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.
Efficient estimation of moments in linear mixed models
Wu, Ping; Zhu, Li-Xing; 10.3150/10-BEJ330
2012-01-01
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means. Generally, estimators may be obtained as solutions of estimating equations. It turns out that there may be several equations, each of them leading to consistent estimators, in which case finding the efficient estimator becomes a crucial problem. In this paper, we systematically study estimation of moments of the errors and random effects in linear mixed models.
Simulation of a Broadband Antenna with the Method of Moments
Directory of Open Access Journals (Sweden)
M. Czarnecki
2005-12-01
Full Text Available In the paper selected problems of computer simulations of abroadband antenna containing large metallic surfaces with the Method ofMoments have been discussed. A novel broadband combined spiral-disconeantenna, built of a complementary spiral and a cone has been analyzed.Since the antenna contains large metallic surfaces wire-grid models hadto be developed in order to simulate the antenna with the thin-wirekernel method of moments. Several wire-grid models of the antenna havebeen proposed and analyzed. The simulation results for input impedancehave been compared to those obtained from measurements and the bestmodel of the antenna has been identified.
Magnetic dipole moment estimates for an ancient lunar dynamo
Anderson, K. A.
1983-01-01
The four measured planetary magnetic moments combined with a recent theoretical prediction for dynamo magnetic fields suggests that no dynamo exists in the moon's interior today. For the moon to have had a magnetic moment in the past of sufficient strength to account for at least some of the lunar rock magnetism, the rotation would have been about twenty times faster than it is today and the radius of the fluid, conducting core must have been about 750 km. The argument depends on the validity of the Busse solution to the validity of the MHD problem of planetary dynamos.
Nuclear Quadrupole Moments and Nuclear Shell Structure
Townes, C. H.; Foley, H. M.; Low, W.
1950-06-23
Describes a simple model, based on nuclear shell considerations, which leads to the proper behavior of known nuclear quadrupole moments, although predictions of the magnitudes of some quadrupole moments are seriously in error.
Beam structures classical and advanced theories
Carrera, Erasmo; Petrolo, Marco
2011-01-01
Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for be
Wigner function statistics in classically chaotic systems
Horvat, M; Horvat, Martin; Prosen, Tomaz
2003-01-01
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int delta(w-W(x)) dx, which has, by definition, fixed first and second moment. In particular, we concentrate on relaxation of time evolving quantum state in terms of W(x), starting from a coherent state. We have shown that for a classically chaotic quantum counterpart the distribution P(w) in the semi-classical limit becomes a Gaussian distribution that is fully determined by the first two moments. Numerical simulations have been performed for the quantum sawtooth map and the quantized kicked top. In a quantum system with Hilbert space dimension N (similar 1/hbar) the transition of P(w) to a Gaussian distribution was observed at times t proportional to log N. In addition, it has been shown that the statistics of Wigner functions of propagator eigenstates is Gaussian as well in the...
Vortical sources of aerodynamic force and moment
Wu, J. Z.; Wu, J. M.
1989-01-01
It is shown that the aerodynamic force and moment can be expressed in terms of vorticity distribution (and entropy variation for compressible flow) on near wake plane, or in terms of boundary vorticity flux on the body surface. Thus the vortical sources of lift and drag are clearly identified, which is the real physical basis of optimal aerodynamic design. Moreover, these sources are highly compact, hence allowing one to concentrate on key local regions of the configuration, which have dominating effect to the lift and drag. A detail knowledge of the vortical low requires measuring or calculating the vorticity and dilatation field, which is however still a challenging task. Nevertheless, this type of formulation has some unique advantages; and how to set up a well-posed problem, in particular how to establish vorticity-dilatation boundary conditions, is addressed.
Classical mechanics of nonconservative systems.
Galley, Chad R
2013-04-26
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics. Thus, dissipative effects, for example, can be studied with new tools that may have applications in a variety of disciplines. The new formalism is demonstrated by two examples of nonconservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.
Energy Technology Data Exchange (ETDEWEB)
Vatankhah, Ramin; Salarieh, Hassan; Alasty, Aria [Sharif University of Technology, Tehran (Iran, Islamic Republic of); Najafi, Ali [Shiraz Branch, Islamic Azad University, Shiraz (Iran, Islamic Republic of)
2014-02-15
In non-classical micro-beams, the strain energy of the system is obtained based on the non-classical continuum mechanics. This paper presents the problem of boundary control of a vibrating non-classical micro-cantilever Timoshenko beam to achieve the asymptotic decay rate of the closed loop system. For this aim, we need to establish the well- posedness of the governing partial differential equations (PDEs) of motion in presence of boundary feedbacks. A linear control law is constructed to suppress the system vibration. The control forces and moments consist of feedbacks of the velocities and spatial derivatives of them at tip of the micro-beam. To verify the effectiveness of the proposed boundary controllers, numerical simulations of the open loop and closed loop PDE models of the system are worked out using finite element method (FEM). New Timoshenko beam element stiffness and mass matrices are derived based on the strain gradient theory and verification of this new beam element is accomplished.
Overuse injuries in classical ballet.
Khan, K; Brown, J; Way, S; Vass, N; Crichton, K; Alexander, R; Baxter, A; Butler, M; Wark, J
1995-05-01
Successful management of classical ballet dancers with overuse injuries requires an understanding of the art form, precise knowledge of anatomy and awareness of certain conditions. Turnout is the single most fundamental physical attribute in classical ballet and 'forcing turnout' frequently contributes to overuse injuries. Common presenting conditions arising from the foot and ankle include problems at the first metatarsophalangeal joint, second metatarsal stress fractures, flexor hallucis longus tendinitis and anterior and posterior ankle impingement syndromes. Persistent shin pain in dancers is often due to chronic compartment syndrome, stress fracture of the posteromedial or anterior tibia. Knee pain can arise from patellofemoral syndrome, patellar tendon insertional pathologies, or a combination of both. Hip and back problems are also prevalent in dancers. To speed injury recovery of dancers, it is important for the sports medicine team to cooperate fully. This permits the dancer to benefit from accurate diagnosis, technique correction where necessary, the full range of manual therapies to joint and soft tissue, appropriate strengthening programmes and maintenance of dance fitness during any time out of class with Pilates-based exercises and nutrition advice. Most overuse ballet conditions respond well to a combination of conservative therapies. Those dancers that do require surgical management still depend heavily on ballet-specific rehabilitation for a complete recovery.
Inference in partially identified models with many moment inequalities using Lasso
DEFF Research Database (Denmark)
Bugni, Federico A.; Caner, Mehmet; Kock, Anders Bredahl;
This paper considers the problem of inference in a partially identified moment (in)equality model with possibly many moment inequalities. Our contribution is to propose a novel two-step new inference method based on the combination of two ideas. On the one hand, our test statistic and critical va...
Metric of a Slow Rotating Body with Quadrupole Moment from the Erez-Rosen Metric
Frutos-Alfaro, Francisco; Cordero-García, Iván; Ulloa-Esquivel, Oscar
2012-01-01
A metric representing a slow rotating object with quadrupole moment is obtained using the Newman-Janis formalism to include rotation into the weak limit of the Erez-Rosen metric. This metric is intended to tackle relativistic astrometry and gravitational lensing problems in which a quadrupole moment has to be taken into account.
Raw and Central Moments of Binomial Random Variables via Stirling Numbers
Griffiths, Martin
2013-01-01
We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…
Defining moments in leadership character development.
Bleich, Michael R
2015-06-01
Critical moments in life define one's character and clarify true values. Reflective leadership is espoused as an important practice for transformational leaders. Professional development educators can help surface and explore defining moments, strengthen leadership behavior with defining moments as a catalyst for change, and create safe spaces for leaders to expand their leadership capacity.
On the interpretation of the support moment
Hof, AL
2000-01-01
It has been suggested by Winter (J. Biomech. 13 (1980) 923-927) that the 'support moment', the sum of the sagittal extension moments, shows less variability in walking than any of the joint moments separately. A simple model is put forward to explain this finding. It is proposed to reformulate the d
Driven topological systems in the classical limit
Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel
2017-03-01
Periodically driven quantum systems can exhibit topologically nontrivial behavior, even when their quasienergy bands have zero Chern numbers. Much work has been conducted on noninteracting quantum-mechanical models where this kind of behavior is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The noninteracting model, proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013), 10.1103/PhysRevX.3.031005], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time-dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.
Landsman, N P
2005-01-01
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit of a large system, and through decoherence and consistent histores. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain "...
Discrete Classical Electromagnetic Fields
De Souza, M M
1997-01-01
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
Lapped Block Image Analysis via the Method of Legendre Moments
Directory of Open Access Journals (Sweden)
El Fadili Hakim
2003-01-01
Full Text Available Research investigating the use of Legendre moments for pattern recognition has been performed in recent years. This field of research remains quite open. This paper proposes a new technique based on block-based reconstruction method (BBRM using Legendre moments compared with the global reconstruction method (GRM. For alleviating the blocking artifact involved in the processing, we propose a new approach using lapped block-based reconstruction method (LBBRM. For the problem of selecting the optimal number of moment used to represent a given image, we propose the maximum entropy principle (MEP method. The main motivation of the proposed approaches is to allow fast and efficient reconstruction algorithm, with improvement of the reconstructed images quality. A binary handwritten musical character and multi-gray-level Lena image are used to demonstrate the performance of our algorithm.
Piecewise Filter of Infrared Image Based on Moment Theory
Institute of Scientific and Technical Information of China (English)
GAO Yang; LI Yan-jun; ZHANG Ke
2007-01-01
The disadvantages of IR images mostly include high noise, blurry edge and so on. The characteristics make the existent smoothing methods ineffective in preserving edge. To solve this problem, a piecewise moment filter (PMF) is put forward. By using moment and piecewise linear theory, the filter can preserve edge. Based on the statistical model of random noise, a related-coefficient method is presented to estimate the variance of noise. The edge region and model are then detected by the estimated variance. The expectation of first-order derivatives is used in getting the reliable offset of edge.At last, a fast moment filter of double-stair edge model is used to gain the piecewise smoothing results and reduce the calculation. The experimental result shows that the new method has a better capability than other methods in suppressing noise and preserving edge.
Higher order statistical moment application for solar PV potential analysis
Basri, Mohd Juhari Mat; Abdullah, Samizee; Azrulhisham, Engku Ahmad; Harun, Khairulezuan
2016-10-01
Solar photovoltaic energy could be as alternative energy to fossil fuel, which is depleting and posing a global warming problem. However, this renewable energy is so variable and intermittent to be relied on. Therefore the knowledge of energy potential is very important for any site to build this solar photovoltaic power generation system. Here, the application of higher order statistical moment model is being analyzed using data collected from 5MW grid-connected photovoltaic system. Due to the dynamic changes of skewness and kurtosis of AC power and solar irradiance distributions of the solar farm, Pearson system where the probability distribution is calculated by matching their theoretical moments with that of the empirical moments of a distribution could be suitable for this purpose. On the advantage of the Pearson system in MATLAB, a software programming has been developed to help in data processing for distribution fitting and potential analysis for future projection of amount of AC power and solar irradiance availability.
Classical Orbital Paramagnetism in Non-equilibrium Steady State
Indian Academy of Sciences (India)
Avinash A. Deshpande; N. Kumar
2017-09-01
We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-Markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be paramagnetic for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo–Anderson type non-Markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-Markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr–van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.
Classical Orbital Paramagnetism in Non-equilibrium Steady State
Deshpande, Avinash A.; Kumar, N.
2017-09-01
We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-Markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be paramagnetic for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo-Anderson type non-Markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-Markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr-van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.
Equilibration properties of classical integrable field theories
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
Classical crystal formation of dipoles in two dimensions
DEFF Research Database (Denmark)
Hansen, Kenneth Christian Klochmann; Fedorov, D. V.; Jensen, A. S.;
2015-01-01
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are assumed to be aligned by an external field and we consider...... different orientations of the dipolar moments with respect to the two-dimensional plane of motion. We observe that when the orientation angle changes away from perpendicular and towards the plane, the crystal structure will change from a hexagonal form to one that has the dipoles sitting in equidistant rows...
Covariantizing Classical Field Theories
López, Marco Castrillón
2010-01-01
We show how to enlarge the covariance group of any classical field theory in such a way that the resulting "covariantized" theory is 'essentially equivalent' to the original. In particular, our technique will render any classical field theory generally covariant, that is, the covariantized theory will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kucha\\v{r}. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and St\\"uckelberg tricks.
Elementary classical hydrodynamics
Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C
1967-01-01
Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c
Brehm, Enrico M
2016-01-01
In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.
Learning Classical Music Club
2010-01-01
There is a new CERN Club called “Learning Classical Music at CERN”. We are aiming to give classical music lessons for different instruments (see link) for students from 5 to 100 years old. We are now ready to start our activities in the CERN barracks. We are now in the enrollment phase and hope to start lessons very soon ! Club info can be found in the list of CERN Club: http://user.web.cern.ch/user/Communication/SocialLifeActivities/Clubs/Clubs.html Salvatore Buontempo Club President
Fermion Dipole Moment and Holography
Kulaxizi, Manuela
2015-01-01
In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued with superluminal modes. Requiring consistency of the dual CFT amounts to constraining the strength of the dipole coupling by an upper bound. We briefly discuss the implications of our results for the physics of holographic non-Fermi liquids.
Multipole Moments of numerical spacetimes
Pappas, George
2012-01-01
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes that can approximate well the previously mentioned numerical spacetimes. We also present expressions that give the quadrupole and the spin octupole as functions of the spin parameter of a neutron star for various equations of state and in a range of masses for every equation of state used. These results are relevant for describing the exterior spacetime of rotating neutron stars that are made up of matter obeying realistic equations of state.
Experimental review on moment analyses
Calvi, M
2003-01-01
Moments of photon energy spectrum in B->Xs gamma decays, of hadronic mass spectrum and of lepton energy spectrum in B->Xc l nu decays are sensitive to the masses of the heavy quarks as well as to the non-perturbative parameters of the heavy quark expansion. Several measurements have been performed both at the Upsilon(4S) resonance and at Z0 center of mass energies. They provide constraints on the non-perturbative parameters, give a test of the consistency of the theoretical predictions and of the underlying assumptions and allow to reduce the indetermination in the |Vcb| extraction.
Anomalous center of mass shift gravitational dipole moment
Jeong, E J
1996-01-01
The anomalous, energy dependent shift of the center of mass of an idealized, perfectly rigid, uniformly rotating hemispherical shell which is caused by the relativistic mass increase effect is investigated in detail. It is shown that a classical object on impact which has the harmonic binding force between the adjacent constituent particles has the similar effect of the energy dependent, anomalous shift of the center of mass. From these observations, the general mode of the linear acceleration is suggested to be caused by the anomalous center of mass shift whether it's due to classical or relativistic origin. The effect of the energy dependent center of mass shift perpendicular to the plane of rotation of a rotating hemisphere appears as the non zero gravitational dipole moment in general relativity. Controlled experiment for the measurement of the gravitational dipole field and its possible links to the cylindrical type line formation of a worm hole in the extreme case are suggested. The jets from the black ...
Moment-specific compliance with hand hygiene.
Lau, Tiffany; Tang, Grace; Mak, Ka-lun; Leung, Gilberto
2014-06-01
Hand hygiene is an important component of patient-safety education. The World Health Organization recommends the use of hand hygiene measures at five clinical moments. While previous studies have treated hand hygiene as a single entity, we investigated whether and how the compliance of students may vary across the five clinical moments. We also studied their reasons for non-compliance with a view to inform teaching. A voluntary self-administered questionnaire survey was conducted on a convenient sample of 339 medical and nursing students. The five clinical moments studied were: before touching a patient (moment 1); before a clean/aseptic procedure (moment 2); after body fluid exposure risk (moment 3); after touching a patient (moment 4); and after touching the patient's surroundings (moment 5). The overall reported compliance rate was 83.0 per cent. The compliance rates were significantly lower at moments 1 and 5. Nursing students reported better overall compliance (p = 0.01), and at moments 2 (p = 0.0001) and 3 (p = 0.0001), than medical students. Medical students fared better at moment 4 (p = 0.009). The most common reason reported for non-compliance was 'forgetfulness'. We identified differences in compliance rates across the five clinical moments of hand hygiene. Education programmes should not treat the hand hygiene process as a single entity, but should adopt a moment-specific approach to promote recall, with particular emphases on moments 1 and 5. Nursing and medical students may require different education strategies. Future studies on hand hygiene may also adopt a moment-specific approach. © 2014 John Wiley & Sons Ltd.
Relative Equilibria in the Spherical, Finite Density 3-Body Problem
Scheeres, D J
2016-01-01
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
Performance improvement of a moment method for reliability analysis using kriging metamodels
Energy Technology Data Exchange (ETDEWEB)
Ju, Byeong Hyeon; Cho, Tae Min; Lee, Byung Chai [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Jung, Do Hyun [Korea Automotive Technology Institute, Chonan (Korea, Republic of)
2006-08-15
Many methods for reliability analysis have been studied and one of them, a moment method, has the advantage that it doesn't require sensitivities of performance functions. The moment method for reliability analysis requires the first four moments of a performance function and then Pearson system is used for the probability of failure where the accuracy of the probability of failure greatly depends on that of the first four moments. But it is generally impossible to assess them analytically for multidimensional functions, and numerical integration is mainly used to estimate the moment. However, numerical integration requires many function evaluations and in case of involving finite element analyses, the calculation of the first four moments is very time-consuming. To solve the problem, this research proposes a new method of approximating the first four moments based on kriging metamodel. The proposed method substitutes the kriging metamodel for the performance function and can also evaluate the accuracy of the calculated moments adjusting the approximation range. Numerical examples show the proposed method can approximate the moments accurately with the less function evaluations and evaluate the accuracy of the calculated moments.
Mecanica Clasica (Classical Mechanics)
Rosu, H C
1999-01-01
First Internet undergraduate course on Classical Mechanics in Spanish (Castellano). This is about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. English and Romanian versions are in (slow) progress and hopefully will be arXived. For a similar course on Quantum Mechanics, see physics/9808031
Huddleston, Gregory H.
1993-01-01
Describes one teacher's methods for introducing to secondary English students the concepts of Classicism and Romanticism in relation to pictures of gardens, architecture, music, and literary works. Outlines how the unit leads to a writing assignment based on collected responses over time. (HB)
Mecanica Clasica (Classical Mechanics)
Rosu, H. C.
1999-01-01
First Internet graduate course on Classical Mechanics in Spanish (Castellano). This is about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. English and Romanian versions are in (slow) progress and hopefully will be arXived. For a similar course on Quantum Mechanics, see physics/9808031
Huddleston, Gregory H.
1993-01-01
Describes one teacher's methods for introducing to secondary English students the concepts of Classicism and Romanticism in relation to pictures of gardens, architecture, music, and literary works. Outlines how the unit leads to a writing assignment based on collected responses over time. (HB)
Classical Mythology. Fourth Edition.
Morford, Mark P. O.; Lenardon, Robert J.
Designed for students with little or no background in classical literature, this book introduces the Greek and Roman myths of creation, myths of the gods, Greek sagas and local legends, and presents contemporary theories about the myths. Drawing on Homer, Hesiod, Pindar, Vergil, and others, the book provides many translations and paraphrases of…
Classical galactosaemia revisited
A.M. Bosch
2006-01-01
Classical galactosaemia (McKusick 230400) is an: autosomal recessive disorder of galactose metabolism, caused by a deficiency of the enzyme galactose-1-phosphate uridyltransferase (GALT; EC 2.7.712). Most patients present in the neonatal period, after ingestion of galactose, with jaundice, hepatospl
Frank, Irmgard
2016-01-01
The notion from ab-initio molecular dynamics simulations that nuclear motion is best described by classical Newton dynamics instead of the time-dependent Schr{\\"o}dinger equation is substantiated. In principle a single experiment should bring clarity. Caution is however necessary, as temperature dependent effects must be eliminated when trying to determine the existence of a zero-point energy.
Children's Classics. Fifth Edition.
Jordan, Alice M.
"Children's Classics," a 1947 article by Alice M. Jordan reprinted from "The Horn Book Magazine," examines the dynamics and appeal of some of the most famous books for young readers, including "Alice in Wonderland,""The Wind in the Willows,""Robinson Crusoe," and "Andersen's Fairy Tales." Paul Hein's annotated bibliography, a revision of Jordan's…
Children's Classics. Fifth Edition.
Jordan, Alice M.
"Children's Classics," a 1947 article by Alice M. Jordan reprinted from "The Horn Book Magazine," examines the dynamics and appeal of some of the most famous books for young readers, including "Alice in Wonderland,""The Wind in the Willows,""Robinson Crusoe," and "Andersen's Fairy Tales." Paul Hein's annotated bibliography, a revision of Jordan's…
Modeling Classical Heat Conduction in FLAG
Energy Technology Data Exchange (ETDEWEB)
Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Hendon, Raymond Cori [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-01-12
The Los Alamos National Laboratory FLAG code contains both electron and ion heat conduction modules; these have been constructed to be directly relevant to user application problems. However, formal code verification of these modules requires quantitative comparison to exact solutions of the underlying mathematical models. A wide variety of exact solutions to the classical heat conduction equation are available for this purpose. This report summarizes efforts involving the representation of the classical heat conduction equation as following from the large electron-ion coupling limit of the electron and ion 3T temperature equations, subject to electron and ion conduction processes. In FLAG, this limiting behavior is quantitatively verified using a simple exact solution of the classical heat conduction equation. For this test problem, both heat conduction modules produce nearly identical spatial electron and ion temperature profiles that converge at slightly less than 2nd order to the corresponding exact solution.
Classical and non-classical effective medium theories: New perspectives
Energy Technology Data Exchange (ETDEWEB)
Tsukerman, Igor, E-mail: igor@uakron.edu
2017-05-18
Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.
Mathematics of classical and quantum physics
Byron, Frederick W
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
On the regularization procedure in classical electrodynamics
Yaremko, Yu
2003-01-01
We consider the self-action problem in classical electrodynamics. A strict geometrical sense of commonly used renormalization of mass is made. A regularization procedure is proposed which relies on energy-momentum and angular momentum balance equations. We correct the expression for angular momentum tensor obtained by us in a previous paper (2002 J. Phys. A: Math. Gen. 35 831).
The Many Classical Faces of Quantum Structures
Directory of Open Access Journals (Sweden)
Chris Heunen
2017-03-01
Full Text Available Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory.
Khrennikov, Andrei
2011-03-01
The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a "quantum system" is just a label for (so to say "prequantum") classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger's equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The "effect of entanglement" is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.
The influence of aerodynamic coefficients on the elements of classic projectile paths
Directory of Open Access Journals (Sweden)
Damir D. Jerković
2011-04-01
Full Text Available The article deals with the results of the research on the influence of aerodynamic coefficient values on the trajectory elements and the stability parameters of classic axisymmetric projectiles. It presents the characteristic functions of aerodynamic coefficients with regard to aerodynamic parameters and the projectile body shape. The trajectory elements of the model of classic axisymmetric projectiles and the analyses of their changes were presented with respect to the aerodynamic coefficient values. Introduction Classic axisymmetric projectiles fly through atmosphere using muzzle velocity as initial energy resource, so the aerodynamic force and moment have the most significant influence on the motion of projectiles. The aerodynamic force and moment components represented as aerodynamic coefficients depend on motion velocity i. e. flow velocity, the flow features produced by projectile shape and position in the flow, and angular velocity (rate of the body. The functional dependence of aerodynamic coefficients on certain influential parameters, such as angle of attack and angular velocity components is expressed by the derivative of aerodynamic coefficients. The determination of aerodynamic coefficients and derivatives enables complete definition of the aerodynamic force and moment acting on the classic projectile. The projectile motion problem is considered in relation to defining the projectile stability parameters and the conditions under which the stability occurs. The comparative analyses of aerodynamic coefficient values obtained by numerical methods, semi empirical calculations and experimental research give preliminary evaluation of the quality of the determined values. The flight simulation of the motion of a classic axisymetric projectile, which has the shape defined by the aerodynamic coefficient values, enables the comparative analyses of the trajectory elements and stability characteristics. The model of the classic projectile
The 4.36-th moment of the Riemann zeta function
Radziwill, Maksym
2011-01-01
Conditionally on the Riemann Hypothesis we obtain bounds of the correct order of magnitude for the 2k-th moment of the Riemann zeta function for all positive real k 2; the case of k = 2 corresponds to a classical result of Ingham. We prove our result by establishing a connection between moments with k > 2 and the so-called "twisted fourth moment". This allows us to appeal to a recent result of Hughes and Young. Furthermore we obtain a point-wise bound for |zeta(1/2 + it)|^{2r} (with 0 < r < 1) that can be regarded as a multiplicative analogue of Selberg's bound for S(T). We also establish asymptotic formulae for moments (k < 2.181) slightly off the half-line.
Stimulated Raman adiabatic passage analogues in classical physics
Energy Technology Data Exchange (ETDEWEB)
Rangelov, A A [University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel (Germany); Vitanov, N V [Department of Physics, Sofia University, James Bourchier 5 blvd., 1164 Sofia (Bulgaria); Shore, B W [618 Escondido Cir., Livermore, CA (United States)
2009-03-14
Stimulated Raman adiabatic passage (STIRAP) is a well-established technique for producing coherent population transfer in a three-state quantum system. We here exploit the resemblance between the Schroedinger equation for such a quantum system and the Newton equation of motion for a classical system undergoing torque to discuss several classical analogues of STIRAP, notably the motion of a moving charged particle subject to the Lorentz force of a quasistatic magnetic field, the orientation of a magnetic moment in a slowly varying magnetic field and the Coriolis effect. Like STIRAP, these phenomena occur for counterintuitive motion of the torque and are robustly insensitive to small changes in the interaction properties.
Magnetic Moments of Excited Baryons
Directory of Open Access Journals (Sweden)
Metag Volker
2017-01-01
Full Text Available In project A.3, the reaction γ p → π0γ’p has been studied using the TAPS photon spectrometer in the energy range √s= 1221-1331 MeV. Energy tagged photon beams have been produced with the Glasgow tagging spectrometer from electron beams provided by the MAMI-B accelerator. Angle and energy differential cross sections have been measured and compared to theoretical calculations. This comparison allows the magnetic moment of the Δ+ isobar to be extracted for the first time to μΔ+ = [2.7+1.3−1.0(stat±1.5(syst±3(theo] μN. In an extension of the A3 project to the meson sector, the time-like transition form factor of the η meson has been measured with the Crystal Ball/TAPS detector system at MAMI-C.
Ollerton, Joanne Emma; Sugrue, Michael
2005-02-01
The evolution of trauma may be analyzed by review of articles most frequently cited by scientific articles worldwide. This study identified the "trauma classics" by reviewing the most-cited articles ever published in The Journal of Trauma. The Science Citation Index of the Institute for Scientific Information was searched for the 50 most-cited articles in The Journal of Trauma. Of the 12,672 articles published since 1961, 80 were cited over 100 times and 17 over 200 times. The most-cited article was by Baker, a hallmark publication on injury scoring published in 1974. Feeding postinjury, bacterial translocation, and multiple organ failure were common themes. Overall, 32% involved gastrointestinal topics and 18% involved injury scoring, with institutions in the United States publishing 80% of the articles. This study identified the trauma classics from the last 42 years of The Journal of Trauma. Citation analysis has recognized limitations but gives a fascinating insight into the evolution of trauma care.
Classical and statistical thermodynamics
Rizk, Hanna A
2016-01-01
This is a text book of thermodynamics for the student who seeks thorough training in science or engineering. Systematic and thorough treatment of the fundamental principles rather than presenting the large mass of facts has been stressed. The book includes some of the historical and humanistic background of thermodynamics, but without affecting the continuity of the analytical treatment. For a clearer and more profound understanding of thermodynamics this book is highly recommended. In this respect, the author believes that a sound grounding in classical thermodynamics is an essential prerequisite for the understanding of statistical thermodynamics. Such a book comprising the two wide branches of thermodynamics is in fact unprecedented. Being a written work dealing systematically with the two main branches of thermodynamics, namely classical thermodynamics and statistical thermodynamics, together with some important indexes under only one cover, this treatise is so eminently useful.
Franklin, Joel
2017-01-01
Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...
Directory of Open Access Journals (Sweden)
Adriana Coutinho de Azevedo Guimarães
2008-06-01
Full Text Available This study aimed to elucidate what injuries are most likely to occur due to classical ballet practice. The research used national and international bibliography. The bibliography analysis indicated that technical and esthetical demands lead to a practice of non-anatomical movements, causing the ballet dancer to suffer from a number of associated lesions. Most of the injuries are caused by technical mistakes and wrong training. Troubles in children are usually due to trying to force external rotation at hip level and to undue use of point ballet slippers. The commonest lesions are in feet and ankles, followed by knees and hips. The rarest ones are in the upper limbs. These injuries are caused by exercise excess, by repetitions always in the same side and by wrong and early use of point slippers. The study reached the conclusion that incorrect application of classical ballet technique predisposes the dancers to characteristic injuries.
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Classical Weyl Transverse Gravity
Oda, Ichiro
2016-01-01
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally-invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally-invariant scalar tensor gravity and the WTDiff gravity is a "fake" symmetry. We find it possible to extend this proof to all matter fields,...
Rogers, Ibram
2008-01-01
As a 26-year-old English teacher in 1958, Chinua Achebe had no idea that the book he was writing would become a literary classic, not only in Africa but also throughout the world. He could only try to articulate the feelings he had for his countrymen and women. Achebe had a burning desire to tell the true story of Africa and African humanity. The…
Lectures on classical electrodynamics
Englert, Berthold-Georg
2014-01-01
These lecture notes cover classical electrodynamics at the level of advanced undergraduates or postgraduates. There is a strong emphasis on the general features of the electromagnetic field and, in particular, on the properties of electromagnetic radiation. It offers a comprehensive and detailed, as well as self-contained, account of material that can be covered in a one-semester course for students with a solid undergraduate knowledge of basic electricity and magnetism.
Invitation to classical analysis
Duren, Peter
2012-01-01
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differ
Strong, John
2004-01-01
An intermediate course in optics, this volume explores both experimental and theoretical concepts, offering practical knowledge of geometrical optics that will enhance students' comprehension of any relevant applied science. Its exposition of the concepts of classical optics is presented with a minimum of mathematical detail but presumes some knowledge of calculus, vectors, and complex numbers.Subjects include light as wave motion; superposition of wave motions; electromagnetic waves; interaction of light and matter; velocities and scattering of light; polarized light and dielectric boundarie
Classical Maxwellian polarization entanglement
Carroll, John E
2015-01-01
An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting waves,with a principal direction of propagation in the laboratory frame, travel along that direction at speeds ever so slightly less than c.This allows nontrivial Lorentz transformations that can act on selected forward F waves or selected waves R traveling in the opposite direction to show that both can arise from a single zero momentum frame where all the waves are transverse to the original principal direction.Such F and R waves then both belong to a single relativistic entity where correlations between the two are unremarkable.The second feature requires the avoidance of using the Coulomb gauge.Waves, tending to plane waves in the limit of zero diffraction,can then be shown to be composed of two coupled sets of E and B fields that demonstrate the classical entanglement of F an...
Classical Weyl transverse gravity
Energy Technology Data Exchange (ETDEWEB)
Oda, Ichiro [University of the Ryukyus, Department of Physics, Faculty of Science, Nishihara, Okinawa (Japan)
2017-05-15
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a ''fake'' symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact solutions. (orig.)
From classical to quantum fields
Baulieu, Laurent; Sénéor, Roland
2017-01-01
Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a re...
Theoretical physics 1 classical mechanics
Nolting, Wolfgang
2016-01-01
This textbook offers a clear and comprehensive introduction to classical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction to the mathematical tools needed, to make this textbook self-contained for learning. The second part of the book introduces the mechanics of the free mass point and details conservation principles. The third part expands the previous to mechanics of many particle systems. Finally the mechanics of the rigid body is illustrated with rotational forces, inertia and gyroscope movement. Ideally suited to undergraduate students in their first year, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series...
Inflation and classical scale invariance
Racioppi, Antonio
2014-01-01
BICEP2 measurement of primordial tensor modes in CMB suggests that cosmological inflation is due to a slowly rolling inflaton taking trans-Planckian values and provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance solves the problem and allows for a remarkably simple scale-free inflaton model without any gauge group. Due to trans-Planckian inflaton values and VEVs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range. Precise determination of $r$ in future experiments will allow to test the proposed field-theoretic framework.
Solving moment hierarchies for chemical reaction networks
Krishnamurthy, Supriya; Smith, Eric
2017-10-01
The study of chemical reaction networks (CRN’s) is a very active field. Earlier well-known results (Feinberg 1987 Chem. Enc. Sci. 42 2229, Anderson et al 2010 Bull. Math. Biol. 72 1947) identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments. Using these, we can recursively predict values for lower moments from higher moments, reversing the procedure usually used to solve moment hierarchies. We show, for non-trivial examples, that in this manner we can predict any moment of interest, for CRN’s with non-zero deficiency and non-factorizable steady states.
Gastrointestinal Health in Classic Galactosemia.
Shaw, Kelly A; Mulle, Jennifer G; Epstein, Michael P; Fridovich-Keil, Judith L
2016-07-01
Classic galactosemia (CG) is an autosomal recessive disorder of galactose metabolism that affects approximately 1/50,000 live births in the USA. Following exposure to milk, which contains large quantities of galactose, affected infants may become seriously ill. Early identification by newborn screening with immediate dietary galactose restriction minimizes or prevents the potentially lethal acute symptoms of CG. However, more than half of individuals with CG still experience long-term complications including cognitive disability, behavioral problems, and speech impairment. Anecdotal reports have also suggested frequent gastrointestinal (GI) problems, but this outcome has not been systematically addressed. In this study we explored the prevalence of GI symptoms among 183 children and adults with CG (cases) and 190 controls. Cases reported 4.5 times more frequent constipation (95% CI 1.8-11.5) and 4.2 times more frequent nausea (95% CI 1.2-15.5) than controls. Cases with genotypes predicting residual GALT activity reported less frequent constipation than cases without predicted GALT activity but this difference was not statistically significant. Because the rigor of dietary galactose restriction varies among individuals with galactosemia, we further tested whether GI symptoms associated with diet in infancy. Though constipation was almost four times as common among cases reporting a more restrictive diet in infancy, this difference was not statistically significant. These data confirm that certain GI symptoms are more common in classic galactosemia compared to controls and suggest that future studies should investigate associations with residual GALT activity and dietary galactose restriction in early life.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Gursel, Yekta
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
Unification of Quantum and Gravity by Non Classical Information Entropy Space
Directory of Open Access Journals (Sweden)
Davide Fiscaletti
2013-09-01
Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
Moments of inertia of relativistic magnetized stars
Konno, K
2001-01-01
We consider principal moments of inertia of axisymmetric, magnetically deformed stars in the context of general relativity. The general expression for the moment of inertia with respect to the symmetric axis is obtained. The numerical estimates are derived for several polytropic stellar models. We find that the values of the principal moments of inertia are modified by a factor of 2 at most from Newtonian estimates.
Fox-Wolfram Moments in Higgs Physics
Bernaciak, Catherine; Butter, Anja; Plehn, Tilman
2012-01-01
Geometric correlations between jets as part of hard processes or in addition to hard processes are key ingredients to many LHC analyses. Fox--Wolfram moments systematically describe these correlations in terms of spherical harmonics. These moments, either computed from the tagging jets or from all jets in each event, can significantly improve Higgs searches in weak boson fusion. Applications of Fox--Wolfram moments in LHC analyses obviously surpass jets as analysis objects as well as Higgs searches in terms of analyses.
Classical Higgs fields on gauge gluon bundles
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Palese Marcella
2016-01-01
Full Text Available Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group. As an illustrative example we exploit the ‘gluon Lagrangian’, i.e. a Yang-Mills Lagrangian on the (1, 1-order gauge-natural bundle of SU(3-principal connections. The kernel of the gauge-natural Jacobi morphism for such a Lagrangian, by inducing a reductive split structure, canonically defines a ‘gluon classical Higgs field’.
Exact Classical Correspondence in Quantum Cosmology
John, Moncy V
2014-01-01
We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model for the universe, which agrees well with cosmological expansion indicated by SNe Ia data.
Thermodynamic integration from classical to quantum mechanics.
Habershon, Scott; Manolopoulos, David E
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
A modern approach to classical mechanics
Iro, Harald
2002-01-01
The approach to classical mechanics adopted in this book includes and stresses recent developments in nonlinear dynamical systems. The concepts necessary to formulate and understand chaotic behavior are presented. Besides the conventional topics (such as oscillators, the Kepler problem, spinning tops and the two centers problem) studied in the frame of Newtonian, Lagrangian, and Hamiltonian mechanics, nonintegrable systems (the Hénon-Heiles system, motion in a Coulomb force field together with a homogeneous magnetic field, the restricted three-body problem) are also discussed. The question of the integrability (of planetary motion, for example) leads finally to the KAM-theorem. This book is the result of lectures on 'Classical Mechanics' as the first part of a basic course in Theoretical Physics. These lectures were given by the author to undergraduate students in their second year at the Johannes Kepler University Linz, Austria. The book is also addressed to lecturers in this field and to physicists who wa...
Practical Fast Computation of Zernike Moments
Institute of Scientific and Technical Information of China (English)
Al-Rawi Mohammed; 杨杰
2002-01-01
The fast computation of Zernike moments from normalized geometric moments has been developed in this paper. The computation is multiplication free and only additions are needed to generate Zernike moments. Geometric moments are generated using Hatamian's filter up to high orders by a very simple and straightforward computation scheme. Other kinds of moments (e.g., Legendre, pseudo Zernike) can be computed using the same algorithm after giving the proper transformations that state their relations to geometric moments. Proper normalizations of geometric moments are necessary so that the method can be used in the efficient computation of Zernike moments. To ensure fair comparisons, recursive algorithms are used to generate Zernike polynomials and other coefficients. The computational complexity model and test programs show that the speed-up factor of the proposed algorithm is superior with respect to other fast and/or direct computations. It perhaps is the first time that Zernike moments can be computed in real time rates, which encourages the use of Zernike momentfeatures in different image retrieval systems that support huge databases such as the XM experimental model stated for the MPEG-7 experimental core. It is concluded that choosing direct computation would be impractical.
Optimized Set of RST Moment Invariants
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Khalid M. Hosny
2008-01-01
Full Text Available Moment invariants are widely used in image processing, pattern recognition and computer vision. Several methods and algorithms have been proposed for fast and efficient calculation of moment's invariants where numerical approximation errors are involved in most of these methods. In this paper, an optimized set of moment invariants with respect to rotation, scaling and translation is presented. An accurate method is used for exact computation of moment invariants for gray level images. A fast algorithm is applied to accelerate the process of computation. Error analysis is presented and a comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.
The growth of children's moment of inertia.
Jensen, R K
1986-08-01
As children grow, their moments of inertia increase. The magnitude and timing of these changes can affect the rotations of the body. The present study evaluated inter-individual differences in the transverse centroidal moment of inertia for 12 boys between 5 and 16 yr, using intra-individual data from three successive years. Segmental masses and moments of inertia were estimated using the elliptical zone model and the model then repositioned into two configurations: a layout position from a back handspring and a tuck position from a back somersault. In each case, the mass centroid and the moment of inertia about the transverse axis were calculated. With growth indexed by age, it was shown that the rate of change increases with age. For the children 10 yr and younger, the rate of change of moment of inertia was approximately 30% of the rate for the older children. Also, at each age level, there was a wide range of moments of inertia. In order to improve the prediction of moment of inertia, height and mass were tried as predictors with a noticeable improvement in correlation and linearity. The best predictor, however, was found to be the product of mass and height squared (M X H2) with correlations of 0.99 and 0.97. It is suggested that, because of the effects of growth on the moment of inertia. M X H2 could be used in conjunction with age in order to better appreciate the potential effects of change of moment of inertia.
A uniform parameterization of moment tensors
Tape, C.; Tape, W.
2015-12-01
A moment tensor is a 3 x 3 symmetric matrix that expresses an earthquake source. We construct a parameterization of the five-dimensional space of all moment tensors of unit norm. The coordinates associated with the parameterization are closely related to moment tensor orientations and source types. The parameterization is uniform, in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favor double couples. An appropriate choice of a priori moment tensor probability is a prerequisite for parameter estimation. As a seemingly sensible choice, we consider the homogeneous probability, in which equal volumes of moment tensors are equally likely. We believe that it will lead to improved characterization of source processes.
Solid-boundary treatment for moment systems
Khieu, Loc Huu
Hyperbolic-relaxation systems for describing fluid flow, such as Grad's 13-moment (13M) system, are an alternative to the systems generated by the Chapman-Enskog expansion, which include derivatives of increasing order. The former have a number of numerical advantages stemming from the compactness of their spatial operator. They have been demonstrated to be suited for subsonic and transonic flow. In this dissertation we explore the solid-wall boundary conditions that have to supplement these moment systems. Starting from the boundary treatment proposed by Grad, we first remove an inconsistency in his theory that would lead to ambiguous results. We formulate two boundary conditions, 1— C and 2—C, containing one and two parameters, respectively; these are used to satisfy the non-penetration condition in 1— C and 2—C, and an additional normalization condition in 2—C. The boundary conditions are implemented in a computational code based on the 13M system. In order to study the accuracy of the new boundary condition we also develop a benchmark code based on the Boltzmann equation with Bhatnagar—Gross—Krook collision model (BGK equation), and implement the same boundary conditions in there. Both codes include a Finite-Volume (FV) and a Discontinuous Galerkin (DG) option (piecewise-linear discretization). These codes are used to solve three types of flow problems: low-speed Couette flow with zero difference in wall temperatures, zero-speed Couette flow with appreciable wall-temperature difference, and low-speed Poiseuille flow. The Knudsen number ranged from 0.01 to 10. For these problems, incompressible Navier—Stokes—Fourier (NSF) solutions are available for comparison (except for the temperature-driven flow); here the boundary condition used is a first-or second-order velocity-slip boundary condition. The numerical experiments indicate that the 13M/1—C system consistently predicts a flow velocity at the wall that is closer to the BGK solution than
Mechanics classical and quantum
Taylor, T T
2015-01-01
Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e
Directory of Open Access Journals (Sweden)
Laurent Chusseau
2013-02-01
Full Text Available We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion, aside from the law of energy conservation. Only a single corpuscle in contact with a heat bath submitted to a z and t-invariant force is considered. Most of the end results are known but the method appears to be novel. The mathematics being elementary, the present paper should facilitate the understanding of the ideal gas law and of classical thermodynamics even though not-usually-taught concepts are being introduced.
Classical cytogenetics: karyotyping techniques.
Bates, Steven E
2011-01-01
Classical cytogenetics by karyotyping has been utilized in clinical research laboratories for more than 50 years and remains the key method used in the stem cell laboratory to assess the genetic stability of stem cell cultures. It is currently the most readily accessible method for detecting chromosomal abnormalities in pluripotent stem cell cultures. This chapter will describe (1) how to prepare a culture to maximize the number of metaphase cells, (2) how to prepare slides containing chromosome spreads (3) methods used to stain chromosomes, and (4) how to interpret the cytogenetic report.
Farhoudi, M.
1995-01-01
We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation sh...
Institute of Scientific and Technical Information of China (English)
2002-01-01
FIVE years ago, an ancient Chinese air was beamed to outer space as a PR exercise. To humankind, music is a universal language, so the tune seemed an ideal medium for communication with extraterrestrial intelligence. So far there has been no response, but it is believed that the tune will play for a billion years, and eventually be heard and understood. The melody is called High Mountain and Flowing Stream, and it is played on the guqin, a seven-stringed classical musical instrument similar to the zither.
Supernovae in Binary Systems: An Application of Classical Mechanics.
Mitalas, R.
1980-01-01
Presents the supernova explosion in a binary system as an application of classical mechanics. This presentation is intended to illustrate the power of the equivalent one-body problem and provide undergraduate students with a variety of insights into elementary classical mechanics. (HM)
Characterization of beam position monitors for measurement of second moment
Energy Technology Data Exchange (ETDEWEB)
Russell, S.J.; Gilpatrick, J.D.; Power, J.F.; Shurter, R.B.
1995-05-01
A dual-axis beam position monitor (BPM) consists of four electrodes placed at 90{degree} intervals around the probe aperture. The response signals of these lobes can be expressed as a sum of moments. The first order moment gives the centroid of the beam. The second order moment contains information about the rms size of the beam. It has been shown previously that the second order moment can be used to determine beam emittance. To make this measurement, the authors must characterize the BPM appropriately. The approach to this problem is to use a pulsed wire test fixture. By using the principle of superposition, they can build up a diffuse beam by taking the signals from different wire positions and summing them. This is done two ways: first by physically moving a wire about the aperture and building individual distributions, and, second, by taking a two dimensional grid of wire positions versus signal and using a computer to interpolate between the grid points to get arbitrary wire positions and, therefore, distributions. The authors present the current results of this effort.
MOMENT-METHOD ESTIMATION BASED ON CENSORED SAMPLE
Institute of Scientific and Technical Information of China (English)
NI Zhongxin; FEI Heliang
2005-01-01
In reliability theory and survival analysis,the problem of point estimation based on the censored sample has been discussed in many literatures.However,most of them are focused on MLE,BLUE etc;little work has been done on the moment-method estimation in censoring case.To make the method of moment estimation systematic and unifiable,in this paper,the moment-method estimators(abbr.MEs) and modified momentmethod estimators(abbr.MMEs) of the parameters based on type I and type Ⅱ censored samples are put forward involving mean residual lifetime. The strong consistency and other properties are proved. To be worth mentioning,in the exponential distribution,the proposed moment-method estimators are exactly MLEs. By a simulation study,in the view point of bias and mean square of error,we show that the MEs and MMEs are better than MLEs and the "pseudo complete sample" technique introduced in Whitten et al.(1988).And the superiority of the MEs is especially conspicuous,when the sample is heavily censored.
General linear dynamics - quantum, classical or hybrid
Elze, H-T; Vallone, F
2011-01-01
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. This is of practical as well as of foundational interest and no fully satisfactory solution of this problem has been established to date. Related aspects will be observed in a general linear ensemble theory, which comprises classical and quantum dynamics in the form of Liouville and von Neumann equations, respectively, as special cases. Considering the simplest object characterized by a two-dimensional state-space, we illustrate how quantum mechanics is special in several respects among possible linear generalizations.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Molecular dynamics simulations of classical stopping power.
Grabowski, Paul E; Surh, Michael P; Richards, David F; Graziani, Frank R; Murillo, Michael S
2013-11-22
Molecular dynamics can provide very accurate tests of classical kinetic theory; for example, unambiguous comparisons can be made for classical particles interacting via a repulsive 1/r potential. The plasma stopping power problem, of great interest in its own right, provides an especially stringent test of a velocity-dependent transport property. We have performed large-scale (~10(4)-10(6) particles) molecular dynamics simulations of charged-particle stopping in a classical electron gas that span the weak to moderately strong intratarget coupling regimes. Projectile-target coupling is varied with projectile charge and velocity. Comparisons are made with disparate kinetic theories (both Boltzmann and Lenard-Balescu classes) and fully convergent theories to establish regimes of validity. We extend these various stopping models to improve agreement with the MD data and provide a useful fit to our results.
Classical Ergodicity and Modern Portfolio Theory
Directory of Open Access Journals (Sweden)
Geoffrey Poitras
2015-01-01
Full Text Available What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.
Probability representation of classical states
Man'ko, OV; Man'ko, [No Value; Pilyavets, OV
2005-01-01
Probability representation of classical states described by symplectic tomograms is discussed. Tomographic symbols of classical observables which are functions on phase-space are studied. Explicit form of kernel of commutative star-product of the tomographic symbols is obtained.
Schiff moment of the Mercury nucleus and the proton dipole moment
Dmitriev, V. F.; Sen'kov, R. A.
2003-01-01
We calculated the contribution of internal nucleon electric dipole moments to the Schiff moment of $^{199}$Hg. The contribution of the proton electric dipole moment was obtained via core polarization effects that were treated in the framework of random phase approximation with effective residual forces. We derived a new upper bound $|d_p|< 5.4\\times 10^{-24} e\\cdot$cm of the proton electric dipole moment.
Magnetic moments of odd spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Levon, A.I.; Fedotkin, S.N.; Vdovin, A.I.
1986-06-01
Using the quasiparticle-phonon model, the magnetic moments of the ground state and several of the excited states are calculated for spherical nuclei. The polarization of the core is taken into account, by means of 1+ phonons, as well as 2/sup +/ and 3/sup -/ excitations, which give a collective contribution to the magnetic moment.
Neutrino induced magnetic moment and spin precession
Ternov, A. I.
2016-07-01
When propagating through a dispersing medium, a massive neutrino acquires an induced magnetic moment that may give rise to a helicity flip in an external magnetic field with a larger probability than that caused by the anomalous magnetic moment. This phenomenon is investigated in the framework of relativistic quantum mechanics and of the generalized Bargmann-Michel-Telegdi equation.
Balancing Beams--For a Few Moments
Kibble, Bob
2008-01-01
A 2 m long wooden beam provides an ideal demonstration tool for exploring moments. A class set is cheap and can be used at introductory and advanced levels. This article explores how such beams can be used to support learning about moments, equilibrium, vectors, and simultaneous equations. (Contains 7 figures.)
Learn to Live in the Present Moment
Institute of Scientific and Technical Information of China (English)
贾庆文
2002-01-01
To a large degree, the measure of our peace of mind is determined by how much we are able to live in the present moment. Irrespective of what happened yesterday or last year, and what may or may not happen tomorrow, the present moment is where you are-always!
Teachable Moment: Google Earth Takes Us There
Williams, Ann; Davinroy, Thomas C.
2015-01-01
In the current educational climate, where clearly articulated learning objectives are required, it is clear that the spontaneous teachable moment still has its place. Authors Ann Williams and Thomas Davinroy think that instructors from almost any discipline can employ Google Earth as a tool to take advantage of teachable moments through the…
HELMHOLTZ COILS FOR MEASURING MAGNETIC MOMENTS
Directory of Open Access Journals (Sweden)
P. N. Dobrodeyev
2013-01-01
Full Text Available The optimal configuration of the double Helmholtz coils for measuring of the magnetic dipole moments was defined. It was determined that measuring coils should have round shape and compensative coils – the square one. Analytically confirmed the feasibility of the proposed configuration of these coils as primary transmitters of magnetic dipole moments.
How to Introduce the Magnetic Dipole Moment
Bezerra, M.; Kort-Kamp, W. J. M.; Cougo-Pinto, M. V.; Farina, C.
2012-01-01
We show how the concept of the magnetic dipole moment can be introduced in the same way as the concept of the electric dipole moment in introductory courses on electromagnetism. Considering a localized steady current distribution, we make a Taylor expansion directly in the Biot-Savart law to obtain, explicitly, the dominant contribution of the…
Closed forms and multi-moment maps
DEFF Research Database (Denmark)
Madsen, Thomas Bruun; Swann, Andrew Francis
2013-01-01
We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are gu...
Teachable Moment: Google Earth Takes Us There
Williams, Ann; Davinroy, Thomas C.
2015-01-01
In the current educational climate, where clearly articulated learning objectives are required, it is clear that the spontaneous teachable moment still has its place. Authors Ann Williams and Thomas Davinroy think that instructors from almost any discipline can employ Google Earth as a tool to take advantage of teachable moments through the…
Fluid moments of the nonlinear Landau collision operator
Hirvijoki, E.; Lingam, M.; Pfefferlé, D.; Comisso, L.; Candy, J.; Bhattacharjee, A.
2016-08-01
An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.
The moment of proof mathematical epiphanies
Benson, Donald C
2000-01-01
When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many and varied. The book is packed with intriguing conundrums--Loyd''s Fifteen Puzzle, the Petersburg Paradox, the Chaos Game, the Monty Hall Problem, the Prisoners'' Dilemma--as well as many mathematical curiosities. We learn how to perform the arithmetical proof called "casting out nines" and are introduced to Russian peasant multiplication, a bizarre way to multiply numbers that actually works. The book shows us how to calculate the number of ways a chef can combine ten or fewer spices to flavor his soup (1,024) and ...
Electric dipole moments in natural supersymmetry
Nakai, Yuichiro; Reece, Matthew
2017-08-01
We discuss electric dipole moments (EDMs) in the framework of CP-violating natural supersymmetry (SUSY). Recent experimental results have significantly tightened constraints on the EDMs of electrons and of mercury, and substantial further progress is expected in the near future. We assess how these results constrain the parameter space of natural SUSY. In addition to our discussion of SUSY, we provide a set of general formulas for two-loop fermion EDMs, which can be applied to a wide range of models of new physics. In the SUSY context, the two-loop effects of stops and charginos respectively constrain the phases of A t μ and M 2 μ to be small in the natural part of parameter space. If the Higgs mass is lifted to 125 GeV by a new tree-level superpotential interaction and soft term with CP-violating phases, significant EDMs can arise from the two-loop effects of W bosons and tops. We compare the bounds arising from EDMs to those from other probes of new physics including colliders, b → sγ, and dark matter searches. Importantly, improvements in reach not only constrain higher masses, but require the phases to be significantly smaller in the natural parameter space at low mass. The required smallness of phases sharpens the CP problem of natural SUSY model building.
Conditions of the Classical Transmission Line Equations at High Frequency
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
New transmission line equations are deduced applying Maxwell's equations in this paper. The conditions of the classical transmission line equations have been discussed, which is important to solve the EM problems in high frequency case.
Darboux Transformations and Soliton Solutions for Classical Boussinesq-Burgers Equation
Institute of Scientific and Technical Information of China (English)
XU Rui
2008-01-01
Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgers equation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgers equation.
Innovative moments and change in narrative therapy.
Matos, Marlene; Santos, Anita; Gonçalves, Miguel; Martins, Carla
2009-01-01
Narrative therapy suggests that change happens by paying close attention in therapy to "unique outcomes," which are narrative details outside the main story (White & Epston, 1990). In this exploratory study, unique outcomes were analyzed in five good-outcome and five poor-outcome psychotherapy cases using the Innovative Moments Coding System (Gonçalves, Matos, & Santos, 2008). Across 127 sessions, innovative moments were coded in terms of salience and type. In accordance with the theory, results suggest that innovative moments are important to therapeutic change. Poor- and good-outcome groups have a global difference in the salience of the innovative moments. In addition, results suggest that two particular types of innovative moments are needed in narrative therapy for therapeutic change to take place: re-conceptualization and new experiences. Implications for future research using this model of analysis are discussed.
Perspective: Quantum or classical coherence?
Miller, William H
2012-06-07
Some coherence effects in chemical dynamics are described correctly by classical mechanics, while others only appear in a quantum treatment--and when these are observed experimentally it is not always immediately obvious whether their origin is classical or quantum. Semiclassical theory provides a systematic way of adding quantum coherence to classical molecular dynamics and thus provides a useful way to distinguish between classical and quantum coherence. Several examples are discussed which illustrate both cases. Particularly interesting is the situation with electronically non-adiabatic processes, where sometimes whether the coherence effects are classical or quantum depends on what specific aspects of the process are observed.
Magnetic properties of a classical XY spin dimer in a "planar" magnetic field
Ciftja, Orion; Prenga, Dode
2016-10-01
Single-molecule magnetism originates from the strong intra-molecular magnetic coupling of a small number of interacting spins. Such spins generally interact very weakly with the neighboring spins in the other molecules of the compound, therefore, inter-molecular spin couplings are negligible. In certain cases the number of magnetically coupled spins is as small as a dimer, a system that can be considered the smallest nanomagnet capable of storing non-trivial magnetic information on the molecular level. Additional interesting patterns arise if the spin motion is confined to a two-dimensional space. In such a scenario, clusters consisting of spins with large-spin values are particularly attractive since their magnetic interactions can be described well in terms of classical Heisenberg XY spins. In this work we calculate exactly the magnetic properties of a nanomagnetic dimer of classical XY spins in a "planar" external magnetic field. The problem is solved by employing a mathematical approach whose idea is the introduction of auxiliary spin variables into the starting expression of the partition function. Results for the total internal energy, total magnetic moment, spin-spin correlation function and zero-field magnetic susceptibility can serve as a basis to understand the magnetic properties of large-spin dimer building blocks.
Supersymmetric classical cosmology
Escamilla-Rivera, Celia; Urena-Lopez, L Arturo
2010-01-01
In this work a supersymmetric cosmological model is analyzed in which we consider a general superfield action of a homogeneous scalar field supermultiplet interacting with the scale factor in a supersymmetric FRW model. There appear fermionic superpartners associated with both the scale factor and the scalar field, and classical equations of motion are obtained from the super-Wheeler-DeWitt equation through the usual WKB method. The resulting supersymmetric Einstein-Klein-Gordon equations contain extra radiation and stiff matter terms, and we study their solutions in flat space for different scalar field potentials. The solutions are compared to the standard case, in particular those corresponding to the exponential potential, and their implications for the dynamics of the early Universe are discussed in turn.
Classical and Quantum Polyhedra
Schliemann, John
2014-01-01
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum polyhedra. Regarding tetrahedra, we compare the results from a canonical quantization of the classical system with a recent wave function based approach to the large-volume sector of the quantum system. Both methods agree in the leading order of the resulting effective operator (given by an harmonic oscillator), while minor differences occur in higher corrections. Perturbative inclusion of such corrections improves the approximation to the eigenstates. Moreover, the comparison of both methods leads also to a full wave function description of the eigenstates of the (square of the) volume operator at negative eigenvalues of large modulus. For the case of general quantum polyhedra described by discrete angular momentum quantum numbers we formulate a set of quantum operators fulfill...
Classically Isospinning Hopf Solitons
Battye, Richard A
2013-01-01
We perform full 3-dimensional numerical relaxations of isospinning Hopf solitons with Hopf charge up to 8 in the Skyrme-Faddeev model with mass terms included. We explicitly allow the soliton solution to deform and to break the symmetries of the static configuration. It turns out that the model with its rich spectrum of soliton solutions, often of similiar energy, allows for transmutations, formation of new solution types and the rearrangement of the spectrum of minimal-energy solitons in a given topological sector when isospin is added. We observe that the shape of isospinning Hopf solitons can differ qualitatively from that of the static solution. In particular the solution type of the lowest energy soliton can change. Our numerical results are of relevance for the quantization of the classical soliton solutions.
Magnetic moment conservation and particles acceleration in turbulence
Dalena, S.; Greco, A.; Matthaeus, W. H.
2010-12-01
The present work concerns the study of particle magnetic moment conservation in the presence of turbulent magnetic fields. As we know from the particle orbit theory, for slow temporal and spatial magnetic field variations(i.e. if their characteristic length and time are greater than the particle orbit diameter and the time spent by a particle to execute one orbit, respectively), the magnetic moment, defined as μ = (v^2⊥ /B) (averaged over the particle gyroperiod) is an adiabatic invariant and remains constant during particle motion. But in presence of a well developed magnetic turbulence μ can undergo rapid variations and might not be constant anymore. Of course, this fact could influence particle acceleration and could have a considerable implications in many astrophysical problems, such as coronal heating. In order to reproduce and extend some of the results obtained by Karimabadi et al. 1992, we study the interaction between ions and a single or a couple of electromagnetic waves. We varied both the wave frequency and the cosine of pitch angle at which particles are injected, in order to observe in this very simple case which is the limit for magnetic moment conservation. We also will reconsider the results of Dmitruk and Matthaeus (2006) regarding particle acceleration in turbulence, taking into account statistics of the magnetic moment (see also Lehe et al., 2010). Later we will add more waves to obtain a complete turbulent spectrum. The final aim of this research work is the understanding the behavior of particles magnetic moment during magnetic reconnection phenomena. H. Karimabadi, D. Krauss-Varban and T. Teresawa, JGR, 97, 13853, 1992. P. Dmitruk and W. H. Matthaeus, JGR, 11, A12110, 2006. R. Lehe, I. J. Parrish and E. Quataert, Astrophys. J. 707, 404, 2009.
A Top-down View of the Classical Limit of Quantum Mechanics
Fortin, Sebastian; Lombardi, Olimpia
The problem of the classical limit of quantum mechanics consists in explaining how the classical realm "emerges" from the quantum domain. Although along the history of quantum mechanics the problem has been addressed from many different perspectives, at present it is recognized that the classical limit also involves some kind of physical process, which transforms quantum states in such a way that they finally can be interpreted as classical states. This process is known as quantum decoherence.
Moment Maps and Equivariant Volumes
Institute of Scientific and Technical Information of China (English)
Alberto DELLA VEDOVA; Roberto PAOLETTI
2007-01-01
The study of the volume of big line bundles on a complex projective manifold M has been one of the main veins in the recent interest in the asymptotic properties of linear series. In this article,we consider an equivariant version of this problem, in the presence of a linear action of a reductive group on M.
Directory of Open Access Journals (Sweden)
Maryann Wilson
2013-01-01
Full Text Available BACKGROUND: The impact of a scientific article is proportional to the citations it has received. In this study, we set out to identify the most cited works in epileptology in order to evaluate research trends in this field. METHODS: According to the Web of Science database, articles with more than 400 citations qualify as "citation classics". We conducted a literature search on the ISI Web of Science bibliometric database for scientific articles relevant to epilepsy. RESULTS: We retrieved 67 highly cited articles (400 or more citations, which were published in 31 journals: 17 clinical studies, 42 laboratory studies, 5 reviews and 3 classification articles. Clinical studies consisted of epidemiological analyses (n=3, studies on the clinical phenomenology of epilepsy (n=5 – including behavioral and prognostic aspects – and articles focusing on pharmacological (n=6 and non-pharmacological (n=3 treatment. The laboratory studies dealt with genetics (n=6, animal models (n=27, and neurobiology (n=9 – including both neurophysiology and neuropathology studies. The majority (61% of citation classics on epilepsy were published after 1986, possibly reflecting the expansion of research interest in laboratory studies driven by the development of new methodologies, specifically in the fields of genetics and animal models. Consequently, clinical studies were highly cited both before and after the mid 80s, whilst laboratory researches became widely cited after 1990. CONCLUSIONS: Our study indicates that the main drivers of scientific impact in the field of epileptology have increasingly become genetic and neurobiological studies, along with research on animal models of epilepsy. These articles are able to gain the highest numbers of citations in the time span of a few years and suggest potential directions for future research.
How quantum are classical spin ices?
Gingras, Michel J. P.; Rau, Jeffrey G.
The pyrochlore spin ice compounds Dy2TiO7 and Ho2Ti2O7 are well described by classical Ising models down to low temperatures. Given the empirical success of this description, the question of the importance of quantum effects in these materials has been mostly ignored. We argue that the common wisdom that the strictly Ising moments of non-interacting Dy3+ and Ho3+ ions imply Ising interactions is too naive and that a more complex argument is needed to explain the close agreement between the classical Ising model theory and experiments. By considering a microscopic picture of the interactions in rare-earth oxides, we show that the high-rank multipolar interactions needed to induce quantum effects in these two materials are generated only very weakly by superexchange. Using this framework, we formulate an estimate of the scale of quantum effects in Dy2Ti2O7 and Ho2Ti2O7, finding it to be well below experimentally relevant temperatures. Published as: PHYSICAL REVIEW B 92, 144417 (2015).
A necessary moment condition for the fractional functional central limit theorem
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)^{-1}) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u_{t}, the existence of q≥max(2,(d+1/2)^{-1}) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1....../2)^{-1}) moments are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition...
A Necessary Moment Condition for the Fractional Functional Central Limit Theorem
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^(-d)u(t), where d ¿ (-1/2,1/2) is the fractional integration parameter and u(t) is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)-¹) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u(t), the existence of q=max(2,(d+1/2)-¹) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1/2)-¹) moments...... are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition. As a corollary...
Classical oscillators in the control of quantum tunneling: Numerical experiments
Kar, Susmita; Bhattacharyya, S. P.
2016-06-01
The dynamics of a classical anharmonic oscillator is exploited to control the tunneling dynamics of a quantum particle to which the classical oscillator is coupled. The mixed quantum classical problem is investigated at a mean-field like level. The anharmonic strength (λ) , particle mass (Mc) and harmonic stiffness (ωc) of the classical controller are explored as possible control parameters for the tunneling dynamics. The strength, the type of coupling between the quantum system and classical controller and the effective frequency of the controller emerge as crucial factors in shaping the nature and extent of the control. A whole spectrum of possibilities starting from enhancement, suppression to complete destruction of tunneling emerge depending on values assigned to the control parameters, the type of coupling and the control configuration used. When classical controller is replaced by a quantum controller, the control landscape becomes much simpler.
End effects on elbows subjected to moment loadings. [PWR; BWR
Energy Technology Data Exchange (ETDEWEB)
Rodabaugh, E.C.; Moore, S.E.
1982-01-01
So-called end effects for moment loadings on short-radius and long-radius butt welding elbows of various arc lengths are investigated with a view toward providing more accurate design formulas for critical piping systems. Data developed in this study, along with published information, were used to develop relatively simple design equations for elbows attached at both ends to long sections of straight pipe. These formulas are the basis for an alternate ASME Code procedure for evaluating the bending moment stresses in Class 1 nuclear piping (ASME Code Case N-319). The more complicated problems of elbows with other end conditions, e.g., flanges at one or both ends, are also considered. Comparisons of recently published experimental and theoretical studies with current industrial code design rules for these situations indicate that these rules also need to be improved.
Approximate maximum-entropy moment closures for gas dynamics
McDonald, James G.
2016-11-01
Accurate prediction of flows that exist between the traditional continuum regime and the free-molecular regime have proven difficult to obtain. Current methods are either inaccurate in this regime or prohibitively expensive for practical problems. Moment closures have long held the promise of providing new, affordable, accurate methods in this regime. The maximum-entropy hierarchy of closures seems to offer particularly attractive physical and mathematical properties. Unfortunately, several difficulties render the practical implementation of maximum-entropy closures very difficult. This work examines the use of simple approximations to these maximum-entropy closures and shows that physical accuracy that is vastly improved over continuum methods can be obtained without a significant increase in computational cost. Initially the technique is demonstrated for a simple one-dimensional gas. It is then extended to the full three-dimensional setting. The resulting moment equations are used for the numerical solution of shock-wave profiles with promising results.
Table of nuclear electric quadrupole moments
Stone, N. J.
2016-09-01
This Table is a compilation of experimental measurements of static electric quadrupole moments of ground states and excited states of atomic nuclei throughout the periodic table. To aid identification of the states, their excitation energy, half-life, spin and parity are given, along with a brief indication of the method and any reference standard used in the particular measurement. Experimental data from all quadrupole moment measurements actually provide a value of the product of the moment and the electric field gradient [EFG] acting at the nucleus. Knowledge of the EFG is thus necessary to extract the quadrupole moment. A single recommended moment value is given for each state, based, for each element, wherever possible, upon a standard reference moment for a nuclear state of that element studied in a situation in which the electric field gradient has been well calculated. For several elements one or more subsidiary EFG/moment reference is required and their use is specified. The literature search covers the period to mid-2015.
Semi-classical methods in nuclear physics
Brink, David M.
These lecture notes present an introduction to some semi-classical techniques which have applications in nuclear physics. Topics discussed include the WKB method, approaches based on the Feynman path integral, the Gutzwiller trace formula for level density fluctuations and the Thomas-Fermi approximation and the Vlasov equation for many-body problems. There are applications to heavy ion fusion reactions, bremsstrahlung emission in alpha decay and nuclear response functions.
On optimum strategies for minimizing the exponential moments of a given cost function
Merhav, Neri
2011-01-01
We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the same cost function. In particular, our main result is a theorem that gives simple sufficient conditions for a strategy to be optimum in the exponential moment sense. This theorem may be useful in various situations, and application examples are given. We also examine the asymptotic regime and investigate universal asymptotically optimum strategies in light of the aforementioned sufficient conditions, as well as phenomena of irregularities, or phase transitions, in the behavior of the asymptotic performance, which can be viewed and understood from a statistical-mechanical perspective. Finally, we propose a new route for deriving lower bounds on exponential moments of certain cost functions (like the square error in estimation problems) on the basis of well known lower bounds on...
Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
Lensky, Vadim; Pascalutsa, Vladimir
2014-01-01
We obtain leading- and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on all of the considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$ GeV$^2$). Especially surprising is the situation for the $\\delta_{LT}$ moment, which thus far was not reproducible for proton and neutron simultaneously in chiral perturbation theory. This problem, known as the "$\\delta_{LT}$ puzzle," is not seen in the present calculation.
Neural Network Model for Moment-Curvature Relationship of Reinforced Concrete Sections
Bağcı, Muhiddin
2010-01-01
The analysis of moment-curvature relationship of reinforced concrete sections is complex due to large number of variables as well as non-linear material behavior involved. Artificial Neural Networks (ANNs) are found to be a tool capable of solving such problems. This has led to increasing use of ANN for analyzing the behavior of reinforced concrete sections. This paper reports the details of a study conducted using ANN for predicting moment-curvature relationship of a reinforced concrete sect...
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.
Institute of Scientific and Technical Information of China (English)
XU Wei; NIU Yudun; RONG HaiWu; SUN ZhongKui
2009-01-01
The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul-sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.
Directory of Open Access Journals (Sweden)
F. P. Santos
2013-09-01
Full Text Available Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0,∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.
Crowder, Martin J
2001-01-01
If something can fail, it can often fail in one of several ways and sometimes in more than one way at a time. There is always some cause of failure, and almost always, more than one possible cause. In one sense, then, survival analysis is a lost cause. The methods of Competing Risks have often been neglected in the survival analysis literature. Written by a leading statistician, Classical Competing Risks thoroughly examines the probability framework and statistical analysis of data of Competing Risks. The author explores both the theory of the subject and the practicalities of fitting the models to data. In a coherent, self-contained, and sequential account, the treatment moves from the bare bones of the Competing Risks setup and the associated likelihood functions through survival analysis using hazard functions. It examines discrete failure times and the difficulties of identifiability, and concludes with an introduction to the counting-process approach and the associated martingale theory.With a dearth of ...
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Extended symmetrical classical electrodynamics.
Fedorov, A V; Kalashnikov, E G
2008-03-01
In this paper, we discuss a modification of classical electrodynamics in which "ordinary" point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field, E and B . It is shown that the vectors E and B can be defined in terms of two four-potentials and the components of k are the components of a four-tensor of the third rank. The Lagrangian of the modified electrodynamics is defined. The conditions are derived at which only one four-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of an electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy, and angular momentum of the monopole are found for different eigenvalues of k .
Sullivan, Woodruff Turner
1982-01-01
Radio techniques were the nrst to lead astronomy away from the quiescent and limited Universe revealed by traditional observations at optical wave lengths. In the earliest days of radio astronomy, a handful of radio physicists and engineers made one startling discovery after another as they opened up the radio sky. With this collection of classic papers and the extensive intro ductory material, the reader can experience these exciting discoveries, as well as understand the developing techniques and follow the motivations which prompted the various lines of inquiry. For instance he or she will follow in detail the several attempts to detect radio waves from the sun at the turn of the century; the unravelling by Jansky of a "steady hiss type static"; the incredible story of Reber who built a 9 meter dish in his backyard in 1937 and then mapped the Milky Way; the vital discoveries by Hey and colleagues of radio bursts from the Sun and of a discrete source in the constellation of Cygnus; the development of re...
Classical and quantum motion in an inverse square potential
Energy Technology Data Exchange (ETDEWEB)
Avila-Aoki, M. [Centro Universitario Valle de Chalco, Universidad Autonoma del Estado de Mexico, Valle de Chalco, CP 56615, Estado de Mexico (Mexico)], E-mail: manvlk@yahoo.com; Cisneros, C. [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Apartado Postal 6-96, CP 62131, Cuernavaca, Morelos (Mexico)], E-mail: carmen@ce.fis.unam.mx; Martinez-y-Romero, R.P. [Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Apartado Postal 21-267, CP 04000, Coyoacan DF (Mexico)], E-mail: rodolfo@dirac.fciencias.unam.mx; Nunez-Yepez, H.N. [Departamento Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, CP 09340, Iztapalapa DF (Mexico)], E-mail: nyhn@xanum.uam.mx; Salas-Brito, A.L. [Laboratorio de Sistemas Dinamicos, Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, CP 04000, Coyoacan DF (Mexico)], E-mail: asb@correo.azc.uam.mx
2009-01-19
Classical motion in an inverse square potential is shown to be equivalent to free motion on a hyperbola. The existence of a classical splitting between the q>0 and q<0 regions of motion is demonstrated. We show that this last property may be regarded as the classical counterpart of the superselection rule occurring in the corresponding quantum problem. We solve the quantum problem in momentum space finding that there is no way of quantizing its energy but that the eigenfunctions suffice to describe the single renormalized bound state of the system. The dynamical symmetry of the classical problem is found to be O(1,1). Both this symmetry and the symmetry of inversion through the origin are found to be broken.
Multipole moments for embedding potentials
DEFF Research Database (Denmark)
Nørby, Morten Steen; Olsen, Jógvan Magnus Haugaard; Kongsted, Jacob
2016-01-01
Polarizable quantum mechanical (QM)/molecular mechanics (MM)-embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins...... extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well-known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we...
THE DECISIONAL MOMENT AND ETHICS
Directory of Open Access Journals (Sweden)
Loredana TEREC-VLAD
2015-02-01
Full Text Available The aim of this article is to analyze the ethical decisions taken by organizations both in everyday life as well as in exceptional circumstances. For this purpose, we thought it would be important to bring into account the ethical issues within organizations, such as: responsibility, morals or trust capital. In this context, we have raised the problem of unethical behaviour, given that knowing the causes of unethical behaviour can help prevent it. Throughout this paper we shall also highlight the aspects related to organizational communication, since the decision making process also involves communicating with the employees or business partners.
Spectral Element Moment Tensor Inversions for Earthquakes in Southern California
Liu, Q.; Komatitsch, D.; Tromp, J.
2003-12-01
We have developed and implemented a Centroid Moment-Tensor (CMT) inversion procedure to determine source parameters for southern California earthquakes. The method is based upon spectral-element simulations of regional seismic wave propagation in a recently developed three-dimensional southern California model. Sensitivity to source parameters is determined by numerically calculating the Fréchet derivatives required for the CMT inversion. We use a combination of waveform and waveform-envelope misfit criteria, and facilitate pure double-couple or zero-trace moment-tensor inversions. The technique is applied to six recent southern California earthquakes: the September~9, 2001, Mw = 4.2 Hollywood event, the October~31, 2001, Mw=4.9 Anza event, the September~3, 2002, Mw = 4.2 Yorba Linda event, the February~22, 2003, Mw = 5.2 Big Bear event and Mw = 4.5 Big Bear aftershock, and the July~15, 2003, Mw =3.8 Lucerne Valley event. Using more than half of the available three-component data at periods of 6~seconds and longer, the focal mechanisms, locations, and magnitudes we obtain are in good agreement with estimates based upon classical body-wave, surface-wave, and first-motion inversions.
Magnetic moments in graphene with vacancies.
Chen, Jing-Jing; Wu, Han-Chun; Yu, Da-Peng; Liao, Zhi-Min
2014-08-07
Vacancies can induce local magnetic moments in graphene, paving the way to make magnetic functional graphene. Due to the interaction between magnetic moments and conduction carriers, the magnetotransport properties of graphene can be modulated. Here, the effects of vacancy induced magnetic moments on the electrical properties of graphene are studied via magnetotransport measurements and spin-polarized density functional theory calculations. We show by quantum Hall measurements that a sharp resonant Vπ state is introduced in the midgap region of graphene with vacancies, resulting in the local magnetic moment. The coupling between the localized Vπ state and the itinerant carrier is tuned by varying the carrier concentration, temperature, magnetic field, and vacancy density, which results in a transition between hopping transport and the Kondo effect and a transition between giant negative magnetoresistance (MR) and positive MR. This modulated magnetotransport is valuable for graphene based spintronic devices.
Moment of Inertia of a Physical Pendulum.
Reidl, Charles J., Jr.
1996-01-01
Presents a simple and inexpensive procedure for determining the moment of inertia of a physical pendulum both experimentally and analytically. The simplicity of the apparatus enables students to easily change parameters and obtain a wide variety of measurements. (JRH)
Tinker Toys Have Their Moments of Inertia.
Taylor, Kenneth Neal
1983-01-01
Describes use of Tinker Toys in several moment of inertia laboratory experiments at the advanced high school or introductory college levels. Includes procedures to be followed, arrangements of the Tinker Toy parts during experiments, and typical student data obtained. (JM)
Anomalous magnetic moment with heavy virtual leptons
Energy Technology Data Exchange (ETDEWEB)
Kurz, Alexander [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Deutsches Elektronen Synchrotron (DESY), 15738 Zeuthen (Germany); Liu, Tao [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Marquard, Peter [Deutsches Elektronen Synchrotron (DESY), 15738 Zeuthen (Germany); Steinhauser, Matthias [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany)
2014-02-15
We compute the contributions to the electron and muon anomalous magnetic moment induced by heavy leptons up to four-loop order. Asymptotic expansion is applied to obtain three analytic expansion terms which show rapid convergence.
Anomalous magnetic moment with heavy virtual leptons
Kurz, Alexander; Marquard, Peter; Steinhauser, Matthias
2013-01-01
We compute the contributions to the electron and muon anomalous magnetic moment induced by heavy leptons up to four-loop order. Asymptotic expansion is applied to obtain three analytic expansion terms which show rapid convergence.
Anomalous magnetic moment with heavy virtual leptons
Energy Technology Data Exchange (ETDEWEB)
Kurz, Alexander [Karlsruher Institut fuer Technologie (Germany). Inst. fuer Theoretische Teilchenphysik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Liu, Tao; Steinhauser, Matthias [Karlsruher Institut fuer Technologie (Germany). Inst. fuer Theoretische Teilchenphysik; Marquard, Peter [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-11-15
We compute the contributions to the electron and muon anomalous magnetic moment induced by heavy leptons up to four-loop order. Asymptotic expansion is applied to obtain three analytic expansion terms which show rapid convergence.
Moments of the folded logistic distribution
Institute of Scientific and Technical Information of China (English)
Saralees Nadarajah; Samuel Kotz
2007-01-01
The recent paper by Cooray et al. introduced the folded logistic distribution. The moments properties given in the paper appear too complicated. In this note, a simple formula is derived in terms of the well known Lerch function.
Relaxation properties in classical diamagnetism
Carati, A.; Benfenati, F.; Galgani, L.
2011-06-01
It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out.
Truncated Moment Analysis of Nucleon Structure Functions
Energy Technology Data Exchange (ETDEWEB)
A. Psaker; W. Melnitchouk; M. E. Christy; C. E. Keppel
2007-11-16
We employ a novel new approach using "truncated" moments, or integrals of structure functions over restricted regions of x, to study local quark-hadron duality, and the degree to which individual resonance regions are dominated by leading twists. Because truncated moments obey the same Q^2 evolution equations as the leading twist parton distributions, this approach makes possible for the first time a description of resonance region data and the phenomenon of quark-hadron duality directly from QCD.
Link between chips and cutting moments evolution
Cahuc, Olivier; Gérard, Alain; 10.4028/WWW.scientific.net/AMR.423.89
2012-01-01
The better understanding of the material cutting process has been shown with the benefit of the forces and moments measurement since some years ago. In paper, simultaneous six mechanical components and chip orientation measurements were realized during turning tests. During these tests, the influence of the depth of cut or feed rate has been observed and a link between the chip orientation and the moment vector orientation or the central axis characteristics has been shown.
On the Neutron Electric Dipole Moment
Institute of Scientific and Technical Information of China (English)
Z. Bentalha; O. Lazrec
2004-01-01
@@ Within the Kobayashi-Maskawa mechanism of electroweak interaction and using the recent measured mass of the top quark, we estimate the neutron electric dipole moment (NEDM) via the diquark electroweak interaction.The resulting moment is about 10-30 e cm. The actual upper bound on the NEDM is 6.3 × 10-26 ecm and it can reach the value 5 × 10-28 ecm predicted by experiments in recent years.
On the dipole moment of CO/+/.
Certain, P. R.; Woods, R. C.
1973-01-01
Results of self-consistent field calculations on neutral CO, its positive ion, and on neutral CN to verify an earlier estimate of the dipole moment of CO(+) in its ground super 2 Sigma state. Based on the above-mentioned calculations, direct evidence is obtained that the dipole moment (relative to the center of mass) is approximately 2.5 plus or minus 0.5 C, as previously determined by Kopelman and Klemperer (1962).
From Moments to Functions in Quantum Chromodynamics
Blümlein, J; Klein, S; Schneider, C
2009-01-01
Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.
An online database of nuclear electromagnetic moments
Mertzimekis, T. J.; Stamou, K.; Psaltis, A.
2016-01-01
Measurements of nuclear magnetic dipole and electric quadrupole moments are considered quite important for the understanding of nuclear structure both near and far from the valley of stability. The recent advent of radioactive beams has resulted in a plethora of new, continuously flowing, experimental data on nuclear structure - including nuclear moments - which hinders the information management. A new, dedicated, public and user friendly online database
Moment matrices, border bases and radical computation
Mourrain, B.; J. B. Lasserre; Laurent, Monique; Rostalski, P.; Trebuchet, Philippe
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming. While the border basis algorithms of [17] are ecient and numerically stable for computing complex roots, algorithms based on moment matrices [12] allow the incorporation of additional polynomials, ...
From moments to functions in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes; Klein, Sebastian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Kauers, Manuel; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2009-02-15
Single-scale quantities, like the QCD anomalous dimensions andWilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order. (orig.)
The classic: Bone morphogenetic protein.
Urist, Marshall R; Strates, Basil S
2009-12-01
This Classic Article is a reprint of the original work by Marshall R. Urist and Basil S. Strates, Bone Morphogenetic Protein. An accompanying biographical sketch of Marshall R. Urist, MD is available at DOI 10.1007/s11999-009-1067-4; a second Classic Article is available at DOI 10.1007/s11999-009-1069-2; and a third Classic Article is available at DOI 10.1007/s11999-009-1070-9. The Classic Article is copyright 1971 by Sage Publications Inc. Journals and is reprinted with permission from Urist MR, Strates BS. Bone morphogenetic protein. J Dent Res. 1971;50:1392-1406.
On the dynamics of classicalization
Energy Technology Data Exchange (ETDEWEB)
Brouzakis, N. [Department of Physics, University of Athens, University Campus, Zographou 15784 (Greece); Rizos, J., E-mail: irizos@uoi.gr [Theory Division, Department of Physics, University of Ioannina, Ioannina 45110 (Greece); Tetradis, N., E-mail: ntetrad@phys.uoa.gr [Department of Physics, University of Athens, University Campus, Zographou 15784 (Greece)
2012-02-14
We discuss the mechanism through which classicalization may occur during the collapse of a spherical field configuration modeled as a wavepacket. We demonstrate that the phenomenon is associated with the dynamical change of the equation of motion from a second-order partial differential equation of hyperbolic to one of elliptic type. Within this approach, we rederive the known expression for the classicalization radius. We also find indications that classicalization is associated with the absence of wave propagation at distances below the classicalization radius and the generation of shock waves. The full quantitative picture can be obtained only through the numerical integration of a partial differential equation of mixed type.
Liu, Yongsuo; Meng, Qinghua; Chen, Rong; Wang, Jiansong; Jiang, Shumin; Hu, Yuzhu
2004-01-01
The Pearson product-moment correlation coefficient is being used to evaluate the similarity of the high-performance liquid chromatographic fingerprints of traditional Chinese medicine (TCM) in China. It is confirmed that a large range of peak areas produced the wrong results. A new algorithm concerning weighted Pearson product-moment correlation coefficient is proposed in this article. The results for both real cases and simulated data sets show that the weighted Pearson product-moment correlation coefficients allow relatively larger differences for large values, smaller differences for small values, and more reliable results than the unweighted Pearson product-moment correlation coefficients. Weight selection depends on the specific scientific problem.
Planck's radiation law: is a quantum-classical perspective possible?
Marrocco, Michele
2016-05-01
Planck's radiation law provides the solution to the blackbody problem that marks the decline of classical physics and the rise of the quantum theory of the radiation field. Here, we venture to suggest the possibility that classical physics might be equally suitable to deal with the blackbody problem. A classical version of the Planck's radiation law seems to be achievable if we learn from the quantum-classical correspondence between classical Mie theory and quantum-mechanical wave scattering from spherical scatterers (partial wave analysis). This correspondence designs a procedure for countable energy levels of the radiation trapped within the blackbody treated within the multipole approach of classical electrodynamics (in place of the customary and problematic expansion in terms of plane waves that give rise to the ultraviolet catastrophe). In turn, introducing the Boltzmann discretization of energy levels, the tools of classical thermodynamics and statistical theory become available for the task. On the other hand, the final result depends on a free parameter whose physical units are those of an action. Tuning this parameter on the value given by the Planck constant makes the classical result agree with the canonical Planck's radiation law.
Innovation: the classic traps.
Kanter, Rosabeth Moss
2006-11-01
Never a fad, but always in or out of fashion, innovation gets rediscovered as a growth enabler every half dozen years. Too often, though, grand declarations about innovation are followed by mediocre execution that produces anemic results, and innovation groups are quietly disbanded in cost-cutting drives. Each managerial generation embarks on the same enthusiastic quest for the next new thing. And each generation faces the same vexing challenges- most of which stem from the tensions between protecting existing revenue streams critical to current success and supporting new concepts that may be crucial to future success. In this article, Harvard Business School professor Rosabeth Moss Kanter reflects on the four major waves of innovation enthusiasm she's observed over the past 25 years. She describes the classic mistakes companies make in innovation strategy, process, structure, and skills assessment, illustrating her points with a plethora of real-world examples--including AT&T Worldnet, Timberland, and Ocean Spray. A typical strategic blunder is when managers set their hurdles too high or limit the scope of their innovation efforts. Quaker Oats, for instance, was so busy in the 1990s making minor tweaks to its product formulas that it missed larger opportunities in distribution. A common process mistake is when managers strangle innovation efforts with the same rigid planning, budgeting, and reviewing approaches they use in their existing businesses--thereby discouraging people from adapting as circumstances warrant. Companies must be careful how they structure fledgling entities alongside existing ones, Kanter says, to avoid a clash of cultures and agendas--which Arrow Electronics experienced in its attempts to create an online venture. Finally, companies commonly undervalue and underinvest in the human side of innovation--for instance, promoting individuals out of innovation teams long before their efforts can pay off. Kanter offers practical advice for avoiding
Gov, S; Thomas, H
1999-01-01
Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum-mechanics of magnetic traps. The 1D toy model that was used in this study was physically unrealistic because the magnetic field was not curl-free. Here, we study, both classically and quantum-mechanically, the problem of a neutral particle with spin S, mass m and magnetic moment mu, moving in 3D in an inhomogeneous magnetic field corresponding to traps of the Ioffe-Pritchard, `clover-leaf' and `baseball' type. Defining by omega_p, omega_z and omega_r the precessional, the axial and the lateral vibrational frequencies, respectively, of the particle in the adiabatic potential, we find classically the region in the $(ømega_{r}% (omega_r -- omega_z) plane where the particle is trapped. Quantum-mechanically, we study the problem of a spin-one particle in the same field. Treating omega_r / omega_p and omega_z / omega_p as small parame...
The Transdisciplinary Moment(um
Directory of Open Access Journals (Sweden)
Julie Thompson Klein
2013-06-01
Full Text Available There is no universal theory, methodology, or definition of transdisciplinarity (TD. Nevertheless, keywords reveal similarities and differences across explanations. This overview tracks five major clusters of meaning: (a meta-level conceptions of interdisciplinarity, (b the changing nature and status of unity in the discourse of TD, (c new alignments with participatory and collaborative problem-oriented research, (d the forms of knowledge that TD engages, and (e a transgressive imperative that interrogates the existing structure of knowledge, culture, and education. These categories of meaning are not air-tight. However, with widening use of the core word “transdisciplinarity,” it is important to be alert to these patterns and their underlying values and priorities.
Temporal moments revisited: Why there is no better way for physically based model reduction in time
Leube, P. C.; Nowak, W.; Schneider, G.
2012-11-01
Many hydro(geo)logical problems are highly complex in space and time, coupled with scale issues, variability, and uncertainty. Especially time-dependent models often consume enormous computational resources, but model reduction techniques can alleviate this problem. Temporal moments (TM) offer an approach to reduce the time demands of transient hydro(geo)logical simulations. TM reduce transient governing equations to steady state and directly simulate the temporal characteristics of the system, if the equations are linear and coefficients are time independent. This is achieved by an integral transform, projecting the dynamic system response onto monomials in time. In comparison to classical approaches of model reduction that involve orthogonal base functions, however, the monomials for TM are nonorthogonal, which might impair the quality and efficiency of model reduction. Thus, we raise the question of whether there are more suitable temporal base functions than the monomials that lead to TM. In this work, we will derive theoretically that there is only a limited class of temporal base functions that can reduce hydro(geo)logical models. By comparing those to TM we conclude that, in terms of gained efficiency versus maintained accuracy, TM are the best possible choice. While our theoretical results hold for all systems of linear partial or ordinary differential equations (PDEs, ODEs) with any order of space and time derivatives, we illustrate our study with an example of pumping tests in a confined aquifer. For that case, we demonstrate that two (four) TM are sufficient to represent more than 80% (90%) of the dynamic behavior, and that the information content strictly increases with increasing TM order.
Energy Technology Data Exchange (ETDEWEB)
McGraw, Robert [Atmospheric Sciences Division, Environmental Sciences Department Brookhaven National Laboratory, Upton, NY 11973 (United States)
2007-07-15
Nonlinear transport algorithms designed to reduce numerical diffusion fail to preserve correlations between moments, isotope abundances, etc. when these scalar densities are transported in models as separate tracers. In case of the particle size/composition coordinates of an aerosol, such loss can give rise to unphysical moment sets. New statistical approaches to aerosol dynamics, which involve tracking moments directly, offer highly efficient alternatives to sectional and modal methods for representing aerosols in climate models, but it is essential that moment set integrity be preserved throughout a simulation. In this paper we review the problem and weaknesses of previous attempts at solution, including vector transport - a scheme in which the moments, as internal aerosol coordinates, are transported together with a single lead tracer such as number or mass. A non-negative least squares (NNLS) solution that finally eliminates the problem without requiring modification of the transport algorithm itself is presented. Following each transport step, new moment sets are resolved into sums of previously validated sets with non-negative coefficients using NNLS Transport errors are removed and the now guaranteed-to-be-valid moment sets are ready for passage to the aerosol dynamics module. In addition to moment set validation, the new scheme reduces numerical diffusion during transport and provides greater accuracy for the source apportionment of aerosol mixtures. The method is not limited to moment transport - similar improvements in accuracy are expected using NNLS in conjunction with modal and sectional methods.
Religious ecstasy in classical Sufism
Directory of Open Access Journals (Sweden)
Göran Ogén
1982-01-01
Full Text Available The purpose of this essay is to shed some light on the phenomenon of religious ecstasy as met within Islamic mysticism and there particularly during its classical period. In this case, the expression "classical Sufism" refers to the period of Sufi history from about 850 A.D. until circa 1100 A.D. In the Sufi vocabulary there is even a rather differentiated terminology concerning these ecstatic experiences or states; whether different descriptions of one and the same experience are involved or whether the terms actually describe different experiences is a question that we must set aside for the present. There are, however, Sufis expressing the opinion that these different states of mind are based on one single experience in spite of the difference in terms. A generic term for these experiences or states is not to be found in the Sufi terminology however, so the problem of which of these phenomena must be present in order for ecstasy to be evidenced—or which of them would be sufficient— does not therefore arise for the Sufis. So instead of speaking of religious ecstasy in general, they either refer to the single specific terms in question or else use the plural of one of the words employed to designate one of the terms we include in "religious ecstasy". They thus speak of "ecstasies", mawagid from the singular form wagd—if one should at all attempt a translation of this plural. This plural is a genuine Sufi construction and does not otherwise seem to occur in the Arabic language, except as a later borrowing. Psalmody based on the Koranic vocabulary remains the main procedure for putting oneself in ecstasy. If we add 'and listening to psalmody', we then obtain a fairly satisfactory picture of the external conditions for the Sufis' ecstasy until the eleventh century, when various innovations begin to appear. As far as the darwiš-dance is concerned, it is not until the thirteenth century with Rumi that it becomes transformed from an expression
A Comparison of Geodetic Strain Rates With Earthquake Moment Tensors
Zhu, W.; Holt, W. E.
2004-12-01
In this paper we compare the global model from interpolation of GPS data with the global model inferred from earthquake moment tensors. We use the Harvard CMT catalog to calculate moment rates based on 3 assumptions: a. we assume earthquakes are self-similar; b. we assume a uniform Beta value of the Gutenberg-Richter distribution; c. we assume that all of the long-term strain is accommodated seismically. If these assumptions are correct then the seismicity rate is proportional to the tectonic moment rate. We then inferred a long-term moment rate tensor field estimate for all plate boundary zones from which we inferred a long-term seismic strain rate estimate. Using this estimate we solved for a self-consistent kinematic global solution (motions of rigid spherical caps and motions within plate boundary zones) using bi-cubic spline interpolation of the inferred strain rates. We tested the above assumptions by comparing the global kinematic model obtained from earthquake data with a global model inferred from interpolation of space geodetic data [Kreemer et al., 2003]. A comparison between the two models shows good agreement for motion directions of the North American, and Eurasian plates and for the plate boundary zones within these regions (e.g., Tibet). Problems arise, and our assumptions break down, for plates adjacent to fast spreading ridges where divergence of plates appears to be accommodated aseismically. We next investigated the correlation of strain rate tensor inferred from the interpolation of GPS observations within deforming Asia with the earthquake moment tensors, using both elastic and viscous rheologies. Our solutions satisfy the force balance equations for a given rheology. Our goal for this exercise is to investigate whether the interseismic signal, inferred from GPS, correlates better with moment tensor style for an elastic rheology as opposed to a viscous rheology. Results to date suggest that the viscous models only provide a better agreement
Novel Moment Features Extraction for Recognizing Handwritten Arabic Letters
Directory of Open Access Journals (Sweden)
Gheith Abandah
2009-01-01
Full Text Available Problem statement: Offline recognition of handwritten Arabic text awaits accurate recognition solutions. Most of the Arabic letters have secondary components that are important in recognizing these letters. However these components have large writing variations. We targeted enhancing the feature extraction stage in recognizing handwritten Arabic text. Approach: In this study, we proposed a novel feature extraction approach of handwritten Arabic letters. Pre-segmented letters were first partitioned into main body and secondary components. Then moment features were extracted from the whole letter as well as from the main body and the secondary components. Using multi-objective genetic algorithm, efficient feature subsets were selected. Finally, various feature subsets were evaluated according to their classification error using an SVM classifier. Results: The proposed approach improved the classification error in all cases studied. For example, the improvements of 20-feature subsets of normalized central moments and Zernike moments were 15 and 10%, respectively. Conclusion/Recommendations: Extracting and selecting statistical features from handwritten Arabic letters, their main bodies and their secondary components provided feature subsets that give higher recognition accuracies compared to the subsets of the whole letters alone.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
What is the Magnetic Moment of the Electron?
Steinmann, Othmar
Because of infrared effects the charged sectors of QED contain no eigenstates of the mass operator. The electron is therefore not definable as a Wigner particle. There exists no sharp, unambiguous, definition of the notion of a 1-electron state. The assignment of a fixed value of the magnetic moment - or similar quantities - to the electron is therefore at first problematic. It is not clear a priori that such a notion is meaningful. Conventionally this problem is solved by first calculating the desired quantity in an IR-regularized theory and then removing the regularization. If this method yields a finite value, that is considered sufficient proof of its soundness. This is clearly less than satisfactory. Here we propose a more convincing way of defining the intrinsic magnetic moment of the electron, which does not use any regularizations and is not based on an interaction with external fields. A pseudostatic 1-electron state is defined in a phenomenological way. Its magnetic moment, as defined here, does not depend on the unavoidable ambiguities inherent in this definition. The method leads to the same analytic expression as the conventional approach, thus preserving the excellent agreement between theory and experiment.
Optimal prediction for moment models: Crescendo diffusion and reordered equations
Seibold, Benjamin
2009-01-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived...
Optimal prediction for moment models: crescendo diffusion and reordered equations
Seibold, Benjamin; Frank, Martin
2009-12-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N , diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered P N equations, that are similar to the simplified P N equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Relative Equilibria in the Spherical, Finite Density Three-Body Problem
Scheeres, D. J.
2016-10-01
The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
Classical Aberration And Obliquation
Adewole, A I A
2002-01-01
This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that the laws of optics are unwavering in their support of the view that extragalactic redshifts need not be velocity doppler shifts nor cosmological recession shifts. In the latter context the first few monographs of the series may be viewed as providing a basis for the demonstration to be given in a latter monograph.
Anomalous center of mass shift: gravitational dipole moment.
Jeong, Eue Jin
1997-02-01
The anomalous, energy dependent shift of the center of mass of an idealized, perfectly rigid, uniformly rotating hemispherical shell which is caused by the relativistic mass increase effect is investigated in detail. It is shown that a classical object on impact which has the harmonic binding force between the adjacent constituent particles has the similar effect of the energy dependent, anomalous shift of the center of mass. From these observations, the general mode of the linear acceleration is suggested to be caused by the anomalous center of mass shift whether it's due to classical or relativistic origin. The effect of the energy dependent center of mass shift perpendicular to the plane of rotation of a rotating hemisphere appears as the non zero gravitational dipole moment in general relativity. Controlled experiment for the measurement of the gravitational dipole field and its possible links to the cylindrical type line formation of a worm hole in the extreme case are suggested. The jets from the black hole accretion disc and the observed anomalous red shift from far away galaxies are considered to be the consequences of the two different aspects of the dipole gravity.
Nonadiabatic Induced Dipole Moment by High Intensity Femtosecond Optical Pulses
Koprinkov, I. G.
2006-01-01
Nonadiabtic dressed states and nonadiabatic induced dipole moment in the leading order of nonadiabaticity is proposed. The nonadiabatic induced dipole moment is studied in the femtosecond time domain.
The Diversity of Classical Archaeology
DEFF Research Database (Denmark)
This book is the first volume in the series Studies in Classical Archaeology, founded and edited by professors of classical archaeology, Achim Lichtenberger and Rubina Raja. This volume sets out the agenda for this series. It achieves this by familiarizing readers with a wide range of themes and ...
Classic African American Children's Literature
McNair, Jonda C.
2010-01-01
The purpose of this article is to assert that there are classic African American children's books and to identify a sampling of them. The author presents multiple definitions of the term classic based on the responses of children's literature experts and relevant scholarship. Next, the manner in which data were collected and analyzed in regard to…
Classic writings on instructional technology
Ely, D.P.; Ely, Donald P.; Plomp, T.
1996-01-01
This paper describes the selection process of 17 articles for inclusion in the book, "Classic Writings on Instructional Technology." The book brings together original "classic" educational technology articles into one volume to document the history of the field through its literature. It is also an