On Chudnovsky-Based Arithmetic Algorithms in Finite Fields
Atighehchi, Kevin; Ballet, Stéphane; Bonnecaze, Alexis; Rolland, Robert
2015-01-01
Thanks to a new construction of the so-called Chudnovsky-Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field ${\\mathbb F}_{16^{13}}$.
Effective arithmetic in finite fields based on Chudnovsky's multiplication algorithm
Atighehchi , Kévin; Ballet , Stéphane; Bonnecaze , Alexis; Rolland , Robert
2016-01-01
International audience; Thanks to a new construction of the Chudnovsky and Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized, while maintaining a low number of bilinear multiplications.À partir d'une nouvelle construction de l'algorithme de multiplication de Chudnovsky et Chudnovsky, nous concevons des algorithmes ef...
Groups and fields in arithmetic
Kosters, Michiel F.
2014-01-01
This thesis consists of 8 chapters in which we discuss various aspects of arithmetic. In the first chapter, we give an introduction to the algebraic theory of valued fields. In the second chapter, we give an introduction to the theory of normal projective curves. In particular, we study curves over
Verification of Linear (In)Dependence in Finite Precision Arithmetic
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2014-01-01
Roč. 8, č. 3-4 (2014), s. 323-328 ISSN 1661-8289 Institutional support: RVO:67985807 Keywords : linear dependence * linear independence * pseudoinverse matrix * finite precision arithmetic * verification * MATLAB file Subject RIV: BA - General Mathematics
The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
Czech Academy of Sciences Publication Activity Database
Meurant, G.; Strakoš, Zdeněk
2006-01-01
Roč. 15, - (2006), s. 471-542 ISSN 0962-4929 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lanczos method * conjugate gradient method * finite precision arithmetic * numerical stability * iterative methods Subject RIV: BA - General Mathematics
Arithmetic geometry over global function fields
Longhi, Ignazio; Trihan, Fabien
2014-01-01
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the con...
Arithmetics, geometry and conformal fields
Itzykson, Claude
1992-03-17
The last few years have witnessed a remarkeble conjunction of methods in such diverse domains as strings and topological field theory, two dimensional statistical physics, classical and quantum integrable systems. The lectures will aim to present some of the underlying mathematics at an elementary and pedagogical level, for their intrinsic value.
Algebra 1 groups, rings, fields and arithmetic
Lal, Ramji
2017-01-01
This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.
Finite fields and applications
Mullen, Gary L
2007-01-01
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
Finite temperature field theory
Das, Ashok
1997-01-01
This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al
International Nuclear Information System (INIS)
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
On finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1984-01-01
The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)
Toward finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1986-01-01
The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)
Finiteness of quantum field theories and supersymmetry
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)
Features of finite quantum field theories
International Nuclear Information System (INIS)
Boehm, M.; Denner, A.
1987-01-01
We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)
Finite spatial volume approach to finite temperature field theory
International Nuclear Information System (INIS)
Weiss, Nathan
1981-01-01
A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)
Lectures on zeta functions over finite fields
Wan, Daqing
2007-01-01
These are the notes from the summer school in G\\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.
Factoring polynomials over arbitrary finite fields
Lange, T.; Winterhof, A.
2000-01-01
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of
A software framework for pipelined arithmetic algorithms in field programmable gate arrays
Kim, J. B.; Won, E.
2018-03-01
Pipelined algorithms implemented in field programmable gate arrays are extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms increases rapidly. For development of such hardware triggers, algorithms are developed in C++, ported to hardware description language for synthesizing firmware, and then ported back to C++ for simulating the firmware response down to the single bit level. We present a C++ software framework which automatically simulates and generates hardware description language code for pipelined arithmetic algorithms.
A note on powers in finite fields
Aabrandt, Andreas; Lundsgaard Hansen, Vagn
2016-08-01
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.
Clifford algebra in finite quantum field theories
International Nuclear Information System (INIS)
Moser, M.
1997-12-01
We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
A Note on Powers in Finite Fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2016-01-01
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analys...... for squares in odd prime fields, giving it a formulation which is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom....
Lamps, Factorizations and Finite Fields
Bartholdi, Laurent
1999-01-01
I answer a question from the 1993 International Mathematical Olympiads by constructing an equivalent algebraic problem, and unearth a surprising behaviour of some polynomials over the two-element field.
A Note on Powers in Finite Fields
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2016-01-01
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…
Finite-temperature field theory
International Nuclear Information System (INIS)
Kapusta, J.I.; Landshoff, P.V.
1989-01-01
Particle number is not conserved in relativistic theories although both lepton and baryon number are. Therefore when discussing the thermodynamics of a quantum field theory one uses the grand canonical formalism. The entropy S is maximised, keeping fixed the ensemble averages E and N of energy and lepton number. Two lagrange multipliers are introduced. (author)
Finite N=1 SUSY gauge field theories
International Nuclear Information System (INIS)
Kazakov, D.I.
1986-01-01
The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established
Field emission from finite barrier quantum structures
Energy Technology Data Exchange (ETDEWEB)
Biswas Sett, Shubhasree, E-mail: shubhasree24@gmail.com [The Institution of Engineers - India, 8, Gokhale Road, Kolkata 700 020 (India); Bose, Chayanika, E-mail: chayanikab@ieee.org [Electronics and Telecommunication Engg. Dept., Jadavpur University, Kolkata 700 032 (India)
2014-10-01
We study field emission from various finite barrier quasi-low dimensional structures, taking image force into account. To proceed, we first formulate an expression for field emission current density from a quantum dot. Transverse dimensions of the dot are then increased in turn, to obtain current densities respectively from quantum wire and quantum well with infinite potential energy barriers. To find out field emission from finite barrier structures, the above analysis is followed with a correction in the energy eigen values. In course, variations of field emission current density with strength of the applied electric field and structure dimensions are computed considering n-GaAs and n-GaAs/Al{sub x}Ga{sub 1−x}As as the semiconductor materials. In each case, the current density is found to increase exponentially with the applied field, while it oscillates with structure dimensions. The magnitude of the emission current is less when the image force is not considered, but retains the similar field dependence. In all cases, the field emission from infinite barrier structures exceeds those from respective finite barrier ones.
The circle equation over finite fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2017-01-01
Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we es...
Thermo field dynamics: a quantum field theory at finite temperature
International Nuclear Information System (INIS)
Mancini, F.; Marinaro, M.; Matsumoto, H.
1988-01-01
A brief review of the theory of thermo field dynamics (TFD) is presented. TFD is introduced and developed by Umezawa and his coworkers at finite temperature. The most significant concept in TFD is that of a thermal vacuum which satisfies some conditions denoted as thermal state conditions. The TFD permits to reformulate theories at finite temperature. There is no need in an additional principle to determine particle distributions at T ≠ 0. Temperature and other macroscopic parameters are introduced in the definition of the vacuum state. All operator formalisms used in quantum field theory at T=0 are preserved, although the field degrees of freedom are doubled. 8 refs
Neutrix calculus and finite quantum field theory
International Nuclear Information System (INIS)
Ng, Y Jack; Dam, H van
2005-01-01
In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like quantum electrodynamics are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework. (letter to the editor)
Topics on field theories at finite temperature
International Nuclear Information System (INIS)
Eboli, O.J.P.
1985-01-01
The dynamics of a first order phase transition through the study of the decay rate of the false vacuum in the high temperature limit are analysed. An alternative approach to obtain the phase diagram of a field theory which is based on the study of the free energy of topological defects, is developed the behavior of coupling constants with the help of the Dyson-Schwinger equations at finite temperature, is evaluated. (author) [pt
Towers of Function Fields over Non-prime Finite Fields
DEFF Research Database (Denmark)
Bassa, Alp; Beelen, Peter; Garcia, Arnaldo
2015-01-01
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modu...
Blockspin transformations for finite temperature field theories with gauge fields
International Nuclear Information System (INIS)
Kerres, U.
1996-08-01
A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)
Finite field dependent mixed BRST transformation
International Nuclear Information System (INIS)
Upadhyay, Sudhaker; Mandal, Bhabani Prasad
2013-01-01
Joglekar and Mandal have generalized the usual Bechhi-Rouet-Stora-Tyutin (BRST) transformation by allowing infinitesimal BRST parameter finite and field dependent. Such a generalized BRST transformation (so-called FFBRST transformation) is also the symmetry of the effective action but not of the generating functional of the theory. We generalize the mixed BRST (sum of totally anti-commuting BRST and anti-BRST) symmetry transformation in same manner. We show that such a generalized mixed BRST transformation is the symmetry of the effective action as well as of the generating functional. We show our result by considering several explicit examples. (author)
Quantum fields at finite temperature and density
International Nuclear Information System (INIS)
Blaizot, J.P.
1991-01-01
These lectures are an elementary introduction to standard many-body techniques applied to the study of quantum fields at finite temperature and density: perturbative expansion, linear response theory, quasiparticles and their interactions, etc... We emphasize the usefulness of the imaginary time formalism in a wide class of problems, as opposed to many recent approaches based on real time. Properties of elementary excitations in an ultrarelativistic plasma at high temperature or chemical potential are discussed, and recent progresses in the study of the quark-gluon plasma are briefly reviewed
Socio-economic applications of finite state mean field games
Gomes, Diogo A.; Machado Velho, Roberto; Wolfram, Marie Therese
2014-01-01
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite
Algebraic complexities and algebraic curves over finite fields.
Chudnovsky, D V; Chudnovsky, G V
1987-04-01
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields.
Discrete phase space based on finite fields
International Nuclear Information System (INIS)
Gibbons, Kathleen S.; Hoffman, Matthew J.; Wootters, William K.
2004-01-01
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space
De Hon, B. P.; Arnold, J. M.
2016-01-01
Time-domain 3-D lattice Green's function (LGF) sequences can be evaluated using a single-lattice point recurrence scheme, and play an important role in finite-difference Green's function diakoptics. Asymptotically, at large distances, the LGFs in three dimensions can be described in terms of six
Towards an arithmetical logic the arithmetical foundations of logic
Gauthier, Yvon
2015-01-01
This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...
Wall deffects in field theories at finite temperature
International Nuclear Information System (INIS)
Bazeia Filho, D.
1985-01-01
We discuss the effect of restauration of simmetry in field theories at finite temperature and its relation with wall deffects which appear as consequence of the instability of the constant field configuration. (M.W.O.) [pt
Bergstra, J.A.; Middelburg, C.A.
2009-01-01
An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced by a division operation. In the spirit of Peacock's arithmetical algebra, we introduce variants of inversive and divisive meadows without an additive identity element and an additive inverse opera...
Field line diversion properties of finite β-helias equilibria
International Nuclear Information System (INIS)
Hayashi, Takaya; Schwenn, Ulrich; Strumberger, Erika.
1992-01-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite pressure equilibria. The results indicate that a divertor concept which has been developed from the diversion properties of the corresponding vacuum field can be maintained for finite pressure equilibria. Cross-field particle transport is simulated by a simplified scrape-off layer (SOL) model. (author)
Finite anticanonical transformations in field-antifield formalism
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A.; Tyutin, Igor V. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2015-06-15
We study the role of arbitrary (finite) anticanonical transformations in the field-antifield formalism and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered. (orig.)
Finite field-energy of a point charge in QED
International Nuclear Information System (INIS)
Costa, Caio V; Gitman, Dmitry M; Shabad, Anatoly E
2015-01-01
We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, to show that it possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy of a point elementary charge about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler–Heisenberg local Lagrangian in QED in powers of the field strength. (paper)
Supersymmetric field theories at finite temperature
International Nuclear Information System (INIS)
Dicus, D.A.; Tata, X.R.
1983-01-01
We show by explicit calculations to second and third order in perturbation theory, that finite temperature effects do not break the supersymmetry Ward-Takahashi identities of the Wess-Zumino model. Moreover, it is argued that this result is true to all orders in perturbation theory, and further, true for a wide class of supersymmetric theories. We point out, however, that these identities can be broken in the course of a phase transition that restores an originally broken internal symmetry
Compton scattering at finite temperature: thermal field dynamics approach
International Nuclear Information System (INIS)
Juraev, F.I.
2006-01-01
Full text: Compton scattering is a classical problem of quantum electrodynamics and has been studied in its early beginnings. Perturbation theory and Feynman diagram technique enables comprehensive analysis of this problem on the basis of which famous Klein-Nishina formula is obtained [1, 2]. In this work this problem is extended to the case of finite temperature. Finite-temperature effects in Compton scattering is of practical importance for various processes in relativistic thermal plasmas in astrophysics. Recently Compton effect have been explored using closed-time path formalism with temperature corrections estimated [3]. It was found that the thermal cross section can be larger than that for zero-temperature by several orders of magnitude for the high temperature realistic in astrophysics [3]. In our work we use a main tool to account finite-temperature effects, a real-time finite-temperature quantum field theory, so-called thermofield dynamics [4, 5]. Thermofield dynamics is a canonical formalism to explore field-theoretical processes at finite temperature. It consists of two steps, doubling of Fock space and Bogolyubov transformations. Doubling leads to appearing additional degrees of freedom, called tilded operators which together with usual field operators create so-called thermal doublet. Bogolyubov transformations make field operators temperature-dependent. Using this formalism we treat Compton scattering at finite temperature via replacing in transition amplitude zero-temperature propagators by finite-temperature ones. As a result finite-temperature extension of the Klein-Nishina formula is obtained in which differential cross section is represented as a sum of zero-temperature cross section and finite-temperature correction. The obtained result could be useful in quantum electrodynamics of lasers and for relativistic thermal plasma processes in astrophysics where correct account of finite-temperature effects is important. (author)
Field line diversion properties of finite β Helias equilibria
International Nuclear Information System (INIS)
Hayashi, T.; Schwenn, U.; Strumberger, E.
1992-03-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite β-equilibria. The results support a divertor concept which has been developed from the diversion properties of the corresponding vacuum field. Cross-field transport is simulated by a simplified scrape-off layer (SOL) model. (author)
Equations for arithmetic pointed tori
Sijsling, J.R.
2010-01-01
In 1983, Kisao Takeuchi enumerated all 71 arithmetic (1;e)-groups. This is a special set of discrete subgroups of SL(2,R) of finite covolume and signature (1;e). The corresponding quotients of the upper half plane (called (1;e)-curves) have genus equal to 1 and a single elliptic point of order e.
Uniqueness conditions for finitely dependent random fields
International Nuclear Information System (INIS)
Dobrushin, R.L.; Pecherski, E.A.
1981-01-01
The authors consider a random field for which uniqueness and some additional conditions guaranteeing that the correlations between the variables of the field decrease rapidly enough with the distance between the values of the parameter occur. The main result of the paper states that in such a case uniqueness is true for any other field with transition probabilities sufficiently close to those of the original field. Then they apply this result to some ''degenerate'' classes of random fields for which one can check this condition of correlation to decay, and thus obtain some new conditions of uniqueness. (Auth.)
Continuous time finite state mean field games
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Continuous Time Finite State Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Continuous Time Finite State Mean Field Games
International Nuclear Information System (INIS)
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games
Causality in finite temperature quantum field theory
International Nuclear Information System (INIS)
Paz, J.P.
1991-01-01
Some properties of various 'real time' formalisms are examined. The authors discuss conceptual (and sometimes very important) differences between the Niemi-Semmenoff method, the Closed Time Path formalism, and Thermo Field Dynamics. (author). 15 refs
Precise magnetostatic field using the finite element method
International Nuclear Information System (INIS)
Nascimento, Francisco Rogerio Teixeira do
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Galois towers over non-prime finite fields
DEFF Research Database (Denmark)
Bassa, Alp; Beelen, Peter; Garcia, Arnaldo
2014-01-01
In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field Fℓ; i.e., we construct sequences of function fields N=(N1⊂N2⊂⋯) over Fℓ of increasing genus, such that all the extensions Ni/N1 are Galois extensions and the number of rational places of these...
Local field in finite-size metamaterials
DEFF Research Database (Denmark)
Bordo, Vladimir
2018-01-01
The theory of the optical response of a metamaterial slab which is represented by metal nanoparticles embedded in a dielectric matrix is developed. It is demonstrated that the account of the reflections from the slab boundaries essentially modifies the local field in the slab and leads...
Adaptive finite-element ballooning analysis of bipolar ionized fields
International Nuclear Information System (INIS)
Al-Hamouz, Z.M.
1995-01-01
This paper presents an adaptive finite-element iterative method for the analysis of the ionized field around high-voltage bipolar direct-current (HVDC) transmission line conductors without resort to Deutsch's assumption. A new iterative finite-element ballooning technique is proposed to solve Poisson's equation wherein the commonly used artificial boundary around the transmission line conductors is simulated at infinity. Unlike all attempts reported in the literature for the solution of ionized field, the constancy of the conductors' surface field at the corona onset value is directly implemented in the finite-element formulation. In order to investigate the effectiveness of the proposed method, a laboratory model was built. It has been found that the calculated V-I characteristics and the ground-plane current density agreed well with those measured experimentally. The simplicity in computer programming in addition to the low number of iterations required to achieve convergence characterize this method of analysis
Universal conditions for finite renormalizable quantum field theories
International Nuclear Information System (INIS)
Kranner, G.
1990-10-01
Analyzing general renormalization constants in covariant gauge and minimal subtraction, we consider universal conditions for cancelling UV-divergences in renormalizable field theories with simple gauge groups, and give constructive methods for finding nonsupersymmetric finite models. The divergent parts of the renormalization constants for fields explicitly depend on the gauge parameter ξ. Finite theories simply need finite couplings. We show that respective FinitenessConditions imply a hierarchy, the center of which are the FCs for the gauge coupling g and the Yukawa couplings of the massless theory. To gain more information about F we analyze the Yukawa-FC in greater detail. Doing so algebraically, we find out and fix all inner symmetries. Additionally, Yuakawa-couplings must be invariant under gauge transformation. Then it becomes extremely difficult to obey a FC, yield rational numbers for F ∼ 1, and satisfy the factorization-condition, unless F = 1. The particular structure of the F = 1-system allows for a most general ansatz. We figure out the simplest case, getting precisely just couplings and particle content of a general N=1-supersymmetric theory. We list a class of roughly 4000 types of theories, containing all supersymmetric, completely finite, and many more finite theories as well. (Author, shortened by Quittner) 11 figs., 54 refs
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Socio-economic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese
2014-11-13
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Topics in quantum field theories at finite temperature
International Nuclear Information System (INIS)
Kao, Y.C.
1985-01-01
Studies on four topics in quantum field theories at finite temperature are presented in this thesis. In Chapter 1, it is shown that the chiral anomaly has no finite temperature corrections by Fujikawa's path integral approach. Chapter 2 deals with the chiral condensate in the finite temperature Schwinger model. The cluster decomposition property is employed to find . No finite critical temperature is found and the chiral condensate vanishes only at infinite temperature. In Chapter 3, the finite temperature behavior of the fermion-number breaking (Rubakov-Callan) condensate around a 't Hooft-Polyakov monopole is studied. It is found that the Rubakov-Callan condensate is suppressed exponentially from the monopole core at high temperature. The limitation of the techniques is understanding the behavior of the condensate for all temperature is also discussed. Chapter 4 is on the topological mass terms in (2 + 1)-dimensional gauge theories. The authors finds that if the gauge bosons have no topological mass at tree level, no topological mass induced radiatively up to two-loop order in either Abelian or non-Abelian theories with massive fermions. The Pauli-Villars regularization is used for fermion loops. The one-loop contributions to the topological mass terms at finite temperature are calculated and the quantization constraints in this case are discussed
Stochastic formulation of quantum field at finite temperature
International Nuclear Information System (INIS)
Lim, S.C.
1989-01-01
This paper reports that, based on an extension of the stochastic quantization method of Nelson, it is possible to obtain finite temperature fields in both the imaginary and real time formalisms which are usually quantized by using the functional integral technique
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
a class of finite fields, for odd primes l
Indian Academy of Sciences (India)
We see that the Fermat curves correspond precisely to those curves among each class (for = , 2), that are maximal or minimal over F q . We observe that each Fermat prime gives rise to explicit maximal and minimal curves over finite fields of characteristic 2. For = 2, we explicitly determine the -function(s) for this ...
A finite different field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL
A finite element field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
Finite-element-analysis of fields radiated from ICRF antenna
International Nuclear Information System (INIS)
Yamanaka, Kaoru; Sugihara, Ryo.
1984-04-01
In several simple geometries, electromagnetic fields radiated from a loop antenna, on which a current oscillately flows across the static magnetic field B-vector 0 , are calculated by the finite element method (FEM) as well as by analytic methods in a cross section of a plasma cylinder. A finite wave number along B-vector 0 is assumed. Good agreement between FEM and the analytic solutions is obtained, which indicates the accuracy of FEM solutions. The method is applied to calculations of fields from a half-turn antenna and reasonable results are obtained. It is found that a straightforward application of FEM to problems in an anisotropic medium may bring about erroneous results and that an appropriate coordinate transformation is needed for FEM to become applicable. (author)
Stochastic field theory and finite-temperature supersymmetry
International Nuclear Information System (INIS)
Ghosh, P.; Bandyopadhyay, P.
1988-01-01
The finite-temperature behavior of supersymmetry is considered from the viewpoint of stochastic field theory. To this end, it is considered that Nelson's stochastic mechanics may be generalized to the quantization of a Fermi field when the classical analog of such a field is taken to be a scalar nonlocal field where the internal space is anisotropic in nature such that when quantized this gives rise to two internal helicities corresponding to fermion and antifermion. Stochastic field theory at finite temperature is then formulated from stochastic mechanics which incorporates Brownian motion in the external space as well as in the internal space of a particle. It is shown that when the anisotropy of the internal space is suppressed so that the internal time ξ 0 vanishes and the internal space variables are integrated out one has supersymmetry at finite temperature. This result is true for T = 0, also. However, at this phase equilibrium will be destroyed. Thus for a random process van Hove's result involving quantum mechanical operators, i.e., that when supersymmetry remains unbroken at T = 0 it will also remain unbroken at Tnot =0, occurs. However, this formalism indicates that when at T = 0 broken supersymmetry results, supersymmetry may be restored at a critical temperature T/sub c/
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
the differential equation of the column displacement and the relevant boundarv conditions, it can be expected that the discretization of the flexibility field is preferable over the discretization of the stiffness field. Direct mechanical considerations support this expectation.Keywords: Random stiffness......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field...... variables. Several reported discretization methods define these random variables as integrals of the product of the field and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1999-01-01
the differential equation of the column displacement and the relevant boundary conditions, it can be expected that the discretization of the flexibility field is preferable over the discretization of the stiffness field. Direct mechanical considerations support this expectation. (C) 1998 Published by Elsevier......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field...... variables. Several reported discretization methods define these random variables as integrals of the product of the held and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...
Finite nucleus Dirac mean field theory and random phase approximation using finite B splines
International Nuclear Information System (INIS)
McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)
1989-01-01
We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results
Scattering amplitudes over finite fields and multivariate functional reconstruction
International Nuclear Information System (INIS)
Peraro, Tiziano
2016-01-01
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
Scattering amplitudes over finite fields and multivariate functional reconstruction
Energy Technology Data Exchange (ETDEWEB)
Peraro, Tiziano [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)
2016-12-07
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
[Acquisition of arithmetic knowledge].
Fayol, Michel
2008-01-01
The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).
Adelic divisors on arithmetic varieties
Moriwaki, Atsushi
2016-01-01
In this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors.
Finite field-dependent symmetries in perturbative quantum gravity
International Nuclear Information System (INIS)
Upadhyay, Sudhaker
2014-01-01
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Perturbative algebraic quantum field theory at finite temperature
International Nuclear Information System (INIS)
Lindner, Falk
2013-08-01
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Interpolation of the discrete logarithm in a finite field of characteristic two by Boolean functions
DEFF Research Database (Denmark)
Brandstaetter, Nina; Lange, Tanja; Winterhof, Arne
2005-01-01
We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic....
Finite element modeling of TFTR poloidal field coils
International Nuclear Information System (INIS)
Baumgartner, J.A.; O'Toole, J.A.
1986-01-01
The Tokamak Fusion Test Reactor (TFTR) Poloidal Field (PF) coils were originally analyzed to TFTR design conditions. The coils have been reanalyzed by PPPL and Grumman to determine operating limits under as-built conditions. Critical stress levels, based upon data obtained from the reanalysis of each PF coil, are needed for input to the TFTR simulation code algorithms. The primary objective regarding structural integrity has been to ascertain the magnitude and location of critical internal stresses in each PF coil due to various combinations of electromagnetic and thermally induced loads. For each PF coil, a global finite element model (FEM) of a coil sector is being analyzed to obtain the basic coil internal loads and displacements. Subsequent fine mesh local models of the coil lead stem and lead spur regions produce the magnitudes and locations of peak stresses. Each copper turn and its surrounding insulation are modeled using solid finite elements. The corresponding electromagnetic and thermal analyses are similarly modeled. A series of test beams were developed to determine the best combination of MSC/NASTRAN-type finite elements for use in PF coil analysis. The results of this analysis compare favorably with those obtained by the earlier analysis which was limited in scope
Finite field equation for asymptotically free phi4 theory
International Nuclear Information System (INIS)
Brandt, R.A.; Wing-chiu, N.; Wai-Bong, Y.
1979-01-01
We consider the finite local field equation - (D 7 Alembertian + m 2 ) phi (x) = lim/sub xitsarrow-rightts/0[1/6gZ (xi 2 ):phi (x - xi) phi (x) phi (x + xi):- Δ (xi 2 ) phi (x) + sigma (xi 2 )(xi x partial/sub x/) 2 phi (x)], which rigorously describes gphi 4 scalar field theory, and the operator-product expansion phi (xi) phi (0) /sup approximately/ /sub xitsarrow-rightts0/F (xi 2 ) N[phi 2 ], where N[phi 2 ] denotes a normal product. For g 2 ), Δ (xi 2 ), sigma (xi 2 ), and F (xi 2 ). We perform the R transformation phi (x) → phi (x) + r on the finite field equation and obtain the operator part of the change to be proportional to lim/sub xitsarrow-rightts0/Z (xi 2 ) F (xi 2 ) N[phi 2 ] which vanishes by our knowledge of the functions Z (xi 2 ) and F (xi 2 ). We have therefore verified rigorously the partial R invariance of - vertical-bargvertical-barphi 4 theory. We discuss and solve the technical problem of finding the solution for renormalization-group equations with a matrix γ function where the lowest-order expansions of the various elements do not begin with the same powers of g
Low-dimensional filiform Lie algebras over finite fields
Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vasek, Vladimir (Coordinador); Shmaliy, Yuriy S. (Coordinador); Trcek, Denis (Coordinador); Kobayashi, Nobuhiko P. (Coordinador); Choras, Ryszard S. (Coordinador); Klos, Zbigniew (Coordinador)
2011-01-01
In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5. Pl...
Accurate evaluation of exchange fields in finite element micromagnetic solvers
Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.
2012-04-01
Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.
Aspects of renormalization in finite-density field theory
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
2015-05-26
We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.
Electric field calculations in brain stimulation based on finite elements
DEFF Research Database (Denmark)
Windhoff, Mirko; Opitz, Alexander; Thielscher, Axel
2013-01-01
The need for realistic electric field calculations in human noninvasive brain stimulation is undisputed to more accurately determine the affected brain areas. However, using numerical techniques such as the finite element method (FEM) is methodologically complex, starting with the creation...... of accurate head models to the integration of the models in the numerical calculations. These problems substantially limit a more widespread application of numerical methods in brain stimulation up to now. We introduce an optimized processing pipeline allowing for the automatic generation of individualized...... the successful usage of the pipeline in six subjects, including field calculations for transcranial magnetic stimulation and transcranial direct current stimulation. The quality of the head volume meshes is validated both in terms of capturing the underlying anatomy and of the well-shapedness of the mesh...
Primary decomposition of zero-dimensional ideals over finite fields
Gao, Shuhong; Wan, Daqing; Wang, Mingsheng
2009-03-01
A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp's algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Groebner basis structure can be used to get partial primary decomposition without any root finding.
Reversible arithmetic logic unit for quantum arithmetic
DEFF Research Database (Denmark)
Thomsen, Michael Kirkedal; Glück, Robert; Axelsen, Holger Bock
2010-01-01
This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic...... and logical operations in one unit. Combined with a suitable control unit, the ALU permits the construction of an r-Turing complete computing device. The garbage-free ALU developed in this communication requires only 6n elementary reversible gates for five basic arithmetic-logical operations on two n......-bit operands and does not use ancillae. This remarkable low resource consumption was achieved by generalizing the V-shape design first introduced for quantum ripple-carry adders and nesting multiple V-shapes in a novel integrated design. This communication shows that the realization of an efficient reversible...
STAR/SVT alignment within a finite magnetic field
International Nuclear Information System (INIS)
Barannikova, O.Yu.; Belaga, V.V.; Ososkov, G.A.; Panebrattsev, Yu.A.; Bellweid, R.K.; Pruneau, C.A.; Wilson, W.K.
1999-01-01
We report on the development of SVT (Silicon Vertex Tracker) software for the purpose of the SVT and TPC (Time Projection Chamber) relative alignment as well as the internal alignment of the SVT components. The alignment procedure described complements the internal SVT alignment procedure discussed in Star Note 356. It involves track reconstruction in both the Star TPC and SVT for the calibration of the SVT geometry in the presence of a finite magnetic field. This new software has been integrated under the package SAL already running under STAR. Both the implementation and the performance of the alignment algorithm are described. We find that the current software implementation in SAL should enable a very satisfactory internal SVT alignment as well as an excellent SVT to TPC relative alignment
Development of arithmetical abilities
Directory of Open Access Journals (Sweden)
Tatjana Levstek
2014-02-01
Full Text Available Arithmetic (from the word 'arithmos' which means 'numbers' is an elementary branch of mathematics. Numeracy is essential for understanding mathematics, so the development of arithmetic abilities has been an area of scientific research for a long time. Recent research has shown that the development of arithmetic abilities is not based only on gaining experience and learning. Some arithmetic abilities, especially the sense of quantity, are innate. Even babies are able to distinguish between groups with different number of elements and they perceive numeracy amodally. Six-month-olds distinguish between two groups with the numeracy ratio of 1 : 2. With age this ratio improves rapidly. Five-year-old children already distinguish between groups with the number ratio 7 : 8. The ability to compare two quantities begins to develop after 15 months of age and children learn how to count spontaneously, together with the acquisition of language. Speech enables children to understand number in its abstract, symbolic sense, thus opening the way to symbolic arithmetic. During the preschool period children use intuition when doing calculations, but in school the arithmetic is based on the knowledge of arithmetical algorithms. So, in order to acquire mathematical knowledge, it is necessary to incorporate memory and automate arithmetical processes, without the use of intuition. However, research has shown that intuition is very important and is even a predictive factor for the development of mathematical abilities throughout the schooling process.
Curiosities of arithmetic gases
International Nuclear Information System (INIS)
Bakas, I.; Bowick, M.J.
1991-01-01
Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for boson-parafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail
Oscillations of the static meson fields at finite baryon density
International Nuclear Information System (INIS)
Florkowski, W.; Friman, B.; Technische Hochschule Darmstadt
1996-04-01
The spatial dependence of static meson correlation functions at finite baryon density is studied in the Nambu-Jona-Lasinio model. In contrast to the finite temperature case, we find that the correlation functions at finite density are not screened but exhibit long-range oscillations. The observed phenomenon is analogous to the Friedel oscillations in a degenerate electron gas. (orig.)
Guest Editors' Introduction: Special Section on Computer Arithmetic
DEFF Research Database (Denmark)
Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter
2014-01-01
and their subsequent testing and verification. Many practitioners of the field also focus on the art and science of using computer arithmetic to carry out scientific and engineering computations. Computer arithmetic is therefore an interdisciplinary field that draws upon mathematics, computer science and electrical......The articles in this special issue focus on current trends and developments in the field of computer arithmetic. This is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations...
Finite element solution of quasistationary nonlinear magnetic field
International Nuclear Information System (INIS)
Zlamal, Milos
1982-01-01
The computation of quasistationary nonlinear two-dimensional magnetic field leads to the following problem. There is given a bounded domain OMEGA and an open nonempty set R included in OMEGA. We are looking for the magnetic vector potential u(x 1 , x 2 , t) which satisifies: 1) a certain nonlinear parabolic equation and an initial condition in R: 2) a nonlinear elliptic equation in S = OMEGA - R which is the stationary case of the above mentioned parabolic equation; 3) a boundary condition on delta OMEGA; 4) u as well as its conormal derivative are continuous accross the common boundary of R and S. This problem is formulated in two equivalent abstract ways. There is constructed an approximate solution completely discretized in space by a generalized Galerkin method (straight finite elements are a special case) and by backward A-stable differentiation methods in time. Existence and uniqueness of a weak solution is proved as well as a weak and strong convergence of the approximate solution to this solution. There are also derived error bounds for the solution of the two-dimensional nonlinear magnetic field equations under the assumption that the exact solution is sufficiently smooth
Oscillations of the static meson fields at finite baryon density
International Nuclear Information System (INIS)
Florkowski, W.; Friman, B.; Technische Hochschule Darmstadt
1996-04-01
The spatial dependence of static meson correlation functions at finite baryon density is studied in the Nambu-Jona-Lasinio model. In contrast to the finite temperature case, we find that the correlation functions at finite density are not screened but exhibit long-range oscillations. The observed phenomenon is analogous to the Friedel oscillations in a degenerate electron gas. (author). 19 refs, 6 figs
Pavlichin, Dmitri S.; Mabuchi, Hideo
2014-06-01
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.
Finite field equation of Yang--Mills theory
International Nuclear Information System (INIS)
Brandt, R.A.; Wing-Chiu, N.; Yeung, W.
1980-01-01
We consider the finite local field equation -][1+1/α (1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 N[A/sup c/νA/sup a/μA/sub ν//sup c/] +xxx+(1-s) 2 M 2 A/sup a/μ, introduced by Lowenstein to rigorously describe SU(2) Yang--Mills theory, which is written in terms of normal products. We also consider the operator product expansion A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) approx.ΣM/sup c/abνμlambda/sub c/'a'b'ν'μ'lambda' (xi) N[A/sup nuprimec/'A/sup muprimea/'A/sup lambdaprimeb/'](x), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M/sup ...//sub .../(xi) with the help of a computer, and express the normal products in the field equation in terms of products of the c-number Wilson coefficients and of operator products like A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) at separated points. Our result is -][1+(1/α)(1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 lim/sub xiarrow-right0/] (lnxi)/sup -0.28/2b/[A/sup c/ν (x+xi) A/sup a/μ(x) A/sub ν//sup c/(x-xi) +epsilon/sup a/bcA/sup muc/(x+xi) partial/sup ν/A/sup b//sub ν/(x)+xxx] +xxx]+(1-s) 2 M 2 A/sup a/μ, where β (g) =-bg 3 , and so (lnxi)/sup -0.28/2b/ is the leading behavior of the c-number coefficient multiplying the operator products in the field equation
Kou, Jisheng; Sun, Shuyu
2017-01-01
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated
Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws
Chen, Gui-Qiang; Torres, Monica
2005-02-01
Divergence-measure fields in L∞ over sets of finite perimeter are analyzed. A notion of normal traces over boundaries of sets of finite perimeter is introduced, and the Gauss-Green formula over sets of finite perimeter is established for divergence-measure fields in L∞. The normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak-star limit of the normal traces introduced in Chen & Frid [6] over the Lipschitz deformation surfaces, which implies their consistency. As a corollary, an extension theorem of divergence-measure fields in L∞ over sets of finite perimeter is also established. Then we apply the theory to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.
How to use the Fast Fourier Transform in Large Finite Fields
Petersen, Petur Birgir
2011-01-01
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
Kou, Jisheng
2017-06-09
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.
International Nuclear Information System (INIS)
Naik, S.
1990-01-01
We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data. (orig.)
General renormalized statistical approach with finite cross-field correlations
International Nuclear Information System (INIS)
Vakulenko, M.O.
1992-01-01
The renormalized statistical approach is proposed, accounting for finite correlations of potential and magnetic fluctuations. It may be used for analysis of a wide class of nonlinear model equations describing the cross-correlated plasma states. The influence of a cross spectrum on stationary potential and magnetic ones is investigated. 10 refs. (author)
a constructive approach to the finite wavelet frames over prime fields
Indian Academy of Sciences (India)
6
The motivation of this paper is to establish an alternative constructive formulation for the wavelet coefficients of finite ... is a |G|-dimensional vector space with complex vector entries indexed by elements in the finite group G. The inner product of x,y ∈ CG is defined by .... Construction of Wavelet Frames over Prime Fields.
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
Discrete finite nilpotent Lie analogs: New models for unified gauge field theory
International Nuclear Information System (INIS)
Kornacker, K.
1978-01-01
To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-01-01
-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose
Discontinuities of Green functions in field theory at finite temperature and density
International Nuclear Information System (INIS)
Kobes, R.L.; Semenoff, G.W.
1985-01-01
We derive systematic rules for calculating the imaginary parts of Minkowski space Green functions in quantum field theory at finite temperature and density. Self-energy corrections are used as an example of the application of these rules. (orig.)
Some properties of generalized self-reciprocal polynomials over finite fields
Directory of Open Access Journals (Sweden)
Ryul Kim
2014-07-01
Full Text Available Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynomials over finite fields of odd characteristic.
The Use of Finite Fields and Rings to Compute Convolutions
1975-06-06
showed in Ref. 1 that the convolution of two finite sequences of integers (a, ) and (b, ) for k = 1, 2, . . ., d can be obtained as the inverse transform of...since the T.’S are all distinct. Thus T~ exists and (7) can be solved as a = T A the inverse " transform . Next let us impose on (7) the...the inverse transform d-1 Cn= (d) I Cka k=0 If an a can be found so that multiplications by powers of a are simple in hardware, the
Non-commutative arithmetic circuits with division
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Wigderson, A.
2015-01-01
Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/
Model Theory in Algebra, Analysis and Arithmetic
Dries, Lou; Macpherson, H Dugald; Pillay, Anand; Toffalori, Carlo; Wilkie, Alex J
2014-01-01
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
International Nuclear Information System (INIS)
Mukhanov, O.A.; Rylov, S.V.; Semenov, V.K.; Vyshenskii, S.V.
1989-01-01
Several ways of local timing of the Josephson-junction RSFQ (Rapid Single Flux Quantum) logic elements are proposed, and their peculiarities are discussed. Several examples of serial and parallel pipelined arithmetic blocks using various types of timing are suggested and their possible performance is discussed. Serial devices enable one to perform n-bit functions relatively slowly but using integrated circuits of a moderate integration scale, while parallel pipelined devices are more hardware-wasteful but promise extremely high productivity
Arithmetic of Complex Manifolds
Lange, Herbert
1989-01-01
It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms. In recent years such problems, which are simultaneously of arithmetic and geometric interest, have become increasingly important. This proceedings volume contains 12 original research papers. Its main topics are theta functions, modular forms, abelian varieties and algebraic three-folds.
Statistics about elliptic curves over finite prime fields
Gekeler, Ernst-Ulrich
2006-01-01
We derive formulas for the probabilities of various properties (cyclicity, squarefreeness, generation by random points) of the point groups of randomly chosen elliptic curves over random prime fields.
Ab initio molecular dynamics in a finite homogeneous electric field.
Umari, P; Pasquarello, Alfredo
2002-10-07
We treat homogeneous electric fields within density functional calculations with periodic boundary conditions. A nonlocal energy functional depending on the applied field is used within an ab initio molecular dynamics scheme. The reliability of the method is demonstrated in the case of bulk MgO for the Born effective charges, and the high- and low-frequency dielectric constants. We evaluate the static dielectric constant by performing a damped molecular dynamics in an electric field and avoiding the calculation of the dynamical matrix. Application of this method to vitreous silica shows good agreement with experiment and illustrates its potential for systems of large size.
Finite element electromagnetic field computation on the Sequent Symmetry 81 parallel computer
International Nuclear Information System (INIS)
Ratnajeevan, S.; Hoole, H.
1990-01-01
Finite element field analysis algorithms lend themselves to parallelization and this fact is exploited in this paper to implement a finite element analysis program for electromagnetic field computation on the Sequent Symmetry 81 parallel computer with three processors. In terms of waiting time, the maximum gains are to be made in matrix solution and therefore this paper concentrates on the gains in parallelizing the solution part of finite element analysis. An outline of how parallelization could be exploited in most finite element operations is given in this paper although the actual implemention of parallelism on the Sequent Symmetry 81 parallel computer was in sparsity computation, matrix assembly and the matrix solution areas. In all cases, the algorithms were modified suit the parallel programming application rather than allowing the compiler to parallelize on existing algorithms
Ballet, Stéphane; Baudru, Nicolas; Bonnecaze, Alexis; Tukumuli, Mila
2016-01-01
The Chudnovsky and Chudnovsky algorithm for the multiplication in extensions of finite fields provides a bilinear complexity which is uniformly linear whith respect to the degree of the extension. Recently, Randriambololona has generalized the method, allowing asymmetry in the interpolation procedure and leading to new upper bounds on the bilinear complexity. We describe the effective algorithm of this asymmetric method, without derivated evaluation. Finally, we give examples with the finite ...
Arithmetic groups and their generalizations what, why, and how
Ji, Lizhen
2010-01-01
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \\mathbf{Z} or \\mathrm{SL}(n,\\mathbf{Z}). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics.
Thermoelectric conductivities at finite magnetic field and the Nernst effect
International Nuclear Information System (INIS)
Kim, Keun-Young; Kim, Kyung Kiu; Seo, Yunseok; Sin, Sang-Jin
2015-01-01
We study the thermoelectric conductivities of a strongly correlated system in the presence of a magnetic field by the gauge/gravity duality. We consider a class of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum relaxation. General analytic formulas for the direct current (DC) conductivities and the Nernst signal are derived in terms of the black hole horizon data. For an explicit model study, we analyse in detail the dyonic black hole modified by momentum relaxation. In this model, for small momentum relaxation, the Nernst signal shows a bell-shaped dependence on the magnetic field, which is a feature of the normal phase of cuprates. We compute all alternating current (AC) electric, thermoelectric, and thermal conductivities by numerical analysis and confirm that their zero frequency limits precisely reproduce our analytic DC formulas, which is a non-trivial consistency check of our methods. We discuss the momentum relaxation effects on the conductivities including cyclotron resonance poles.
Arithmetic circuits for DSP applications
Stouraitis, Thanos
2017-01-01
Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review o circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look ...
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
1977-01-01
An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
International Nuclear Information System (INIS)
Vlad, M.; Spineanu, F.; Misguich, J.H.; Balescu, R.
2001-01-01
Particle diffusion in a given electrostatic turbulence with a finite correlation length along the confining magnetic field is studied in the test particle approach. An anomalous diffusion regime of amplified diffusion coefficients is found in the conditions when particle trapping in the structure of the stochastic potential is effective. The auto-generated radial electric field is calculated. (author)
Sets with Prescribed Arithmetic Densities
Czech Academy of Sciences Publication Activity Database
Luca, F.; Pomerance, C.; Porubský, Štefan
2008-01-01
Roč. 3, č. 2 (2008), s. 67-80 ISSN 1336-913X R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : generalized arithmetic density * generalized asymptotic density * generalized logarithmic density * arithmetical semigroup * weighted arithmetic mean * ratio set * R-dense set * Axiom A * delta-regularly varying function Subject RIV: BA - General Mathematics
Digital Arithmetic: Division Algorithms
DEFF Research Database (Denmark)
Montuschi, Paolo; Nannarelli, Alberto
2017-01-01
Division is one of the basic arithmetic operations supported by every computer system. The operation can be performed and implemented by either hardware or software, or by a combination of the two. Although division is not as frequent as addition and multiplication, nowadays, most processors impl...... significant hardware resources and is more suitable for software implementation on the existing multiply units. The purpose of this entry is to provide an introductory survey using a presentation style suitable for the interested non-specialist readers as well....
Introduction to cardinal arithmetic
Holz, M; Weitz, E
1999-01-01
This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.Reviews:'The authors aim their text at beginners in set theory. They start
2d Model Field Theories at Finite Temperature and Density
Schoen, Verena; Thies, Michael
2000-01-01
In certain 1+1 dimensional field theoretic toy models, one can go all the way from microscopic quarks via the hadron spectrum to the properties of hot and dense baryonic matter in an essentially analytic way. This "miracle" is illustrated through case studies of two popular large N models, the Gross-Neveu and the 't Hooft model - caricatures of the Nambu-Jona-Lasinio model and real QCD, respectively. The main emphasis will be on aspects related to spontaneous symmetry breaking (discrete or co...
Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics
International Nuclear Information System (INIS)
Kobayashi, K.; Yamanaka, Y.
2011-01-01
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schroedinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature. -- Highlights: → Utilizing TFD, we extend Nelson's stochastic method to finite temperature. → We introduce stochastic equations for tilde and non-tilde particles. → Our stochastic equations can reproduce the TFD-type Schroedinger equation. → Our formalism satisfies the uncertainly relation at finite temperature.
Relativistic Chiral Mean Field Model for Finite Nuclei
Ogawa, Y.; Toki, H.; Tamenaga, S.; Haga, A.
2009-08-01
We present a relativistic chiral mean field (RCMF) model, which is a method for the proper treatment of pion-exchange interaction in the nuclear many-body problem. There the dominant term of the pionic correlation is expressed in two-particle two-hole (2p-2h) states with particle-holes having pionic quantum number, J^{π}. The charge-and-parity-projected relativistic mean field (CPPRMF) model developed so far treats surface properties of pionic correlation in 2p-2h states with J^{π} = 0^{-} (spherical ansatz). We extend the CPPRMF model by taking 2p-2h states with higher spin quantum numbers, J^{π} = 1^{+}, 2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He nucleus as a pilot calculation for the study of medium and heavy nuclei. We study the behavior of energy convergence with the pionic quantum number, J^{π}, and find convergence around J^{π}_{max} = 6^{-}. We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. The energy contribution of about 50% of the net two-body interaction comes from the tensor part and 20% comes from the spin-spin central part of the pion-exchange interaction.}
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.; Gomes, Diogo A.
2014-01-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
Finite size and dynamical effects in pair production by an external field
International Nuclear Information System (INIS)
Martin, C.; Vautherin, D.
1988-12-01
We evaluate the rate of pair production in a uniform electric field confined into a bounded region in space. Using the Balian-Bloch expansion of Green's functions we obtain explicit expressions for finite size corrections to Schwinger's formula. The case of a time-dependent boundary, relevant to describe energy deposition by quark-antiquark pair production in ultrarelativistic collisions, is also investigated. We find that finite size effects are important in nuclear collisions. They decrease when the strength of the chromo-electric field between the nuclei is large. As a result, the rate of energy deposition increases sharply with the mass number A of the colliding nuclei
Reversed-field pinch configuration with minimum energy and finite beta
International Nuclear Information System (INIS)
Zhang Peng
1989-01-01
The reversed-field pinch (RFP) configuration has been studied for the case of finite beta. Suydam's condition and the sufficient criterion have been used to examine this configuration. Results of numerical calculations show that the critical value of the pinch parameter Θ for the appearance of the reverse toroidal field increases as the β-value increases. The critical value of Θ for the helical state increases with β as well. Suydam's and Robinson's stability regions increase and shift towards higher values of Θ with increasing β. Theoretical results for finite β coincide with recent RFP experimental results
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
A Unified Formal Description of Arithmetic and Set Theoretical Data Types
Tarau, Paul
2010-01-01
We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The s...
Conceptual Knowledge of Fraction Arithmetic
Siegler, Robert S.; Lortie-Forgues, Hugues
2015-01-01
Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…
Conceptual Knowledge of Decimal Arithmetic
Lortie-Forgues, Hugues; Siegler, Robert S.
2017-01-01
In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…
Arithmetic soft-core accelerators
Calderon Rocabado, D.R.H.
2007-01-01
In this dissertation, we address the design of multi-functional arithmetic units working with the most common fixed-point number representations, namely: unsigned, sign-magnitude, fractional, ten's and two's complement notations. The main design goal is to collapse multiple complex arithmetic
Fedorenko, Sergei V.
2011-01-01
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.
Thermodynamics and CP-odd transport in holographic QCD with finite magnetic field
Energy Technology Data Exchange (ETDEWEB)
Drwenski, Tara; Gürsoy, Umut [Institute for Theoretical Physics, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Iatrakis, Ioannis [Department of Physics and Astronomy, Stony Brook University,Stony Brook, New York 11794-3800 (United States)
2016-12-13
We consider a bottom-up holographic model of QCD at finite temperature T and magnetic field B, and study dependence of thermodynamics and CP-odd transport on these variables. As the magnetic field couples to the flavor sector only, one should take the Veneziano limit where the number of flavors and colors are large while their ratio is kept fixed. We investigate the corresponding holographic background in the approximation where the ratio of flavors to colors is finite but small. We demonstrate that B-dependence of the entropy of QCD is in qualitative agreement with the recent lattice studies. Finally we study the CP-odd transport properties of this system. In particular, we determine the Chern-Simons decay rate at finite B and T, that is an important ingredient in the Chiral Magnetic Effect.
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.; Fradkin, E.S.
1987-01-01
A generating functional for expectation values is found for QED at a finite temperature with an external field which destroys the stability of the vacuum. The equations for connected Green functions and the effective action for the mean field are written out. Their representation is obtained in the form of an integral over the proper time for the Green function taking into account temperature effects in a constant uniform field. By means of this representation the polarization operator for the mean field in an external constant uniform field has been calculated
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.; Fradkin, E.S.
1987-01-01
A functional generating expectation values is obtained for QED at a finite temperature in presence of an external field violating the vacuum stability. Equations for connected Green's functions and the effective action for the mean field are derived. The Green function is obtained as an integral with respect of the proper time; the representation takes into account temperature effects in a constant homogeneous field. The polarization operator for the mean field in an external constant homogeneous field is calculated by means of the integral representation
Detailed balance principle and finite-difference stochastic equation in a field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
A finite-difference equation, which is a generalization of the Langevin equation in field theory, has been obtained basing upon the principle of detailed balance for the Markov chain. Advantages of the present approach as compared with the conventional Parisi-Wu method are shown for examples of an exactly solvable problem of zero-dimensional quantum theory and a simple numerical simulation
International Nuclear Information System (INIS)
Benasser Algehawi, Mohammed; Samsudin, Azman
2010-01-01
We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields Z p . Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over Z p . The proposed system is applicable, secure, and reliable.
Photon polarization tensor in the light front field theory at zero and finite temperatures
International Nuclear Information System (INIS)
Silva, Charles da Rocha; Perez, Silvana; Strauss, Stefan
2012-01-01
Full text: In recent years, light front quantized field theories have been successfully generalized to finite temperature. The light front frame was introduced by Dirac , and the quantization of field theories on the null-plane has found applications in many branches of physics. In order to obtain the thermal contribution, we consider the hard thermal loop approximation. This technique was developed by Braaten and Pisarski for the thermal quantum field theory at equal times and is particularly useful to extract the leading thermal contributions to the amplitudes in perturbative quantum field theories. In this work, we consider the light front quantum electrodynamics in (3+1) dimensions and evaluate the photon polarization tensor at one loop for both zero and finite temperatures. In the first case, we apply the dimensional regularization method to extract the finite contribution and find the transverse structure for the amplitude in terms of the light front coordinates. The result agrees with one-loop covariant calculation. For the thermal corrections, we generalize the hard thermal loop approximation to the light front and calculate the dominant temperature contribution to the polarization tensor, consistent with the Ward identity. In both zero as well as finite temperature calculations, we use the oblique light front coordinates. (author)
Principle of detailed balance and the finite-difference stochastic equation in field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
The principle of detailed balance for the Markov chain is used to obtain a finite-difference equation which generalizes the Langevin equation in field theory. The advantages of using this approach compared to the conventional Parisi-Wu method are demonstrated for the examples of an exactly solvable problem in zero-dimensional quantum theory and a simple numerical simulation
Mean-field theory of spin-glasses with finite coordination number
Kanter, I.; Sompolinsky, H.
1987-01-01
The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
Static, self-dual, finite action SU(3) gauge fields in the de Sitter space
International Nuclear Information System (INIS)
Chakrabarti, A.; Comtet, A.; Viswanathan, K.S.; Simon Fraser Univ., Burnaby, British Columbia
1980-01-01
Static, self-dual, finite action SU(3) gauge fields are constructed on the euclidean section of the positive curvature de Sitter metric with periodic time. Their relation to known time dependent flat space solutions is pointed out. Their significances and possible applications are indicated. (orig.)
Normal forms of invariant vector fields under a finite group action
International Nuclear Information System (INIS)
Sanchez Bringas, F.
1992-07-01
Let Γ be a finite subgroup of GL(n,C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in C n . We prove a theorem of invariant conjugation to a normal form and linearization for the subspace of invariant elements and we give a description of these normal forms in dimension n=2. (author)
A finite element method for calculating the 3-dimensional magnetic fields of cyclotron
International Nuclear Information System (INIS)
Zhao Xiaofeng
1986-01-01
A series of formula of the finite element method (scalar potential) for calculating the three-dimensional magnetic field of the main magnet of a sector focused cyclotron, and the realization method of the periodic boundary conditions in the code are given
On the multiplicative order of elements in Wiedemann's towers of finite fields
Directory of Open Access Journals (Sweden)
R. Popovych
2016-01-01
Full Text Available We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} $, $i\\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} $.
A stochastic-field description of finite-size spiking neural networks.
Dumont, Grégory; Payeur, Alexandre; Longtin, André
2017-08-01
Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity-the density of active neurons per unit time-is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.
Modelling arithmetic operations
Energy Technology Data Exchange (ETDEWEB)
Shabanov-kushnarenk, Yu P
1981-01-01
The possibility of modelling finite alphabetic operators using formal intelligence theory, is explored, with the setting up of models of a 3-digit adder and a multidigit subtractor, as examples. 2 references.
International Nuclear Information System (INIS)
Li Bihong; Shuang Na; Liu Qingcheng
2006-01-01
The principle of finite difference method is introduced, and the radon field distribution over sandstone-type uranium deposit is narrated. The radon field distribution theory equation is established. To solve radon field distribution equation using finite difference algorithm is to provide the value computational method for forward calculation about radon field over sandstone-type uranium mine. Study on 2-D finite difference method on the center of either high anomaly radon fields in view of the character of radon field over sandstone-type uranium provide an algorithm for further research. (authors)
Alfven-wave particle interaction in finite-dimensional self-consistent field model
International Nuclear Information System (INIS)
Padhye, N.; Horton, W.
1998-01-01
A low-dimensional Hamiltonian model is derived for the acceleration of ions in finite amplitude Alfven waves in a finite pressure plasma sheet. The reduced low-dimensional wave-particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self-consistent fields within the envelope approximation. As an example, the authors show for a single Alfven wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons
Kosevich, Yuriy A; Gann, Vladimir V
2013-06-19
We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.
International Nuclear Information System (INIS)
Kosevich, Yuriy A; Gann, Vladimir V
2013-01-01
We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier–Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier–Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier–Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier–Zeeman states. (paper)
Arithmetic the foundation of mathematics
2015-01-01
Arithmetic factors into our lives on a daily basis, so it's hard to imagine a world without the six basic operations: addition, subtraction, multiplication, division, raising to powers, and finding roots. Readers will get a solid overview of arithmetic, while offering useful examples of how they are used in routine activities, such as social media applications. It reinforces Common Core math standards, including understanding basic math concepts and how they apply to students' daily lives and challenges. A history of arithmetic helps provide a contextual framework for the course of its develop
The weight hierarchies and chain condition of a class of codes from varieties over finite fields
Wu, Xinen; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.
On identities of free finitely generated alternative algebras over a field of characteristic 3
International Nuclear Information System (INIS)
Pchelintsev, S V
2001-01-01
In 1981 Filippov solved in the affirmative Shestakov's problem on the strictness of the inclusions in the chains of varieties generated by free alternative and Mal'cev algebras of finite rank over a field of characteristic distinct from 2 and 3. In the present paper an analogous result is proved for alternative algebras over a field of characteristic 3. The proof is based on the construction of three families of identities that hold on the algebras of the corresponding rank. A disproof of the identities on algebras of larger rank is carried out with the help of a prime commutative alternative algebra. It is also proved that in varieties of alternative algebras of finite basis rank over a field of characteristic 3 every soluble algebra is nilpotent
Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE
Nelson, Eric M
2005-01-01
We have recently implemented a prototype 3d self magnetic field solver in the finite-element gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curl-curl formulation of the finite-element method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe.
Thermo field dynamics in the treatment of the nuclear pairing problem at finite temperature
International Nuclear Information System (INIS)
Civitarese, O.; DePaoli, A.L.
1993-01-01
The use of the thermo field dynamics, in dealing with the study of nuclear properties at finite temperature, is discussed for the case of a nuclear Hamiltonian which includes a single-particle term and a monopole pairing residual two-body interaction. The rules of the thermo fields dynamics are applied to double the Hilbert space, thus accounting for the thermal occupation of single-particle states, and to construct dual spaces, both for single-particle (BCS) and collective (RPA) degrees of freedom. It is shown that the rules of the thermo field dynamics yield to a temperature dependence of the equations describing quasiparticle and phonon excitations which is similar to the one found in the more conventional finite temperature Wick's theorem approach, namely: By dealing with thermal averages. (orig.)
Lógica y Pensamiento Aritmético (Logic and Arithmetic Thinking
Directory of Open Access Journals (Sweden)
Alfonso Ortiz
2009-01-01
Full Text Available Presentamos los resultados obtenidos en una prueba sobre razonamiento inductivo numérico finito y unas entrevistas clínicas posteriores realizadas a escolares de educación primaria. La primera fue respondida por 400 escolares. Con base en los resultados obtenidos, se seleccionaron 28 alumnos para realizarles entrevistas clínicas individualizadas con el fin de determinar la evolución de las relaciones lógicas que estos escolares pueden establecer en el campo de los números naturales finitos. El origen de este estudio está en problemas históricos sobre los fundamentos lógicos de la aritmética. Buscamos determinar de forma empírica hasta qué punto la lógica juega un papel determinante en el origen de la aritmética o, por el contrario, si los orígenes de la lógica están predeterminados por la aritmética y otros conocimientos. We present the results of two tests performed by primary school students. The first one was on finite numeric inductive reasoning and was performed by 400 students. According to its results, we selected 28 students to whom we clinically interviewed aiming to determine the evolution of the logic relations that they can establish in the field of finite natural numbers. This study originates on historic problems of the logical foundation of arithmetic. We aim to empirically determine the extent to which logic plays a key role in the origin of arithmetic or, on the contrary, if the origins of logic are predetermined by arithmetic and other fields.
Dispersion relation and growth rate in a Cherenkov free electron laser: Finite axial magnetic field
International Nuclear Information System (INIS)
Kheiri, Golshad; Esmaeilzadeh, Mahdi
2013-01-01
A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread
On the stress calculation within phase-field approaches: a model for finite deformations
Schneider, Daniel; Schwab, Felix; Schoof, Ephraim; Reiter, Andreas; Herrmann, Christoph; Selzer, Michael; Böhlke, Thomas; Nestler, Britta
2017-08-01
Numerical simulations based on phase-field methods are indispensable in order to investigate interesting and important phenomena in the evolution of microstructures. Microscopic phase transitions are highly affected by mechanical driving forces and therefore the accurate calculation of the stresses in the transition region is essential. We present a method for stress calculations within the phase-field framework, which satisfies the mechanical jump conditions corresponding to sharp interfaces, although the sharp interface is represented as a volumetric region using the phase-field approach. This model is formulated for finite deformations, is independent of constitutive laws, and allows using any type of phase inherent inelastic strains.
DEFF Research Database (Denmark)
Cai, Hongzhu; Čuma, Martin; Zhdanov, Michael
2015-01-01
This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom signific......This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom...... significantly. The linear system of finite element equations is solved using parallel direct solvers which are robust for ill-conditioned systems and efficient for multiple source electromagnetic (EM) modeling. We also introduce a novel approach to compute the scalar components of the electric field from...... the tangential components along each edge based on field redatuming. The method can produce a more accurate result as compared to conventional approach. We have applied the developed algorithm to compute the EM response for a typical 3D anisotropic geoelectrical model of the off-shore HC reservoir with complex...
If Gravity is Geometry, is Dark Energy just Arithmetic?
Czachor, Marek
2017-04-01
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R+4 and (- L/2, L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a miss-match between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.
Neutron-skin thickness of finite nuclei in relativistic mean-field models with chiral limits
International Nuclear Information System (INIS)
Jiang Weizhou; Li Baoan; Chen Liewen
2007-01-01
We study several structure properties of finite nuclei using relativistic mean-field Lagrangians constructed according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities. The models are consistent with current experimental constraints for the equations of state of symmetric matter at both normal and supranormal densities and of asymmetric matter at subsaturation densities. It is shown that these models can successfully describe the binding energies and charge radii of finite nuclei. Compared to calculations with usual relativistic mean-field models, these models give a reduced thickness of neutron skin in 208 Pb between 0.17 fm and 0.21 fm. The reduction of the predicted neutron skin thickness is found to be due to not only the softening of the symmetry energy but also the scaling property of ρ meson required by the partial restoration of chiral symmetry
Finite element analysis on the electromagnetic fields of active magnetic bearing
Energy Technology Data Exchange (ETDEWEB)
Ren, S; Liu, J [School of Mechanical Engineering, Shenyang Ligong University, Shenyang, 110168 (China); Bian, C [Institute of Information Science and Engineering, Northeastern University, Shenyang, 110004 (China)], E-mail: renshy@sina.com
2008-02-15
To increase the carrying capacity and reduce the weight and size of AMBs, it is necessary to use a ferromagnetic material with high magnetic flux density, which can make AMBs run in the nonlinear region. The simple linear model before is not gratifying, so some more precise analysis methods are demanded, the finite element method(shorted as FEM) is one of such methods. In this paper, the mathematic model and the simplified calculation of AMB rotor are introduced, and the finite elemental model and its boundary condition are produced. Then, the coupling phenomena of the magnetic fields and the effects of different parameters on the magnetic fields of AMB with a non-homocentric rotor are simulated using the FEM analysis software of ANSYS. The distributions of 2D magnetic lines of force and the flux density in rotor and stator are given. The conclusions are of instructed meaning for the design of AMBs.
Finite element analysis on the electromagnetic fields of active magnetic bearing
International Nuclear Information System (INIS)
Ren, S; Liu, J; Bian, C
2008-01-01
To increase the carrying capacity and reduce the weight and size of AMBs, it is necessary to use a ferromagnetic material with high magnetic flux density, which can make AMBs run in the nonlinear region. The simple linear model before is not gratifying, so some more precise analysis methods are demanded, the finite element method(shorted as FEM) is one of such methods. In this paper, the mathematic model and the simplified calculation of AMB rotor are introduced, and the finite elemental model and its boundary condition are produced. Then, the coupling phenomena of the magnetic fields and the effects of different parameters on the magnetic fields of AMB with a non-homocentric rotor are simulated using the FEM analysis software of ANSYS. The distributions of 2D magnetic lines of force and the flux density in rotor and stator are given. The conclusions are of instructed meaning for the design of AMBs
On the calculation of finite-temperature effects in field theories
International Nuclear Information System (INIS)
Brandt, F.T.; Frenkel, J.; Taylor, J.C.
1991-03-01
We discuss an alternative method for computing finite-temperature effects in field theories, within the framework of the imaginary-time formalism. Our approach allows for a systematic calculation of the high temperature expansion in terms of Riemann Zeta functions. The imaginary-time result is analytically continued to the complex plane. We are able to obtain the real-time limit of the real and the imaginary parts of the Green functions. (author)
Zero and finite field μSR spin glass Ag:Mn
International Nuclear Information System (INIS)
Brown, J.A.; Heffner, R.H.; Leon, M.; Olsen, C.E.; Schillaci, M.E.; Dodds, S.A.; Estle, T.L.; MacLaughlin, D.E.
1981-01-01
In this paper we present μSR data taken in both zero and finite fields for a Ag:Mn (1.6 at%) spin glass sample. The data allow us to determine, in the context of a particular model, the fluctuation rate of the Mn ions as a function of temperature. This rate decreases smoothly but very rapidly near the glass temperature, Tsub(g). The corresponding behavior in Cu:Mn is more gradual. (orig.)
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
Liquid metal flow in a finite-length cylinder with a rotating magnetic field
International Nuclear Information System (INIS)
Gelfgat, Yu.M.; Gorbunov, L.A.; Kolevzon, V.
1993-01-01
A liquid metal flow induced by a rotating magnetic field in a cylindrical container of finite height was investigated experimentally. It was demonstrated that the flow in a rotating magnetic field is similar to geophysical flows: the fluid rotates uniformly with depth and the Ekman layer exists at the container bottom. Near the vertical wall the flow is depicted in the form of a confined jet whose thickness determines the instability onset in a rotating magnetic field. It was shown that the critical Reynolds number can be found by using the jet velocity u 0 for Re cr =u 2 0 /ν∂u/∂r. The effect of frequency of a magnetic field on the fluid flow was also studied. An approximate theoretical model is presented for describing the fluid flow in a uniform rotating magnetic field. (orig.)
Electric field analysis of extra high voltage (EHV) underground cables using finite element method
DEFF Research Database (Denmark)
Kumar, Mantosh; Bhaskar, Mahajan Sagar; Padmanaban, Sanjeevikumar
2017-01-01
used for the insulator due electrical, thermal or environmental stress. Most of these problems are related to the electric field stress on the insulation of the underground cables. The objective of the electric field analysis by using different numerical techniques is to find electric field stress...... electric field stress and other parameters of EHV underground cables with given boundary conditions using 2-D electric field analysis software package (IES-ELECTRO module) which is based on the finite element method (FEM).......Transmission and Distribution of electric power through underground cables is a viable alternative to overhead lines, particularly in residential or highly populated areas. The electrical stresses are consequences of regular voltages and over voltages and the thermal stresses are related to heat...
Burtyka, Filipp
2018-01-01
The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.
Finite size effects in the thermodynamics of a free neutral scalar field
Parvan, A. S.
2018-04-01
The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach
Chen, Lipeng; Zhao, Yang
2017-12-01
Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.
Transport properties of finite carbon nanotubes under electric and magnetic fields
International Nuclear Information System (INIS)
Li, T S; Lin, M F
2006-01-01
Electronic and transport properties of finite carbon nanotubes subject to the influences of a transverse electric field and a magnetic field with varying polar angles are studied by the tight-binding model. The external fields will modify the state energies, destroy the state degeneracy, and modulate the energy gap. Both the state energy and the energy gap exhibit rich dependence on the field strength, the magnetic field direction, and the types of carbon nanotubes. The semiconductor-metal transition would be allowed for certain field strengths and magnetic field directions. The variations of state energies with the external fields will also be reflected in the electrical and thermal conductance. The number, the heights, and the positions of the conductance peaks are strongly dependent on the external fields. The heights of the electrical and thermal conductance peaks display a quantized behaviour, while that of the Peltier coefficient does not. Finally, it is found that the validity of the Wiedemann-Franz law depends upon the temperature, the field strength, the electronic structure, and the chemical potential
Controlling the sign problem in finite-density quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Garron, Nicolas; Langfeld, Kurt [University of Liverpool, Theoretical Physics Division, Department of Mathematical Sciences, Liverpool (United Kingdom)
2017-07-15
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the ''telegraphic'' approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign-problem regime. (orig.)
Controlling the sign problem in finite-density quantum field theory
Garron, Nicolas; Langfeld, Kurt
2017-07-01
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.
New technological design of arithmetics
International Nuclear Information System (INIS)
Hanitriarivo, R.
2008-01-01
There are illogical and irrational rules in numbers writing and pronunciation in almost of languages. A part of the aim is to show the electronic applications possibility of logical and systematic rules which are proposed by Raoelina Andriambololona to write and pronounce numbers; we had studied and created the arithmetic operations representation corresponding in binary basis and in hexadecimal basis. The brand new found concept corresponds as well as the method which uses the matrix product calculation, in according with the writing and the pronunciation of numbers. It was shown how to concept the arithmetic operators in digital electronics; and we proposed and assumed to make headway and to do amelioration for technical conception of calculator and arithmetic unite those are at the basic function of all computers and almost domestic sophisticated machine. The left hand side- right hand side and increasing order writing of number is exploited to build a new computer programming for a scientific calculator. [fr
Kinetic transport properties of a bumpy torus with finite radial ambipolar field
International Nuclear Information System (INIS)
Spong, D.A.; Harris, E.G.; Hedrick, C.L.
1978-04-01
Bumpy torus neoclassical transport coefficients have been calculted including finite values of the radial ambipolar field. These are obtained by solving a bounce-averaged drift kinetic equation in a local approximation for perturbations in the distribution function (away from a stationary Maxwellian) caused by toroidicity and radial gradients in plasma density, temperature, and potential. Particle and energy fluxes along with the associated transport coefficients are then calculated by taking appropriate moments of the distribution function. Particle orbits are treated by breaking them up into a vertical drift component (due to toroidicity) and a theta precessional drift (as a result of Vector E x Vector B and drifts due to the bumpy toroidal field). The kinetic equation has been solved using both a functional expansion method and finite difference techniques [Alternating-Direction-Implicit (ADI)]. The resulting transport coefficients exhibit a strong dependence on the ambipolar electric field and plasma collisionality. In the large electric field limit, our results are in close agreement with the earlier work of Kovrizhnykh
Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity
Sato, N.; Yoshida, Z.
2018-02-01
Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.
Arithmetic learning in advanced age.
Zamarian, Laura; Scherfler, Christoph; Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete
2018-01-01
Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger
Trace formulae for arithmetical systems
International Nuclear Information System (INIS)
Bogomolny, E.B.; Georgeot, B.; Giannoni, M.J.; Schmit, C.
1992-09-01
For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
Curves over finite fields with many rational points obtained by ray class field extensions
Auer, R; Bosma, W
2000-01-01
A general type of ray class fields of global function fields is investigated. The computation of their genera is reduced to the determination of the degrees of these extensions, which turns out to be the main difficulty. While in two special situations explicit formulas for the degrees are known,
Effects of finite-β and radial electric fields on neoclassical transport in the Large Helical Device
International Nuclear Information System (INIS)
Kanno, R.; Nakajima, N.; Sugama, H.; Okamoto, M.; Ogawa, Y.
1997-01-01
Effects of finite-β and radial electric fields on the neoclassical transport in the Large Helical Device are investigated with the DKES (Drift Kinetic Equation Solver) code. In the finite-β configuration, even orbits of deeply trapped particles deviate significantly from magnetic flux surfaces. Thus, neoclassical ripple transport coefficients in the finite-β configuration are several times larger than those in the vacuum configuration under the same condition of temperatures and radial electric fields. When the plasma temperature is several keV, a bifurcation of the electric fields appears under the ambipolarity condition, and sufficient large radial electric fields can be generated. As a result, the ExB drift rectifies orbits of particles and improves significantly the transport coefficients in the finite-β configuration. (author)
Directory of Open Access Journals (Sweden)
Hadi Samadian
2017-04-01
Full Text Available Objective(s: Since the electric field is the main driving force in electrospinning systems, the modeling and analysis of electric field distribution are critical to the nanofibers production. The aim of this study was modeling of the electric field and investigating the various parameters on polyacrylonitrile (PAN nanofibers morphology and diameter. Methods: The electric field profile at the nozzle and electrospinning zone was evaluated by Finite Element Method. The morphology and diameter of nanofibers were examined by Scanning electron microscopy (SEM. Results: The results of the electric field analysis indicated that the electric field was concentrated at the tip of the nozzle. Moreover, in the spinning direction, the electric field was concentrated at the surface of the spinneret and decayed rapidly toward the surface of the collector. Increasing polymer solution concentration from 7 to 11wt.% led to increasing nanofibers diameter form 77.76 ± 19.44 to 202.42 ± 36.85. Conclusions: Base on our results, it could be concluded that concentration of the electric field at the tip of the nozzle is high and initiates jet and nanofibers formation. PAN nanofibers can be transformed to carbon nanofibers which have various applications in biomedicine.
Arithmetic fundamental groups and moduli of curves
International Nuclear Information System (INIS)
Makoto Matsumoto
2000-01-01
This is a short note on the algebraic (or sometimes called arithmetic) fundamental groups of an algebraic variety, which connects classical fundamental groups with Galois groups of fields. A large part of this note describes the algebraic fundamental groups in a concrete manner. This note gives only a sketch of the fundamental groups of the algebraic stack of moduli of curves. Some application to a purely topological statement, i.e., an obstruction to the subjectivity of Johnson homomorphisms in the mapping class groups, which comes from Galois group of Q, is explained. (author)
Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.
1995-01-01
A propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented. The method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function. A finite element propagation model is combined with a coarse/fine grid impedance plane search technique to extract the impedance of the material. Results are presented for three different materials for which the impedance is known. For each material, the input data required for the prediction scheme was computed from modal theory and then contaminated by random error. The finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments. Thus, the method developed here provides a means for determining the impedance of materials in a nonprogressirve wave environment such as that usually encountered in a commercial aircraft engine and most laboratory settings.
Finite element modelling of ionized field quantities around a monopolar HVDC transmission line
International Nuclear Information System (INIS)
Jaiswal, Vinay; Thomas, M Joy
2003-01-01
In this paper, the Poisson's equation describing the ionized field around an HVDC line is solved using an improved finite element based technique. First order isoparametric quadrilateral elements, together with a modified updating criterion for the space charge distribution, are implemented in the iterative procedure. A novel technique is presented for mesh generation in the presence of space charges. Electric field lines and equipotential lines have been computed using the proposed technique. Total corona current at different applied voltages above corona onset voltage, electric field at the ground plane with and without the presence of space charges and current density at the ground plane have also been computed. The results are in agreement with the experimental values available in the published literature
FINITE VOLUME METHOD FOR SOLVING THREE-DIMENSIONAL ELECTRIC FIELD DISTRIBUTION
Directory of Open Access Journals (Sweden)
Paţiuc V.I.
2011-04-01
Full Text Available The paper examines a new approach to finite volume method which is used to calculate the electric field spatially homogeneous three-dimensional environment. It is formulated the problem Dirihle with building of the computational grid on base of space partition, which is known as Delone triangulation with the use of Voronoi cells. It is proposed numerical algorithm for calculating the potential and electric field strength in the space formed by a cylinder placed in the air. It is developed algorithm and software which were for the case, when the potential on the inner surface of the cylinder has been assigned and on the outer surface and the bottom of cylinder it was assigned zero potential. There are presented results of calculations of distribution in the potential space and electric field strength.
Finite-orbit-width effect and the radial electric field in neoclassical transport phenomena
International Nuclear Information System (INIS)
Satake, S.; Okamoto, M.; Nakajima, N.; Sugama, H.; Yokoyama, M.; Beidler, C.D.
2005-01-01
Modeling and detailed simulation of neoclassical transport phenomena both in 2D and 3D toroidal configurations are shown. The emphasis is put on the effect of finiteness of the drift-orbit width, which brings a non-local nature to neoclassical transport phenomena. Evolution of the self-consistent radial electric field in the framework of neoclassical transport is also investigated. The combination of Monte-Carlo calculation for ion transport and numerical solver of ripple-averaged kinetic equation for electrons makes it possible to calculate neoclassical fluxes and the time evolution of the radial electric field in the whole plasma region, including the finite-orbit-width (FOW) effects and global evolution of geodesic acoustic mode (GAM). The simulation results show that the heat conductivity around the magnetic axis is smaller than that obtained from standard neoclassical theory and that the evolution of GAM oscillation on each flux surface is coupled with other surfaces if the FOW effect is significant. A global simulation of radial electric field evolution in a non-axisymmetric plasma is also shown. (author)
International Nuclear Information System (INIS)
Yao, Kai; Shen, Kai; Wang, Zheng-Dao; Wang, Yue-Sheng
2014-01-01
In this study, 3D finite element analysis is presented by calculating the residual magnetic field signals of ferromagnets under the plastic deformation. The contour maps of tangential and normal RMF gradients are given, and the 3D effect is discussed. The results show that the tangential peak–peak amplitude and normal peak–vale amplitude are remarkably different in 2D and 3D simulations, but the tangential peak–peak width and normal peak–vale width are similar. Moreover, some key points are capable of capturing the plastic-zone shape, especially when the lift-off is small enough. The present study suggests an effective defect identification method with Metal magnetic memory (MMM) technique. - Highlights: • Three-dimensional (3D) finite element analysis is presented by calculating the residual magnetic field signals of ferromagnets under the plastic deformation. • The contour maps of gradients of the tangential and normal residual magnetic fields are given, and the 3D effect is discussed. • The present study suggests an effective defect identification method with metal magnetic memory technique
Electronic and optical properties of finite carbon nanotubes in an electric field
International Nuclear Information System (INIS)
Chen, R B; Lee, C H; Chang, C P; Lin, M F
2007-01-01
The effects, caused by the geometric structure and an electric field (E), on the electronic and optical properties of quasi-zero-dimensional finite carbon nanotubes are explored by employing the tight-binding model coupled with curvature effects. Electronic properties (state energies, symmetry of electronic states, energy spacing and state degeneracy) are significantly affected by the magnitude and the direction of the electric field and the geometric structure (radius, length and chirality). The electric field, by lowering the symmetry of finite carbon nanotubes, modifies the electronic properties. Thus, the optical excitation spectra, excited by electric polarization parallel to the nanotube axis, exhibit rich delta-function-like peaks, which reveal the characteristics of the electronic properties. Therefore it follows that geometric structure and E influence the low-energy absorption spectra, i.e. the change of frequency of the first peak, the alternation of the peak height and the production of the new peaks. There are more absorption peaks when E is oriented closer to the cross-section plane. Moreover, the very complicated optical absorption spectra are characteristic for the individual chiral carbon nanotube due to its specific geometric structure. Above all, the predicted absorption spectra and the associated electronic properties could be verified by optical measurements
Mechanical stress calculations for toroidal field coils by the finite element method
International Nuclear Information System (INIS)
Soell, M.; Jandl, O.; Gorenflo, H.
1976-09-01
After discussing fundamental relationships of the finite element method, this report describes the calculation steps worked out for mechanical stress calculations in the case of magnetic forces and forces produced by thermal expansion or compression of toroidal field coils using the SOLID SAP IV computer program. The displacement and stress analysis are based on the 20-node isoparametric solid element. The calculation of the nodal forces produced by magnetic body forces are discussed in detail. The computer programs, which can be used generally for mesh generation and determination of the nodal forces, are published elsewhere. (orig.) [de
Classification of filiform Lie algebras up to dimension 7 over finite fields
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad
2016-01-01
This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie algebras up to dimension 7 over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomor...
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.; Saude, Joao
2017-01-01
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Quark self-energy beyond the mean field at finite temperature
International Nuclear Information System (INIS)
Zhuang, P.
1995-01-01
The Nambu--Jona-Lasinio model, an effective low-energy model of QCD, is extended to the next to the leading order in the 1/N c expansion at finite temperature and density. The contributions to the quark self-energy and the constituent quark mass from the meson dressing are considered in a perturbative approach about the mean field. In particular, the temperature dependence of the quark mass is shown numerically at zero chemical potential. The correction to the quark mass from the meson dressing amounts to 20% compared to the result of the leading order at low temperature, and rapidly approaches zero at high temperature
A heuristic for the distribution of point counts for random curves over a finite field.
Achter, Jeffrey D; Erman, Daniel; Kedlaya, Kiran S; Wood, Melanie Matchett; Zureick-Brown, David
2015-04-28
How many rational points are there on a random algebraic curve of large genus g over a given finite field Fq? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q+1+1/(q-1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Casimir effect at finite temperature for the Kalb-Ramond field
International Nuclear Information System (INIS)
Belich, H.; Silva, L. M.; Helayeel-Neto, J. A.; Santana, A. E.
2011-01-01
We use the thermofield dynamics formalism to obtain the energy-momentum tensor for the Kalb-Ramond field in a topology S 1 xS 1 xR 2 . The compactification is carried out by a generalized thermofield dynamics-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor. The expressions for the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and the results may be important for applications, as in cuprate superconductivity, for instance.
Correspondence between imaginary-time and real-time finite-temperature field theory
International Nuclear Information System (INIS)
Kobes, R.
1990-01-01
It is known that one-particle-irreducible graphs found using the imaginary-time formalism of finite-temperature field theory differ in general with those of the real-time formalism. Here it is shown that within the real-time formalism one can consider a sum of graphs, motivated by causality arguments, which at least in a number of simple examples agree with the corresponding analytically continued imaginary-time result. The occurrence of multiple statistical factors in this sum of graphs is discussed
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.
2017-04-29
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Bent and bent(4) spectra of Boolean functions over finite fields
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Meidl, Wilfried
2017-01-01
For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the ...... a cubic monomial. We show that it is c-bent(4) only for c = 1, the function is then called negabent, which shows that non-quadratic functions exhibit a different behaviour. (C) 2017 Elsevier Inc. All rights reserved....
Ground state metamorphosis for Yang-Mills fields on a finite periodic lattice
International Nuclear Information System (INIS)
Gonzalez-Arroyo, A.; Jurkiewicz, J.; Korthals-Altes, C.P.
1983-01-01
The authors study the weak coupling behaviour of the partition function of non-abelian gauge fields on a finite lattice. Periodic boundary conditions are imposed. Two different power laws in the coupling BETA -1 arise for the partition function, when the dimension d of space time is larger or smaller than a critical dimension d /SUB c/ . For SU(2) d /SUB c/ = 4 and they find at this dimension power behaviour corrected by log BETA. The phenomenon is of practical importance in Monte Carlo simulations of the twisted action
Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J
2018-01-30
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.
Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.
2018-02-01
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.
Solutions to Arithmetic Convolution Equations
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Some arithmetically symmetrical bandpass filters
Paranasi, P.; Roy, S. C. D.
1981-01-01
A combination of the conventional and Matthaei lowpass-bandpass transformations is shown to result in some bandpass filters having very good arithmetic symmetry. The technique presented is applicable to the Butterworth and inverse Chebyshev types of magnitude approximations and the Bessel type of delay approximations. It is not valid, however, for the Chebyshev and elliptic varieties of filters.
Rewrite systems for integer arithmetic
H.R. Walters (Pum); H. Zantema (Hans)
1995-01-01
textabstractWe present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground confluent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by
Rewrite systems for integer arithmetic
Walters, H.R.; Zantema, H.
1994-01-01
We present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground con uent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by successor and
International Nuclear Information System (INIS)
Koch, Stephan
2009-01-01
This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The
International Nuclear Information System (INIS)
Schmid, J.
1985-11-01
A package of updated computer codes for velocity and temperature field calculations for a fast reactor fuel subassembly (or its part) by the finite element method is described. Isoparametric triangular elements of the second degree are used. (author)
International Nuclear Information System (INIS)
Shuman, E.S.; Evans, C.M.; Gallagher, T.F.
2004-01-01
It should be possible to separate experimentally the contributions to dielectronic recombination (DR) of energetically unresolved intermediate autoionizing Rydberg nl states using electric fields. This notion is based on two essential ideas. First, electric fields enhance the DR rate by Stark-mixing low-l states with high autoionization rates with high-l states with low autoionization rates. Second, the field at which an l state becomes Stark mixed is determined by its quantum defect, a known function of l. Consequently, the electric-field dependence of the DR rate should reflect the l dependence of the autoionization rates and thus the contributions of the zero-field nl states to the DR rate. This notion cannot be tested experimentally by examining true DR. However, it can be tested by studying DR from a continuum of finite bandwidth (CFB), for in this case the intermediate Rydberg nl states are restricted to a single value of l. Specifically, we have examined the electric-field dependence of DR from two CFB's, the Ba 6p 3/2 11d and 6p 3/2 8g states. In these two cases the intermediate autoionizing Rydberg states are restricted to the Ba 6p 1/2 nd and 6p 1/2 ng states (l=2 and 4), which have quantum defects of 0.25 and 0.02, respectively. For the same n they are Stark mixed at fields differing by an order of magnitude. We show experimentally that enhancement of the DR rate occurs at fields differing by a factor of 10 for nd and ng states of the same n, as expected, confirming that the field dependence of DR can be used to extract information about the contributions of energetically unresolved l states to the zero-field DR rate
Simulation on Temperature Field of Radiofrequency Lesions System Based on Finite Element Method
International Nuclear Information System (INIS)
Xiao, D; Qian, Z; Li, W; Qian, L
2011-01-01
This paper mainly describes the way to get the volume model of damaged region according to the simulation on temperature field of radiofrequency ablation lesion system in curing Parkinson's disease based on finite element method. This volume model reflects, to some degree, the shape and size of the damaged tissue during the treatment with all tendencies in different time or core temperature. By using Pennes equation as heat conduction equation of radiofrequency ablation of biological tissue, the author obtains the temperature distribution field of biological tissue in the method of finite element for solving equations. In order to establish damage models at temperature points of 60 deg. C, 65 deg. C, 70 deg. C, 75 deg. C, 80 deg. C, 85 deg. C and 90 deg. C while the time points are 30s, 60s, 90s and 120s, Parkinson's disease model of nuclei is reduced to uniform, infinite model with RF pin at the origin. Theoretical simulations of these models are displayed, focusing on a variety of conditions about the effective lesion size on horizontal and vertical. The results show the binary complete quadratic non-linear joint temperature-time models of the maximum damage diameter and maximum height. The models can comprehensively reflect the degeneration of target tissue caused by radio frequency temperature and duration. This lay the foundation for accurately monitor of clinical RF treatment of Parkinson's disease in the future.
Renormalization group and finite size effects in scalar lattice field theories
International Nuclear Information System (INIS)
Bernreuther, W.; Goeckeler, M.
1988-01-01
Binder's phenomenological renormalization group is studied in the context of the O(N)-symmetric euclidean lattice φ 4 theory in dimensions d ≤ 4. By means of the field theoretical formulation of the renormalization group we analyse suitable ratios of Green functions on finite lattices in the limit where the dimensionless lattice length L >> 1 and where the dimensionless bare mass approaches the critical point of the corresponding infinite volume model. If the infrared-stable fixed point which controls this limit is a simple zero of the β-function we are led to formulae which allow the extraction of the critical exponents ν and η. For the gaussian fixed point in four dimensions, discussed as a known example for a multiple zero of the β-function, we derive for these ratios the leading logarithmic corrections to mean field scaling. (orig.)
W.J. Palenstijn (Willem Jan)
2014-01-01
htmlabstractLet K be a field. A radical is an element of the algebraic closure of K of which a power is contained in K. In this thesis we develop a method for determining what we call entanglement. This describes unexpected additive relations between radicals, and is encoded in an entanglement
Palenstijn, Willem Jan
2014-01-01
Let K be a field. A radical is an element of the algebraic closure of K of which a power is contained in K. In this thesis we develop a method for determining what we call entanglement. This describes unexpected additive relations between radicals, and is encoded in an entanglement group. We give
Finite element approximation of the fields of bulk and interfacial line defects
Zhang, Chiqun; Acharya, Amit; Puri, Saurabh
2018-05-01
A generalized disclination (g.disclination) theory (Acharya and Fressengeas, 2015) has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of treating the kinematics and dynamics of terminating lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of a single disclination, a single dislocation treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections, a through twin boundary, a terminating twin boundary, a through grain boundary, a star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate, a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. Our work also represents one systematic way of studying the interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable subtlety and conceptual importance (Aharoni et al., 2017; Mermin, 1979).
International Nuclear Information System (INIS)
Nelson, E.M.
1993-12-01
Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required
International Nuclear Information System (INIS)
Smith, R.A.
1975-06-01
The structural analysis of toroidal field coils in Tokamak fusion machines can be performed with the finite element method. This technique has been employed for design evaluations of toroidal field coils on the Princeton Large Torus (PLT), the Poloidal Diverter Experiment (PDX), and the Tokamak Fusion Test Reactor (TFTR). The application of the finite element method can be simplified with computer programs that are used to generate the input data for the finite element code. There are three areas of data input where significant automation can be provided by supplementary computer codes. These concern the definition of geometry by a node point mesh, the definition of the finite elements from the geometric node points, and the definition of the node point force/displacement boundary conditions. The node point forces in a model of a toroidal field coil are computed from the vector cross product of the coil current and the magnetic field. The computer programs named PDXNODE and ELEMENT are described. The program PDXNODE generates the geometric node points of a finite element model for a toroidal field coil. The program ELEMENT defines the finite elements of the model from the node points and from material property considerations. The program descriptions include input requirements, the output, the program logic, the methods of generating complex geometries with multiple runs, computational time and computer compatibility. The output format of PDXNODE and ELEMENT make them compatible with PDXFORC and two general purpose finite element computer codes: (ANSYS) the Engineering Analysis System written by the Swanson Analysis Systems, Inc., and (WECAN) the Westinghouse Electric Computer Analysis general purpose finite element program. The Fortran listings of PDXNODE and ELEMENT are provided
Finite action for three dimensional gravity with a minimally coupled scalar field
International Nuclear Information System (INIS)
Gegenberg, Jack; Martinez, Cristian; Troncoso, Ricardo
2003-01-01
Three-dimensional gravity with a minimally coupled self-interacting scalar is considered. The falloff of the fields at infinity is assumed to be slower than that of a localized distribution of matter in the presence of a negative cosmological constant. However, the asymptotic symmetry group remains to be the conformal group. The counterterm Lagrangian needed to render the action finite is found by demanding that the action attain an extremum for the boundary conditions implied by the above falloff of the fields at infinity. These counterterms explicitly depend on the scalar field. As a consequence, the Brown-York stress-energy tensor acquires a nontrivial contribution from the matter sector. Static circularly symmetric solutions with a regular scalar field are explored for a one-parameter family of potentials. Their masses are computed via the Brown-York quasilocal stress-energy tensor, and they coincide with the values obtained from the Hamiltonian approach. The thermal behavior, including the transition between different configurations, is analyzed, and it is found that the scalar black hole can decay into the Banados-Teitelboim-Zanelli solution irrespective of the horizon radius. It is also shown that the AdS conformal field theory correspondence yields the same central charge as for pure gravity
Computer arithmetic and validity theory, implementation, and applications
Kulisch, Ulrich
2013-01-01
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties
Energy Technology Data Exchange (ETDEWEB)
Nascimento, Francisco Rogerio Teixeira do
2013-07-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Instantaneous flow field above the free end of finite-height cylinders and prisms
International Nuclear Information System (INIS)
Rostamy, N.; Sumner, D.; Bergstrom, D.J.; Bugg, J.D.
2013-01-01
Highlights: • PIV measurements of the flow above the free end of finite-height bodies. • Effect of cross-sectional shape of the models on the instantaneous flow. • Small-scale structures generated by the separated shear layer were revealed. • Effect of aspect ratio on the reattachment of the separated flow on the free end. -- Abstract: The flow above the free ends of surface-mounted finite-height circular cylinders and square prisms was studied experimentally using particle image velocimetry (PIV). Cylinders and prisms with aspect ratios of AR = 9, 7, 5, and 3 were tested at a Reynolds number of Re = 4.2 × 10 4 . The bodies were mounted normal to a ground plane and were partially immersed in a turbulent zero-pressure-gradient boundary layer, where the boundary layer thickness relative to the body width was δ/D = 1.6. PIV measurements were made above the free ends of the bodies in a vertical plane aligned with the flow centreline. The present PIV results provide insight into the effects of aspect ratio and body shape on the instantaneous flow field. The recirculation zone under the separated shear layer is larger for the square prism of AR = 3 compared to the more slender prism of AR = 9. Also, for a square prism with low aspect ratio (AR = 3), the influence of the reverse flow over the free end surface becomes more significant compared to that for a higher aspect ratio (AR = 9). For the circular cylinder, a cross-stream vortex forms within the recirculation zone. As the aspect ratio of the cylinder decreases, the reattachment point of the separated flow on the free end surface moves closer to the trailing edge. For both the square prism and circular cylinder cases, the instantaneous velocity vector field and associated in-plane vorticity field revealed small-scale structures mostly generated by the separated shear layer
Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics
Directory of Open Access Journals (Sweden)
A Martowicz
2016-04-01
Full Text Available In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.
Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature
International Nuclear Information System (INIS)
Kerres, U.; Mack, G.; Palma, G.
1994-12-01
We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bololiubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for φ 4 -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here. (orig.)
Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field
DEFF Research Database (Denmark)
Grap, Stephan; Andergassen, Sabine; Paaske, Jens
2011-01-01
ridges, which are robust against SOI as time-reversal symmetry is preserved. As a result of the crossing of a spin-up and a spin-down level at vanishing SOI, two additional Kondo plateaus appear at finite B. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left......-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-antibonding state symmetry. In this case, the finite-B Kondo ridges in the Vg-B plane are bent with respect to the Vg axis. For the Kondo ridge to develop, different level renormalizations......We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in the presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo...
Electromagnetic-field amplification in finite one-dimensional photonic crystals
International Nuclear Information System (INIS)
Gorelik, V. S.; Kapaev, V. V.
2016-01-01
The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.
Magnetic hyperfine field at a Cd impurity diluted in RCo{sub 2} at finite temperatures
Energy Technology Data Exchange (ETDEWEB)
Oliveira, A.L. de, E-mail: alexandre.oliveira@ifrj.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, Campus Nilópolis – RJ (Brazil); Chaves, C.M., E-mail: cmch@cbpf.br [Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro (Brazil); Oliveira, N.A. de [Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro, Rio de Janeiro (Brazil); Troper, A. [Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro (Brazil)
2015-06-15
The local magnetic moments and the magnetic hyperfine fields at an s–p Cd impurity diluted in inter-metallic Laves phase compounds RCo{sub 2} (R=Gd, Tb) at finite temperatures are calculated. For other rare earth elements (light or heavy) the pure compounds display a magnetic first order transition and are not describable by our formalism. The host has two coupled lattices (R and Co) both having itinerant d electrons but only the rare earth lattice has localized f electrons. They all contribute to the magnetization of the host and also to the local moment and to the magnetic hyperfine field at the impurity. The investigation of magnetic hyperfine field in these materials then provides valuable information on the d-itinerant electrons and also on the localized (4f) magnetic moments. For the d–d electronic interaction we use the Hubbard–Stratonovich identity thus allowing the employment of functional integral in the static saddle point approximation. Our model reproduces quite well the experimental data. - Highlights: • A functional integral method in the static limit, producing site disorder, is used. • The site disorder is treated with the coherent potential approximation (CPA) • A Friedel sum rule gives a self-consistency condition for the impurity energy. • The experimental curve of hyperfine fields×temperature is very well reproduced.
Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach
Directory of Open Access Journals (Sweden)
Weiping Li
2016-03-01
Full Text Available In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility.
Complexity transitions in global algorithms for sparse linear systems over finite fields
Braunstein, A.; Leone, M.; Ricci-Tersenghi, F.; Zecchina, R.
2002-09-01
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to the changes in the performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary for the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.
Complexity transitions in global algorithms for sparse linear systems over finite fields
International Nuclear Information System (INIS)
Braunstein, A.; Leone, M.; Ricci-Tersenghi, F. . Federico.Ricci@roma1.infn.it; Zecchina, R.
2002-01-01
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to the changes in the performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary for the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem. (author)
Finite element analyses of a heater-interruption in the HAW test field
International Nuclear Information System (INIS)
Horn, B.A. van den.
1991-09-01
In this report the results of two finite element analyses of the HAW field are presented. The determination of the influence of a heater-interruption on the tube load as well as the differences in the evaluation of the tube load for both types of boreholes (type A and type B) are the main objectives of this report. Axisymmetric models are made for both type of boreholes in order to simulate this heater-interruption. It appeared that a heater-interruption of 4 hours leads to a temperature drop of 17.2deg C at the borehole wall and to a maximum reduction of the tube load of 1.76 MPa. About 20 days after reparation of the heaters of the heaters the evolution of the maximum temperature and the maximum tube load will be rehabilitated; the difference with the corresponding evolutions due to an uninterrupted heat-production are negligible. (author). 9 refs.; 25 figs.; 5 tabs
Analysis and Calculation of the Fluid Flow and the Temperature Field by Finite Element Modeling
Dhamodaran, M.; Jegadeesan, S.; Kumar, R. Praveen
2018-04-01
This paper presents a fundamental and accurate approach to study numerical analysis of fluid flow and heat transfer inside a channel. In this study, the Finite Element Method is used to analyze the channel, which is divided into small subsections. The small subsections are discretized using higher number of domain elements and the corresponding number of nodes. MATLAB codes are developed to be used in the analysis. Simulation results showed that the analyses of fluid flow and temperature are influenced significantly by the changing entrance velocity. Also, there is an apparent effect on the temperature fields due to the presence of an energy source in the middle of the domain. In this paper, the characteristics of flow analysis and heat analysis in a channel have been investigated.
Radiation field of an optically finite homogeneous atmosphere with internal sources
International Nuclear Information System (INIS)
Viik, T.
2010-01-01
The equation of radiative transfer in an optically finite homogeneous atmosphere with different internal sources is solved using the method of kernel approximation the essence of which is to approximate the kernel in the equation for the Sobolev resolvent function by a Gauss-Legendre sum. This approximation allows to solve the equation exactly for the resolvent function while the solution is a weighted sum of exponents. Since the resolvent function is closely connected with the Green function of the integral radiative transfer equation, the radiation field for different internal sources can be found by simple integration. In order to simplify the obtained formulas we have defined the x and y functions as the generalization of the well-known Ambarzumian-Chandrasekhar X and Y functions. For some types of internal sources the package of codes in Fortran-77 can be found at (http://www.aai.ee/~viik/HOMOGEN.FOR).
Recent progress on weight distributions of cyclic codes over finite fields
Directory of Open Access Journals (Sweden)
Hai Q. Dinh
2015-01-01
Full Text Available Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions.
Guo, Guang-Yu; Ishibashi, Shoji; Tamura, Tomoyuki; Terakura, Kiyoyuki
2007-03-01
Since the discovery of carbon nanotubes (CNTs) in 1991 by Iijima, carbon and other nanotubes have attracted considerable interest worldwide because of their unusual properties and also great potentials for technological applications. Though CNTs continue to attract great interest, other nanotubes such as BN nanotubes (BN-NTs) may offer different opportunities that CNTs cannot provide. In this contribution, we present the results of our recent systematic ab initio calculations of the static dielectric constant, electric polarizability, Born dynamical charge, electrostriction coefficient and piezoelectric constant of BN-NTs using the latest crystalline finite electric field theory [1]. [1] I. Souza, J. Iniguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002); P. Umari and A. Pasquarello, Phys. Rev. Lett. 89, 157602 (2002).
End-to-end workflow for finite element analysis of tumor treating fields in glioblastomas
Timmons, Joshua J.; Lok, Edwin; San, Pyay; Bui, Kevin; Wong, Eric T.
2017-11-01
Tumor Treating Fields (TTFields) therapy is an approved modality of treatment for glioblastoma. Patient anatomy-based finite element analysis (FEA) has the potential to reveal not only how these fields affect tumor control but also how to improve efficacy. While the automated tools for segmentation speed up the generation of FEA models, multi-step manual corrections are required, including removal of disconnected voxels, incorporation of unsegmented structures and the addition of 36 electrodes plus gel layers matching the TTFields transducers. Existing approaches are also not scalable for the high throughput analysis of large patient volumes. A semi-automated workflow was developed to prepare FEA models for TTFields mapping in the human brain. Magnetic resonance imaging (MRI) pre-processing, segmentation, electrode and gel placement, and post-processing were all automated. The material properties of each tissue were applied to their corresponding mask in silico using COMSOL Multiphysics (COMSOL, Burlington, MA, USA). The fidelity of the segmentations with and without post-processing was compared against the full semi-automated segmentation workflow approach using Dice coefficient analysis. The average relative differences for the electric fields generated by COMSOL were calculated in addition to observed differences in electric field-volume histograms. Furthermore, the mesh file formats in MPHTXT and NASTRAN were also compared using the differences in the electric field-volume histogram. The Dice coefficient was less for auto-segmentation without versus auto-segmentation with post-processing, indicating convergence on a manually corrected model. An existent but marginal relative difference of electric field maps from models with manual correction versus those without was identified, and a clear advantage of using the NASTRAN mesh file format was found. The software and workflow outlined in this article may be used to accelerate the investigation of TTFields in
End-to-end workflow for finite element analysis of tumor treating fields in glioblastomas.
Timmons, Joshua J; Lok, Edwin; San, Pyay; Bui, Kevin; Wong, Eric T
2017-10-12
Tumor Treating Fields (TTFields) therapy is an approved modality of treatment for glioblastoma. Patient anatomy-based finite element analysis (FEA) has the potential to reveal not only how these fields affect tumor control but also how to improve efficacy. While the automated tools for segmentation speed up the generation of FEA models, multi-step manual corrections are required, including removal of disconnected voxels, incorporation of unsegmented structures and the addition of 36 electrodes plus gel layers matching the TTFields transducers. Existing approaches are also not scalable for the high throughput analysis of large patient volumes. A semi-automated workflow was developed to prepare FEA models for TTFields mapping in the human brain. Magnetic resonance imaging (MRI) pre-processing, segmentation, electrode and gel placement, and post-processing were all automated. The material properties of each tissue were applied to their corresponding mask in silico using COMSOL Multiphysics (COMSOL, Burlington, MA, USA). The fidelity of the segmentations with and without post-processing was compared against the full semi-automated segmentation workflow approach using Dice coefficient analysis. The average relative differences for the electric fields generated by COMSOL were calculated in addition to observed differences in electric field-volume histograms. Furthermore, the mesh file formats in MPHTXT and NASTRAN were also compared using the differences in the electric field-volume histogram. The Dice coefficient was less for auto-segmentation without versus auto-segmentation with post-processing, indicating convergence on a manually corrected model. An existent but marginal relative difference of electric field maps from models with manual correction versus those without was identified, and a clear advantage of using the NASTRAN mesh file format was found. The software and workflow outlined in this article may be used to accelerate the investigation of TTFields in
Burtyka, Filipp
2018-03-01
The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.
A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims
International Nuclear Information System (INIS)
Forbes, Lawrence K.; Crozier, Stuart
2001-01-01
This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil. (author)
International Nuclear Information System (INIS)
Yeh, G.T.
1980-01-01
Darcian velocity has been conventionally calculated in the finite-element modeling of groundwater flow by taking the derivatives of the computed pressure field. This results in discontinuities in the velocity field at nodal points and element boundaries. Discontinuities become enormous when the computed pressure field is far from a linear distribution. It is proposed in this paper that the finite element procedure that is used to simulate the pressure field or the moisture content field also be applied to Darcy's law with the derivatives of the computed pressure field as the load function. The problem of discontinuity is then eliminated, and the error of mass balance over the region of interest is much reduced. The reduction is from 23.8 to 2.2% by one numerical scheme and from 29.7 to -3.6% by another for a transient problem
International Nuclear Information System (INIS)
Altherr, T.
1989-12-01
The main topic of this thesis is a perturbative study of Quantum Field Theory at Finite Temperature. The real-time formalism is used throughout this work. We show the cancellation of infrared and mass singularities in the case of the first order QCD corrections to lepton pair production from a quark-gluon plasma. Two methods of calculation are presented and give the same finite result in the limit of vanishing quark mass. These finite terms are analysed and give small corrections in the region of interest for ultra-relativistic heavy ions collisions, except for a threshold factor. Specific techniques for finite temperature calculations are explicited in the case of the fermionic self-energy in QED [fr
Visualization of 2-D and 3-D fields from its value in a finite number of points
International Nuclear Information System (INIS)
Dari, E.A.; Venere, M.J.
1990-01-01
This work describes a method for the visualization of two- and three-dimensional fields, given its value in a finite number of points. These data can be originated in experimental measurements, numerical results, or any other source. For the field interpolation, the space is divided into simplices (triangles or tetrahedrons), using the Watson algorithm to obtain the Delaunay triangulation. Inside each simplex, linear interpolation is assumed. The visualization is accomplished by means of Finite Elements post-processors, capable of handling unstructured meshes, which were also developed by the authors. (Author) [es
Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic
Directory of Open Access Journals (Sweden)
Shirley Rapoport
2016-10-01
Full Text Available The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1 beliefs regarding the contribution of executive functions to reading and arithmetic, (2 pedagogical practices, and (3 a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe executive functions affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices.
Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic
Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami
2016-01-01
The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices. PMID:27799917
Teachers' Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic.
Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami
2016-01-01
The current study investigated early elementary school teachers' beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students' performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers' scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices.
Neuroanthropological Understanding of Complex Cognition – Numerosity and Arithmetics
Directory of Open Access Journals (Sweden)
Zarja Mursic
2013-10-01
Full Text Available Humankind has a long evolutionary history. When we are trying to understand human complex cognition, it is as well important to look back to entire evolution. I will present the thesis that our biological predispositions and culture, together with natural and social environment, are tightly connected. During ontogenetically development we are shaped by various factors, and they enabled humans to develop some aspects of complex cognition, such as mathematics.In the beginning of the article I present the importance of natural and cultural evolution in other animals. In the following part, I briefly examine the field of mathematics – numerosity and arithmetic. Presentation of comparative animal studies, mainly made on primates, provides some interesting examples in animals’ abilities to separate between different quantities. From abilities for numerosity in animals I continue to neuroscientific studies of humans and our ability to solve simple arithmetic tasks. I also mention cross-cultural studies of arithmetic skills. In the final part of the text I present the field neuroanthropology as a possible new pillar of cognitive science. Finally, it is important to connect human evolution and development with animal cognition studies, but as well with cross-cultural studies in shaping of human ability for numerosity and arithmetic.
International Nuclear Information System (INIS)
Kapuria, S; Yaqoob Yasin, M
2013-01-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)
Inversion of potential field data using the finite element method on parallel computers
Gross, L.; Altinay, C.; Shaw, S.
2015-11-01
In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Bering, Klaus [Masaryk University, Faculty of Science, Brno (Czech Republic); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2016-03-15
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived. (orig.)
The arithmetic basis of special relativity
International Nuclear Information System (INIS)
Greenspan, D.
1976-01-01
Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field. (author)
Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model
International Nuclear Information System (INIS)
Hamer, C.J.; Barber, M.N.
1979-01-01
Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ
Conference on Number Theory and Arithmetic Geometry
Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem
1997-01-01
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...
International Nuclear Information System (INIS)
Smith, R.A.
1975-06-01
The design evaluation of toroidal field coils on the Princeton Large Torus (PLT), the Poloidal Diverter Experiment (PDX) and the Tokamak Fusion Test Reactor (TFTR) has been performed by structural analysis with the finite element method. The technique employed has been simplified with supplementary computer programs that are used to generate the input data for the finite element computer program. Significant automation has been provided by computer codes in three areas of data input. These are the definition of coil geometry by a mesh of node points, the definition of finite elements via the node points and the definition of the node point force/displacement boundary conditions. The computer programs by name that have been used to perform the above functions are PDXNODE, ELEMENT and PDXFORC. The geometric finite element modeling options for toroidal field coils provided by PDXNODE include one-fourth or one-half symmetric sections of circular coils, oval shaped coils or dee-shaped coils with or without a beveled wedging surface. The program ELEMENT which defines the finite elements for input to the finite element computer code can provide considerable time and labor savings when defining the model of coils of non-uniform cross-section or when defining the model of coils whose material properties are different in the R and THETA directions due to the laminations of alternate epoxy and copper windings. The modeling features provided by the program ELEMENT have been used to analyze the PLT and the TFTR toroidal field coils with integral support structures. The computer program named PDXFORC is described. It computes the node point forces in a model of a toroidal field coil from the vector crossproduct of the coil current and the magnetic field. The model can be of one-half or one-fourth symmetry to be consistent with the node model defined by PDXNODE, and the magnetic field is computed from toroidal or poloidal coils
International Nuclear Information System (INIS)
Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi
2015-01-01
Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)
Interstructure Lattices and Types of Peano Arithmetic
Abdul-Quader, Athar
The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA. In Chapter 2, we study a problem that had its origin in Simpson ([Sim74]), who used arithmetic forcing to show that every countable model of PA has an expansion to PA* that is pointwise definable. Enayat ([Ena88]) later showed that there are 2N0 models with the property that every expansion to PA* is pointwise definable. In this Chapter, we use techniques involved in representations of lattices to show that there is a model of PA with this property which contains an infinite descending chain of elementary cuts. In Chapter 3, we study the question of when subsets can be coded in elementary end extensions with prescribed interstructure lattices. This problem originated in Gaifman [Gai76], who showed that every model of PA has a conservative, minimal elementary end extension. That is, every model of PA has a minimal elementary end extension which codes only definable sets. Kossak and Paris [KP92] showed that if a model is countable and a subset X can be coded in any elementary end extension, then it can be coded in a minimal extension. Schmerl ([Sch14] and [Sch15]) extended this work by considering which collections of sets can be the sets coded in a minimal elementary end extension. In this Chapter, we extend this work to other lattices. We study two questions: given a countable model M, which sets can be coded in an elementary end extension such that the interstructure lattice is some prescribed finite distributive lattice; and, given an arbitrary model M, which sets can be coded in an elementary end extension whose interstructure lattice is a finite Boolean algebra?
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
DEFF Research Database (Denmark)
Dridi, Kim; Bjarklev, Anders Overgaard
1999-01-01
An electromagnetic vector-field modle for design of optical components based on the finite-difference-time-domain method and radiation integrals in presented. Its ability to predict the optical electromagnetic dynamics in structures with complex material distribution is demonstrated. Theoretical...
Arithmetic of quantum entropy function
International Nuclear Information System (INIS)
Sen, Ashoke
2009-01-01
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
Memory updating and mental arithmetic
Directory of Open Access Journals (Sweden)
Cheng-Ching eHan
2016-02-01
Full Text Available Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults.
A novel QC-LDPC code based on the finite field multiplicative group for optical communications
Yuan, Jian-guo; Xu, Liang; Tong, Qing-zhen
2013-09-01
A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) code is proposed based on the finite field multiplicative group, which has easier construction, more flexible code-length code-rate adjustment and lower encoding/decoding complexity. Moreover, a regular QC-LDPC(5334,4962) code is constructed. The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise (AWGN) channel with iterative decoding sum-product algorithm (SPA). At the bit error rate (BER) of 10-6, the net coding gain (NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB, 0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975, the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method, respectively. So it is more suitable for optical communication systems.
Ying, Wenjun; Henriquez, Craig S
2007-04-01
A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.
International Nuclear Information System (INIS)
Lacey, G.; Thenoux, G.; Rodriguez-Roa, F.
2008-01-01
In accordance with the present development of empirical-mechanistic tools, this paper presents an alternative to traditional analysis methods for flexible pavements using a three-dimensional finite element formulation based on a liner-elastic perfectly-plastic Drucker-Pager model for granular soil layers and a linear-elastic stress-strain law for the asphalt layer. From the sensitivity analysis performed, it was found that variations of +-4 degree in the internal friction angle of granular soil layers did not significantly affect the analyzed pavement response. On the other hand, a null dilation angle is conservatively proposed for design purposes. The use of a Light Falling Weight Deflectometer is also proposed as an effective and practical tool for on-site elastic modulus determination of granular soil layers. However, the stiffness value obtained from the tested layer should be corrected when the measured peak deflection and the peak force do not occur at the same time. In addition, some practical observations are given to achieve successful field measurements. The importance of using a 3D FE analysis to predict the maximum tensile strain at the bottom of the asphalt layer (related to pavement fatigue) and the maximum vertical comprehensive strain transmitted to the top of the granular soil layers (related to rutting) is also shown. (author)
Directory of Open Access Journals (Sweden)
Chi-hyung Ahn
2016-01-01
Full Text Available In the previous research, laboratory tests were performed in order to measure the expansion of vermiculite upon heating and to convert it into expansion pressure. Based on these test results, this study mainly focuses on experimental field tests conducted to verify that expansion pressure obtained by heating vermiculite materials is enough to break massive and hard granite rock with an intention to excavate the tunnel. Hexahedral granite specimens with a circular hole perforated in the center were constructed for the experimental tests. The circular holes were filled with vermiculite plus thermal conduction and then heated using the cartridge heater. As a result, all of hexahedral granite specimens had cracks in the surface after 700-second thermal heating and were finally spilt into two pieces completely. The specimen of larger size only requires more heating time and expansion pressure. The material properties of granite rocks, which were obtained from the experimental tests, were utilized to produce finite element models used for numerical analyses. The analysis results show good agreement with the experimental results in terms of initial cracking, propagation direction, and expansion pressure.
A finite element approach to self-consistent field theory calculations of multiblock polymers
Energy Technology Data Exchange (ETDEWEB)
Ackerman, David M. [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States); Delaney, Kris; Fredrickson, Glenn H. [Materials Research Laboratory, University of California, Santa Barbara (United States); Ganapathysubramanian, Baskar, E-mail: baskarg@iastate.edu [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States)
2017-02-15
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.
Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.
Divall, S A; Humphrey, V F
2000-03-01
Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.
Hano, Mitsuo; Hotta, Masashi
A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.
ASIC For Complex Fixed-Point Arithmetic
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Numerical Magnitude Representations Influence Arithmetic Learning
Booth, Julie L.; Siegler, Robert S.
2008-01-01
This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
Baby Arithmetic: One Object Plus One Tone
Kobayashi, Tessei; Hiraki, Kazuo; Mugitani, Ryoko; Hasegawa, Toshikazu
2004-01-01
Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually…
Interpretability degrees of finitely axiomatized sequential theories
Visser, Albert
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory-like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB-have suprema. This partially answers a question posed
Interpretability Degrees of Finitely Axiomatized Sequential Theories
Visser, Albert
2012-01-01
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory —like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB— have suprema. This partially answers a question
Ceccuzzi, Silvio; Jandieri, Vakhtang; Baccarelli, Paolo; Ponti, Cristina; Schettini, Giuseppe
2016-04-01
Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.
The arithmetic of supersymmetric vacua
Energy Technology Data Exchange (ETDEWEB)
Bourget, Antoine; Troost, Jan [Laboratoire de Physique Théorique de l’École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités,75005 Paris (France)
2016-07-07
We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤ{sub m}){sub n} theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N=1{sup ∗} gauge theories with gauge algebra su(n), compactified on a circle. Using arithmetic, we express that number in an SL(2,ℤ) duality invariant manner. We confirm our tally of massive vacua of the N=1{sup ∗} theories by a count of inequivalent extrema of the exact superpotential.
Xu, Yanlong
2015-01-01
structure and transmission in this paper show that the graded layered media possess very large band gaps. Harmonic wave simulation by finite element method (FEM) confirms that the reason of bandwidth enlargement is that waves within the band gap ranges
Study of two-dimensional transient cavity fields using the finite-difference time-domain technique
International Nuclear Information System (INIS)
Crisp, J.L.
1988-06-01
This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs
Study of two-dimensional transient cavity fields using the finite-difference time-domain technique
Energy Technology Data Exchange (ETDEWEB)
Crisp, J.L.
1988-06-01
This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs.
Ballet, Stéphane; Bonnecaze, Alexis; Tukumuli, Mila
2013-01-01
International audience; We indicate a strategy in order to construct bilinear multiplication algorithms of type Chudnovsky in large extensions of any finite field. In particular, using the symmetric version of the generalization of Randriambololona specialized on the elliptic curves, we show that it is possible to construct such algorithms with low bilinear complexity. More precisely, if we only consider the Chudnovsky-type algorithms of type symmetric elliptic, we show that the symmetric bil...
International Nuclear Information System (INIS)
Casalotti, N.; Magnaud, J.P.
1989-01-01
The possibilities of the TRIO-EF software in the thermal field are presented. The TRIO-EF is a computer program based on the finite element method and used for three-dimensional incompressible flow analysis. It enables the calculation of three-dimensional heat transfer and the fluid/structure analysis. The geometrically complex radiative reactor systems are taken into account in the form factor calculation. The implemented algorithms are described [fr
Shen, Ka
2018-04-01
We study magnon spectra at finite temperature in yttrium iron garnet using a tight-binding model with nearest-neighbor exchange interaction. The spin reduction due to thermal magnon excitation is taken into account via the mean field approximation to the local spin and is found to be different at two sets of iron atoms. The resulting temperature dependence of the spin wave gap shows good agreement with experiment. We find that only two magnon modes are relevant to the ferromagnetic resonance.
Pauchot , Julien; Remache , Djamel; Chambert , Jérôme; Elkhyat , Ahmed; Jacquet , Emmanuelle
2013-01-01
International audience; After performing a V-Y advancement flap, we observed an unusually shaped necrosis, resembling a keyhole at the apex of the flap. As high closing tensions are an accepted cause of skin necrosis, we developed a mathematical model based on the finite element analysis in order to determine the stress field by simulating the mechanical behavior of human skin during suture and to explain this particular shape of necrosis. For the modeling, a planar nonlinear two-dimensional ...
Rigid cohomology over Laurent series fields
Lazda, Christopher
2016-01-01
In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields...
Geddes, Earl Russell
The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and therefore other solution techniques must be used. This study shows that the finite element method can be adapted for use in the study of sound fields in arbitrary shaped enclosures. The finite element acoustics problem is formulated and the modification of a standard program, which is necessary for solving acoustic field problems, is examined. The solution of the semi-non-rectangular room problem (one where the floor and ceiling remain parallel) is carried out by a combined finite element/separation of variables approach. The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4. Case 1, the rectangular room was calculated using both the finite element method and the separation of variables technique. The results for the two methods are compared in order to access the accuracy of the finite element method models. The modal damping coefficient are calculated and the results examined. The statistics of the source and receiver average normalized RMS P('2) responses in the 80 Hz, 100 Hz, and 125 Hz one-third octave bands are developed. The receiver averaged pressure response is developed to determine the effect of the source locations on the response. Twelve source locations are examined and the results tabulated for comparison. The effect of a finite sized source is looked at briefly. Finally, the standard deviation of the
Xu, Yanlong
2015-09-01
Shear horizontal (SH) wave propagation in finite graded piezoelectric layered media is investigated by transfer matrix method. Different from the previous studies on SH wave propagation in completely periodic layered media, calculations on band structure and transmission in this paper show that the graded layered media possess very large band gaps. Harmonic wave simulation by finite element method (FEM) confirms that the reason of bandwidth enlargement is that waves within the band gap ranges are spatially enhanced and stopped by the corresponding graded units. The study suggests that the graded structure possesses the property of manipulating elastic waves spatially, which shows potential applications in strengthening energy trapping and harvesting. © 2015.
Effective field theories of QCD for heavy quarkonia at finite temperature
International Nuclear Information System (INIS)
Ghiglieri, Jacopo
2011-01-01
Quarkonia, i.e. heavy quark-antiquark bound states, represent one of the most important probes in the experimental investigation, through heavy-ion collisions, of the high-temperature region of the phase diagram of QCD, where the onset of a deconfined medium, the quark-gluon plasma, is expected. Such bound states were hypothesized to dissociate in this plasma due to the screening of the colour charges and experimental data from SPS, RHIC and very recently also LHC indeed show a suppression pattern. In this thesis we extend the well-established and successful zero temperature framework of Non-Relativistic (NR) Effective Field Theories (EFTs) (NRQCD, pNRQCD) for the study of heavy quarkonia (production, spectroscopy, decays,..) to finite temperatures. This is achieved by integrating out in sequence the scales that characterize a NR bound state and those that are typical of a thermal medium, in the possible hierarchies that are relevant for quarkonia in the quark-gluon plasma. Within this framework we show how the potential that governs the evolution of the quark-antiquark pair is derived from QCD in a modern and rigorous way, thereby bridging the gap between phenomenological potential models and QCD. We show how the EFTs can be systematically improved and how effects that cannot be encoded in a potential arise naturally in the EFT, giving rise to new mechanisms of dissociation. We use this EFT framework to compute the spectrum and width of quarkonia in a particular setting that is relevant for the phenomenology of the ground states of bottomonium at the LHC. We also analyze within this framework the correlator of Polyakov loops, which is related to the thermodynamical free energy of heavy quark-antiquark pairs in the medium. As such, lattice computations thereof were frequently used as input for potential models. With our approach we are able to clarify the relation between these free energies and the real-time potential describing the dynamics of quarkonia, finding
Effective field theories of QCD for heavy quarkonia at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Ghiglieri, Jacopo
2011-07-27
Quarkonia, i.e. heavy quark-antiquark bound states, represent one of the most important probes in the experimental investigation, through heavy-ion collisions, of the high-temperature region of the phase diagram of QCD, where the onset of a deconfined medium, the quark-gluon plasma, is expected. Such bound states were hypothesized to dissociate in this plasma due to the screening of the colour charges and experimental data from SPS, RHIC and very recently also LHC indeed show a suppression pattern. In this thesis we extend the well-established and successful zero temperature framework of Non-Relativistic (NR) Effective Field Theories (EFTs) (NRQCD, pNRQCD) for the study of heavy quarkonia (production, spectroscopy, decays,..) to finite temperatures. This is achieved by integrating out in sequence the scales that characterize a NR bound state and those that are typical of a thermal medium, in the possible hierarchies that are relevant for quarkonia in the quark-gluon plasma. Within this framework we show how the potential that governs the evolution of the quark-antiquark pair is derived from QCD in a modern and rigorous way, thereby bridging the gap between phenomenological potential models and QCD. We show how the EFTs can be systematically improved and how effects that cannot be encoded in a potential arise naturally in the EFT, giving rise to new mechanisms of dissociation. We use this EFT framework to compute the spectrum and width of quarkonia in a particular setting that is relevant for the phenomenology of the ground states of bottomonium at the LHC. We also analyze within this framework the correlator of Polyakov loops, which is related to the thermodynamical free energy of heavy quark-antiquark pairs in the medium. As such, lattice computations thereof were frequently used as input for potential models. With our approach we are able to clarify the relation between these free energies and the real-time potential describing the dynamics of quarkonia, finding
International Nuclear Information System (INIS)
Dina Al Akhrass; Bruchon, Julien; Drapier, Sylvain; Fayolle, Sebastien
2014-01-01
This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elasto-plasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (authors)
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Handbook of floating-point arithmetic
Muller, Jean-Michel; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge
2018-01-01
This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop programs specifically tailored for the standard’s technical features. Algorithms for floating-point arithmetic are presented throughout the book and illustrated where possible by example programs which show how these techniques appear in actual coding and design. The volume itself breaks its core topic into four parts: the basic concepts and history of floating-point arithmetic; methods of analyzing floating-point algorithms and optimizing them; implementations of IEEE 754-2008 in hardware and software; and useful extensions to the standard floating-point system, such as interval arithmetic, double- and triple-word arithm...
Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency
van Daal, Victor; van der Leij, Aryan; Ader, Herman
2013-01-01
The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading, arithmetic, and listening comprehension disabled…
Quality of Arithmetic Education for Children with Cerebral Palsy
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.; Withagen, Floortje
2010-01-01
The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…
International Nuclear Information System (INIS)
Jesenik, M.; Gorican, V.; Trlep, M.; Hamler, A.; Stumberger, B.
2006-01-01
A lot of magnetic materials are anisotropic. In the 3D finite element method calculation, anisotropy of the material is taken into account. Anisotropic magnetic material is described with magnetization curves for different magnetization directions. The 3D transient calculation of the rotational magnetic field in the sample of the round rotational single sheet tester with circular sample considering eddy currents is made and compared with the measurement to verify the correctness of the method and to analyze the magnetic field in the sample
Husserl, Edmund
2003-01-01
In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics. Husserl's work here provides an alternative model of...
PRIAM: A self consistent finite element code for particle simulation in electromagnetic fields
International Nuclear Information System (INIS)
Le Meur, G.; Touze, F.
1990-06-01
A 2 1/2 dimensional, relativistic particle simulation code is described. A short review of the used mixed finite element method is given. The treatment of the driving terms (charge and current densities), initial, boundary conditions are exposed. Graphical results are shown
International Nuclear Information System (INIS)
Xu, Yanlong
2015-01-01
Shear horizontal (SH) wave propagation in finite graded piezoelectric layered media is investigated by transfer matrix method. Different from the previous studies on SH wave propagation in completely periodic layered media, calculations on band structure and transmission in this paper show that the graded layered media possess very large band gaps. Harmonic wave simulation by finite element method (FEM) confirms that the reason of bandwidth enlargement is that waves within the band gap ranges are spatially enhanced and stopped by the corresponding graded units. The study suggests that the graded structure possesses the property of manipulating elastic waves spatially, which shows potential applications in strengthening energy trapping and harvesting. - Highlights: • Shear horizontal wave propagation in finite graded piezoelectric layered media is investigated by transfer matrix method. • Calculations on band structure and transmission show that the graded layered media possess very large band gaps. • Finite element method confirms that waves in band gaps are spatially enhanced and stopped by the graded units. • The study suggests that the graded structure possesses the property of manipulating elastic waves spatially
Studi Kompresi Data dengan Metode Arithmetic Coding
Santoso, Petrus
2001-01-01
In Bahasa Indonesia : Ada banyak sekali metode kompresi data yang ada saat ini. Sebagian besar metode tersebut bisa dikelompokkan ke dalam salah satu dari dua kelompok besar, statistical based dan dictionary based. Contoh dari dictionary based coding adalah Lempel Ziv Welch dan contoh dari statistical based coding adalah Huffman Coding dan Arithmetic Coding yang merupakan algoritma terbaru. Makalah ini mengulas prinsip-prinsip dari Arithmetic Coding serta keuntungan-keuntungannya dibandi...
How to be Brilliant at Mental Arithmetic
Webber, Beryl
2010-01-01
How to be Brilliant at Mental Arithmetic addresses the twin pillars of mental arithmetic - mental recall and mental agility. Mental recall depends on familiarity with number bonds and plenty of opportunity to practise. Mental agility depends more on confidence with the number system and the four operations. Using the worksheets in this book, students will learn about: tens and units; addition, subtraction, multiplication and division; addition shortcuts; product squares; quick recall; number se
Energy Technology Data Exchange (ETDEWEB)
Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar (Germany); Thamburaja, P., E-mail: prakash.thamburaja@gmail.com [Department of Mechanical & Materials Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi 43600 (Malaysia); Rabczuk, T., E-mail: timon.rabczuk@tdt.edu.vn [Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City (Viet Nam); Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City (Viet Nam)
2016-12-15
A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.
International Nuclear Information System (INIS)
Micic, Miodrag; Klymyshyn, Nicholas A.; Lu, H Peter
2004-01-01
Near-field optical enhancement at metal surfaces and methods such as surface plasmon resonance (SPR), surface-enhanced Raman scattering (SERS), fluorescent quenching and enhancement, and various near-field scanning microscopies (NSOM) all depend on a metals surface properties, mainly on its morphology and SPR resonant frequency. We report on simulations of the influence of different surface morphologies on electromagnetic field enhancements at the rough surfaces of noble metals and also evaluate the optimal conditions for the generation of a surface-enhanced Raman signal of absorbed species on a metallic substrate. All simulations were performed with a classical electrodynamics approach using the full set of Maxwells equations, which were solved with the three-dimensional finite element method (FEM). Two different classes of surfaces where modeled using fractals, representing diffusion limited aggregation growth dendritic structures, such as one on the surface of electrodes, and second one representing the sponge-like structure used to model surfaces of particles with high porosity, such as metal coated catalyst supports. The simulations depict the high inhomogeneity of an enhanced electromagnetic field as both a field enhancement and field attenuation near the surface. While the diffusion limited aggregation dendritical fractals enhanced the near-field electromagnetic field, the sponge fractals significantly reduced the local electromagnetic field intensity. Moreover, the fractal orders of the fractal objects did not significantly alter the total enhancement, and the distribution of a near-field enhancement was essentially invariant to the changes in the angle of an incoming laser beam
Energy Technology Data Exchange (ETDEWEB)
Typel, S; Wolter, H H [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Finite volume spectrum of 2D field theories from Hirota dynamics
International Nuclear Information System (INIS)
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro; Univ. do Porto
2008-12-01
We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luescher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model. (orig.)
Domain-General Factors Influencing Numerical and Arithmetic Processing
Directory of Open Access Journals (Sweden)
André Knops
2017-12-01
Full Text Available This special issue contains 18 articles that address the question how numerical processes interact with domain-general factors. We start the editorial with a discussion of how to define domain-general versus domain-specific factors and then discuss the contributions to this special issue grouped into two core numerical domains that are subject to domain-general influences (see Figure 1. The first group of contributions addresses the question how numbers interact with spatial factors. The second group of contributions is concerned with factors that determine and predict arithmetic understanding, performance and development. This special issue shows that domain-general (Table 1a as well as domain-specific (Table 1b abilities influence numerical and arithmetic performance virtually at all levels and make it clear that for the field of numerical cognition a sole focus on one or several domain-specific factors like the approximate number system or spatial-numerical associations is not sufficient. Vice versa, in most studies that included domain-general and domain-specific variables, domain-specific numerical variables predicted arithmetic performance above and beyond domain-general variables. Therefore, a sole focus on domain-general aspects such as, for example, working memory, to explain, predict and foster arithmetic learning is also not sufficient. Based on the articles in this special issue we conclude that both domain-general and domain-specific factors contribute to numerical cognition. But the how, why and when of their contribution still needs to be better understood. We hope that this special issue may be helpful to readers in constraining future theory and model building about the interplay of domain-specific and domain-general factors.
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Powell, Sarah R.; Seethaler, Pamela M.; Capizzi, Andrea M.; Schatschneider, Christopher; Fletcher, Jack M.
2006-01-01
The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…
Tahmasebibirgani, Mohammad Javad; Maskani, Reza; Behrooz, Mohammad Ali; Zabihzadeh, Mansour; Shahbazian, Hojatollah; Fatahiasl, Jafar; Chegeni, Nahid
2017-04-01
In radiotherapy, megaelectron volt (MeV) electrons are employed for treatment of superficial cancers. Magnetic fields can be used for deflection and deformation of the electron flow. A magnetic field is composed of non-uniform permanent magnets. The primary electrons are not mono-energetic and completely parallel. Calculation of electron beam deflection requires using complex mathematical methods. In this study, a device was made to apply a magnetic field to an electron beam and the path of electrons was simulated in the magnetic field using finite element method. A mini-applicator equipped with two neodymium permanent magnets was designed that enables tuning the distance between magnets. This device was placed in a standard applicator of Varian 2100 CD linear accelerator. The mini-applicator was simulated in CST Studio finite element software. Deflection angle and displacement of the electron beam was calculated after passing through the magnetic field. By determining a 2 to 5cm distance between two poles, various intensities of transverse magnetic field was created. The accelerator head was turned so that the deflected electrons became vertical to the water surface. To measure the displacement of the electron beam, EBT2 GafChromic films were employed. After being exposed, the films were scanned using HP G3010 reflection scanner and their optical density was extracted using programming in MATLAB environment. Displacement of the electron beam was compared with results of simulation after applying the magnetic field. Simulation results of the magnetic field showed good agreement with measured values. Maximum deflection angle for a 12 MeV beam was 32.9° and minimum deflection for 15 MeV was 12.1°. Measurement with the film showed precision of simulation in predicting the amount of displacement in the electron beam. A magnetic mini-applicator was made and simulated using finite element method. Deflection angle and displacement of electron beam were calculated. With
Huang, Sheng; Ao, Xiang; Li, Yuan-yuan; Zhang, Rui
2016-09-01
In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate ( BER) is 10-6, in the same simulation environment, the net coding gain ( NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.
Directory of Open Access Journals (Sweden)
Koichi Narahara
2012-01-01
Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
2015-01-01
Uni-directional glass fiber reinforced polymers play a central role in the task increasing the length of wind turbines blades and thereby lowering the cost of energy from wind turbine installations. During this, optimizing the mechanical performance regarding material stiffness, compression...... strength and fatigue performance is essential. Nevertheless, testing composites includes some challenges regarding stiffness determination using conventional strain gauges and achieving correct material failure unaffected by the gripping region during fatigue testing. Challenges, which in the present study......, has been addressed using the finite element method. During this, a verification of experimental observations, a deeper understanding on the test coupon loading and thereby improved test methods has been achieved....
Directory of Open Access Journals (Sweden)
GUO Wenjie
2017-08-01
Full Text Available Aiming at the current lack of analytical research concerning the cylindrical shell-flow field coupling vibration and sound radiation system under the influence of a free surface, this paper proposes an analytical method which solves the vibration response and far-field acoustic radiation of a finite cylindrical shell immersed at a finite depth. Based on the image method and Graf addition theorem, the analytical expression of the fluid velocity potential can be obtained, then combined with the energy functional of the variation method to deduce the shell-liquid coupling vibration equation, which can in turn solve the forced vibration response. The research shows that, compared with an infinite fluid, a free surface can increase at the same order of resonance frequency; but as the depth of immersion gradually increases, the mean square vibration velocity tends to become the same as that in an infinite fluid. Compared with numerical results from Nastran software, this shows that the present method is accurate and reliable, and has such advantages as a simple method and a small amount of calculation. The far-field radiated pressure can be obtained by the vibration response using the Fourier transformation and stationary phase method. The results indicate that the directivity and volatility of the far-field acoustic pressure of a cylindrical shell is similar to that of an acoustical dipole due to the free surface. However, the far-field acoustic pressure is very different from the vibration characteristics, and will not tend to an infinite fluid as the submerging depth increases. Compared with the numerical method, the method in this paper is simpler and has a higher computational efficiency. It enables the far-field acoustic radiation of an underwater cylindrical shell to be predicted quickly under the influence of external incentives and the free surface, providing guiding significance for acoustic research into the half space structure vibration
International Nuclear Information System (INIS)
Sadooghi, N.; Anaraki, K. Sohrabi
2008-01-01
Using the general structure of the vacuum polarization tensor Π μν (k 0 ,k) in the infrared (IR) limit, k 0 →0, the ring contribution to the QED effective potential at finite temperature and the nonzero magnetic field is determined beyond the static limit, (k 0 →0, k→0). The resulting ring potential is then studied in weak and strong magnetic field limits. In the weak magnetic field limit, at high temperature and for α→0, the improved ring potential consists of a term proportional to T 4 α 5/2 , in addition to the expected T 4 α 3/2 term arising from the static limit. Here, α is the fine structure constant. In the limit of the strong magnetic field, where QED dynamics is dominated by the lowest Landau level, the ring potential includes a novel term consisting of dilogarithmic function (eB)Li 2 (-(2α/π)(eB/m 2 )). Using the ring improved (one-loop) effective potential including the one-loop effective potential and ring potential in the IR limit, the dynamical chiral symmetry breaking of QED is studied at finite temperature and in the presence of the strong magnetic field. The gap equation, the dynamical mass and the critical temperature of QED in the regime of the lowest Landau level dominance are determined in the improved IR as well as in the static limit. For a given value of the magnetic field, the improved ring potential is shown to be more efficient in decreasing the critical temperature arising from the one-loop effective potential.
International Nuclear Information System (INIS)
Hao Kuan-Sheng; Huang Song-Ling; Zhao Wei; Wang Shen
2011-01-01
This paper presents an analytical method for electromagnetic acoustic transducers (EMATs) under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation (FFT). In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting's theorem. Then the currents under different frequencies are calculated according to Ohm's law and the pulsed current excitation is obtained by inverse fast Fourier transformation (IFFT). Lastly, the sequentially coupled finite element method (FEM) is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board (PCB) coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Furthermore, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied. (interdisciplinary physics and related areas of science and technology)
Exact simulation of Brown-Resnick random fields at a finite number of locations
DEFF Research Database (Denmark)
Dieker, Ton; Mikosch, Thomas Valentin
2015-01-01
We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.......We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure....
Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro
2014-05-01
This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if khthe aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.
International Nuclear Information System (INIS)
Isayev, A. A.; Yang, J.
2011-01-01
Spin-polarized states in dense neutron matter with the recently developed Skyrme effective interaction (BSk20 parametrization) are considered in the magnetic fields H up to 10 20 G at finite temperature. In a strong magnetic field, the total pressure in neutron matter is anisotropic, and the difference between the pressures parallel and perpendicular to the field direction becomes significant at H>H th ∼10 18 G. The longitudinal pressure decreases with the magnetic field and vanishes in the critical field 10 18 c 19 G, resulting in the longitudinal instability of neutron matter. With increasing temperature, the threshold H th and critical H c magnetic fields also increase. The appearance of the longitudinal instability prevents the formation of a fully spin-polarized state in neutron matter and only the states with moderate spin polarization are accessible. The anisotropic equation of state is determined at densities and temperatures relevant to the interiors of magnetars. The entropy of strongly magnetized neutron matter turns out to be larger than the entropy of nonpolarized matter. This is caused by some specific details in the dependence of the entropy on the effective masses of neutrons with spin up and spin down in a polarized state.
Relating arithmetical techniques of proportion to geometry
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic....... Considering 6 common Indonesian textbooks in use, we describe how proportion is explained and appears in examples and exercises, using an explicit reference model of the mathematical organizations of both themes. We also identify how the proportion themes of the geometry and arithmetic domains are linked. Our...
Space-Time Convolutional Codes over Finite Fields and Rings for Systems with Large Diversity Order
Directory of Open Access Journals (Sweden)
B. F. Uchôa-Filho
2008-06-01
Full Text Available We propose a convolutional encoder over the finite ring of integers modulo pk,Ã¢Â„Â¤pk, where p is a prime number and k is any positive integer, to generate a space-time convolutional code (STCC. Under this structure, we prove three properties related to the generator matrix of the convolutional code that can be used to simplify the code search procedure for STCCs over Ã¢Â„Â¤pk. Some STCCs of large diversity order (Ã¢Â‰Â¥4 designed under the trace criterion for n=2,3, and 4 transmit antennas are presented for various PSK signal constellations.
Finite element modeling of ground deformation and gravity field at Mt. Etna
Directory of Open Access Journals (Sweden)
G. Ganci
2008-06-01
Full Text Available An elastic 3-D axi-symmetric model based on Finite Element Method (FEM is proposed to compute ground deformation and gravity changes caused by overpressure sources in volcanic areas. The numerical computations are focused on the modeling of a complex description of Mt Etna in order to evaluate the effect of topography, medium heterogeneities and source geometries. Both ground deformation and gravity changes are investigated by solving a coupled numerical problem considering a simplified ground surface profile and a multi-layered crustal structure inferred from seismic tomography. The role of the source geometry is also explored taking into account spherical and ellipsoidal volumetric sources. The comparison between numerical results and those predicted by analytical solutions disclosed significant discrepancies. These differences constrain the applicability of simple spherical source and homogeneous half-space hypotheses, which are usually implicitly assumed when analytical solutions are applied.
Directory of Open Access Journals (Sweden)
CHETAN VASUDEVA
2017-10-01
Full Text Available Researchers have always shown keen interest in predetermining the electromagnetic field behavior inside an electrical machine at the design stage. Material properties of permanent magnet, selection of optimum air gap during the electromagnetic, thermal and structural design of generator are considered to be vital factors for an ideal machine. Generator output, heat rise, weight, and cost are a few of the characteristics which are directly influenced by the selection of the most advantageous material properties. Moreover, most theoretical studies have been conducted assuming that the air gap flux is sinusoidally distributed. The actual conduct of the air gap flux with the length of air gap and its impression on the performance of the generator has not been analyzed so far. In this paper, field analysis of permanent magnet generator using finite element method has been carried out to show the best material properties and air gap for optimum pattern.
Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.
2018-05-01
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.
FFT Algorithm for Binary Extension Finite Fields and Its Application to Reed–Solomon Codes
Lin, Sian Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.
2016-01-01
Recently, a new polynomial basis over binary extension fields was proposed, such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order O(n lg(n)), where n is the number of points evaluated in FFT
On the stabilization of toroidal pinches by finite larmor radius effects and toroidal magnetic field
International Nuclear Information System (INIS)
Singh, R.; Weiland, J.
1989-01-01
The radial eigenvalue problem for internal modes in a large aspect ratio toriodal pinch has been solved. A particularly stable regime for a weak but nonzero toroidal magnetic field has been found. (31 refs.)
SSWL and BWL: finite element models of compressed magnetic field current generators
Energy Technology Data Exchange (ETDEWEB)
Tucker, T.J.; Leeman, J.E.
1976-01-01
Documentation is presented for two new computer codes modeling the behavior of compressed magnetic field current generators. Code output results for the typical generator configurations are presented and compared to experimental results. (auth)
Self-reference in Arithmetic I
Halbach, Volker; Visser, Albert|info:eu-repo/dai/nl/068579985
2014-01-01
A Gödel sentence is often described as a sentence saying about itself that it is not provable, and a Henkin sentence as a sentence stating its own provability. We discuss what it could mean for a sentence of arithmetic to ascribe to itself a property such as provability or unprovability. The
A functional interpretation for nonstandard arithmetic
van den Berg, B.; Briseid, E.; Safarik, P.
2012-01-01
We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our
Fuzzy Logic and Arithmetical Hierarchy III
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2001-01-01
Roč. 68, č. 1 (2001), s. 129-142 ISSN 0039-3215 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * basic fuzzy logic * Lukasiewicz logic * Godel logic * product logic * arithmetical hierarchy Subject RIV: BA - General Mathematics
Secret Codes, Remainder Arithmetic, and Matrices.
Peck, Lyman C.
This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…
PandA : pairings and arithmetic
Chuengsatiansup, C.; Naehrig, M.; Ribarski, P.; Schwabe, P.; Cao, Z.; Zhang, F.
2014-01-01
This paper introduces PandA, a software framework for Pairings and Arithmetic. It is designed to bring together advances in the efficient computation of cryptographic pairings and the development and implementation of pairing-based protocols. The intention behind the PandA framework is to give
Lattice for FPGAs using logarithmic arithmetic
Czech Academy of Sciences Publication Activity Database
Kadlec, Jiří; Matoušek, Rudolf; Heřmánek, Antonín; Líčko, Miroslav; Tichý, Milan
2002-01-01
Roč. 74, č. 906 (2002), s. 53-56 ISSN 0013-4902 Grant - others: ESPRIT (XE) 33544 Institutional research plan: CEZ:AV0Z1075907 Keywords : lattice Rls algorithm * FPGA * logarithmic arithmetic Subject RIV: JC - Computer Hardware ; Software Impact factor: 0.039, year: 2002
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
Circuit lower bounds in bounded arithmetics
Czech Academy of Sciences Publication Activity Database
Pich, Ján
2015-01-01
Roč. 166, č. 1 (2015), s. 29-45 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.582, year: 2015 http://www.sciencedirect.com/science/article/pii/S0168007214000888
Personal Experience and Arithmetic Meaning in Semantic Dementia
Julien, Camille L.; Neary, David; Snowden, Julie S.
2010-01-01
Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…
Specificity and overlap in skills underpinning reading and arithmetical fluency
van Daal, V.; van der Leij, A.; Adèr, H.
2013-01-01
The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading,
Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model
Paga, Pierre; Kühn, Reimer
2017-08-01
We study the large deviations of the magnetization at some finite time in the Curie-Weiss random field Ising model with parallel updating. While relaxation dynamics in an infinite-time horizon gives rise to unique dynamical trajectories [specified by initial conditions and governed by first-order dynamics of the form mt +1=f (mt) ] , we observe that the introduction of a finite-time horizon and the specification of terminal conditions can generate a host of metastable solutions obeying second-order dynamics. We show that these solutions are governed by a Newtonian-like dynamics in discrete time which permits solutions in terms of both the first-order relaxation ("forward") dynamics and the backward dynamics mt +1=f-1(mt) . Our approach allows us to classify trajectories for a given final magnetization as stable or metastable according to the value of the rate function associated with them. We find that in analogy to the Freidlin-Wentzell description of the stochastic dynamics of escape from metastable states, the dominant trajectories may switch between the two types (forward and backward) of first-order dynamics. Additionally, we show how to compute rate functions when uncertainty in the quenched disorder is introduced.
Learning, Realizability and Games in Classical Arithmetic
Aschieri, Federico
2010-12-01
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.
International Nuclear Information System (INIS)
Sulbhewar, Litesh N; Raveendranath, P
2014-01-01
An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)
Near Field Modeling for the Maule Tsunami from DART, GPS and Finite Fault Solutions (Invited)
Arcas, D.; Chamberlin, C.; Lagos, M.; Ramirez-Herrera, M.; Tang, L.; Wei, Y.
2010-12-01
The earthquake and tsunami of February, 27, 2010 in central Chile has rekindled an interest in developing techniques to predict the impact of near field tsunamis along the Chilean coastline. Following the earthquake, several initiatives were proposed to increase the density of seismic, pressure and motion sensors along the South American trench, in order to provide field data that could be used to estimate tsunami impact on the coast. However, the precise use of those data in the elaboration of a quantitative assessment of coastal tsunami damage has not been clarified. The present work makes use of seismic, Deep-ocean Assessment and Reporting of Tsunamis (DART®) systems, and GPS measurements obtained during the Maule earthquake to initiate a number of tsunami inundation models along the rupture area by expressing different versions of the seismic crustal deformation in terms of NOAA’s tsunami unit source functions. Translation of all available real-time data into a feasible tsunami source is essential in near-field tsunami impact prediction in which an impact assessment must be generated under very stringent time constraints. Inundation results from each different source are then contrasted with field and tide gauge data by comparing arrival time, maximum wave height, maximum inundation and tsunami decay rate, using field data collected by the authors.
Phase structure of (φ4)3 field theory at finite temperature
International Nuclear Information System (INIS)
Efimov, G.V.
1992-01-01
Phase structure of φ 4 field theory in the space-time R 3 is investigated at arbitrary coupling constant and temperature. The critical values of the coupling constant and temperature, corresponding to the phase transitions in the system, are calculated by the canonical transformation method within formalism of thermo field dynamics. The Hamiltonians describing the system in each phase are obtained straightforwardly. Comparison with the two-dimensional case shows a crucial influence of higher order renormalization on the phase structure of the model. 13 refs.; 5 figs
Finite element simulation of pressure-loaded phase-field fractures
Singh, N.; Verhoosel, C.V.; van Brummelen, E.H.
2018-01-01
A non-standard aspect of phase-field fracture formulations for pressurized cracks is the application of the pressure loading, due to the fact that a direct notion of the fracture surfaces is absent. In this work we study the possibility to apply the pressure loading through a traction boundary
Electron cyclotron instabilities of finite pressure inhomogeneous plasma in crossed fields
International Nuclear Information System (INIS)
Kirochkin, Yu.A.; Pokroev, A.G.; Stepanov, K.N.
1979-01-01
The stability of inhomogeneous plasma sheet with β<=1 in crossed electric and magnetic fields is investigated. The differential equation describing potential oscillations is obtained. Using the local approximation the sheet is shown to be unstable against the excitation of short wavelength electron cyclotron oscillations. The validity criterion of this method for a given type of waves is derived
Zhang, Xiao; Räsänen, Pekka; Koponen, Tuire; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2017-01-01
The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that…
International Nuclear Information System (INIS)
Lan, Haiqiang; Zhang, Zhongjie
2011-01-01
The finite-difference (FD) method is a powerful tool in seismic wave field modelling for understanding seismic wave propagation in the Earth's interior and interpreting the real seismic data. The accuracy of FD modelling partly depends on the implementation of the free-surface (i.e. traction-free) condition. In the past 40 years, at least six kinds of free-surface boundary condition approximate schemes (such as one-sided, centred finite-difference, composed, new composed, implicit and boundary-modified approximations) have been developed in FD second-order elastodynamic simulation. Herein we simulate seismic wave fields in homogeneous and lateral heterogeneous models using these free-surface boundary condition approximate schemes and evaluate their stability and applicability by comparing with corresponding analytical solutions, and then quantitatively evaluate the accuracies of different approximate schemes from the misfit of the amplitude and phase between the numerical and analytical results. Our results confirm that the composed scheme becomes unstable for the V s /V p ratio less than 0.57, and suggest that (1) the one-sided scheme is only accurate to first order and therefore introduces serious errors for the shorter wavelengths, other schemes are all of second-order precision; (2) the new composed, implicit and boundary-modified schemes are stable even when the V s /V p ratio is less than 0.2; (3) the implicit and boundary-modified schemes are able to deal with laterally varying (heterogeneous) free surface; (4) in the corresponding stability range, the one-sided scheme shows remarkable errors in both phase and amplitude compared to analytical solution (which means larger errors in travel-time and reflection strength), the other five approximate schemes show better performance in travel-time (phase) than strength (amplitude)
International Nuclear Information System (INIS)
Eab, C. H.; Lim, S. C.; Teo, L. P.
2007-01-01
This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed
International Nuclear Information System (INIS)
Bergel'son, A.M.; Rajzer, Yu.P.; Surzhikov, S.T.
1991-01-01
Explosion in vacuum or in rarefied gas in the presence of magnetic field is a prototype of a series of natural cosmic and laboratory processes 'spherical' explosion is considered in MHD approximation. The problem, really two-dimensional in the case of uniform medium, is transformed to unidimensional one in result of corresponding angle averaging. These problems are solved with the use of the scheme of the second order accuracy of large particle method with introduction of artificial viscosity
Relationship between retinal distance and object field angles for finite schematic eyes.
Suheimat, Marwan; Zhu, Hai-Feng; Lambert, Andrew; Atchison, David A
2016-07-01
Retinal anatomical studies have used the Drasdo & Fowler three-refracting surface schematic eye to convert between retinal distances and object field angles. We compared its performance at this task with those of more sophisticated four-refracting surface schematic eyes. Raytracing was performed for Drasdo & Fowler, Lotmar, Navarro, Liou & Brennan, Kooijman and Atchison schematic eyes, and some of their variants. The Drasdo & Fowler eye gives a greater rate of change of object field angle with retinal distance at the retinal centre of about 5% than the other schematic eyes. This rate of change also increases much more quickly into the peripheral retina for the Drasdo & Fowler eye than for the other eyes. The reason for these differences is only that the Drasdo & Fowler eye is shorter than the other eyes. The relationship between retinal distance and visual field angle appears robust to changes in retinal radius of curvature when the retina is spherical. The retinal asphericity of Kooijman and Atchison eyes appears to play a role beyond 14 mm (~50°). Changing the length of the Drasdo & Fowler eye, to match those of the four-refracting surface schematic eyes, gives similar relationships between retinal distance and object field angle up to a retinal distance of approximately 14 mm (~50°). The relationship will change with refractive error as this is related to axial length and to retinal shape, and this should be taken into consideration for accurate conversions. For distances and angles beyond 14 mm and ~50°, retinal shape should be taken into account. © 2016 The Authors Ophthalmic & Physiological Optics © 2016 The College of Optometrists.
Bosons system with finite repulsive interaction: self-consistent field method
International Nuclear Information System (INIS)
Renatino, M.M.B.
1983-01-01
Some static properties of a boson system (T = zero degree Kelvin), under the action of a repulsive potential are studied. For the repulsive potential, a model was adopted consisting of a region where it is constant (r c ), and a decay as 1/r (r > r c ). The self-consistent field approximation used takes into account short range correlations through a local field corrections, which leads to an effective field. The static structure factor S(q-vector) and the effective potential ψ(q-vector) are obtained through a self-consistent calculation. The pair-correlation function g(r-vector) and the energy of the collective excitations E(q-vector) are also obtained, from the structure factor. The density of the system and the parameters of the repulsive potential, that is, its height and the size of the constant region were used as variables for the problem. The results obtained for S(q-vector), g(r-vector) and E(q-vector) for a fixed ratio r o /r c and a variable λ, indicates the raising of a system structure, which is more noticeable when the potential became more repulsive. (author)
FFT Algorithm for Binary Extension Finite Fields and Its Application to Reed–Solomon Codes
Lin, Sian Jheng
2016-08-15
Recently, a new polynomial basis over binary extension fields was proposed, such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order O(n lg(n)), where n is the number of points evaluated in FFT. In this paper, we reformulate this FFT algorithm, such that it can be easier understood and be extended to develop frequency-domain decoding algorithms for (n = 2(m), k) systematic Reed-Solomon (RS) codes over F-2m, m is an element of Z(+), with n-k a power of two. First, the basis of syndrome polynomials is reformulated in the decoding procedure so that the new transforms can be applied to the decoding procedure. A fast extended Euclidean algorithm is developed to determine the error locator polynomial. The computational complexity of the proposed decoding algorithm is O(n lg(n-k)+(n-k)lg(2)(n-k)), improving upon the best currently available decoding complexity O(n lg(2)(n) lg lg(n)), and reaching the best known complexity bound that was established by Justesen in 1976. However, Justesen\\'s approach is only for the codes over some specific fields, which can apply Cooley-Tukey FFTs. As revealed by the computer simulations, the proposed decoding algorithm is 50 times faster than the conventional one for the (2(16), 2(15)) RS code over F-216.
Palchaudhuri, Ayan
2016-01-01
This book describes the optimized implementations of several arithmetic datapath, controlpath and pseudorandom sequence generator circuits for realization of high performance arithmetic circuits targeted towards a specific family of the high-end Field Programmable Gate Arrays (FPGAs). It explores regular, modular, cascadable, and bit-sliced architectures of these circuits, by directly instantiating the target FPGA-specific primitives in the HDL. Every proposed architecture is justified with detailed mathematical analyses. Simultaneously, constrained placement of the circuit building blocks is performed, by placing the logically related hardware primitives in close proximity to one another by supplying relevant placement constraints in the Xilinx proprietary “User Constraints File”. The book covers the implementation of a GUI-based CAD tool named FlexiCore integrated with the Xilinx Integrated Software Environment (ISE) for design automation of platform-specific high-performance arithmetic circuits from us...
Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids
Svendsen, Bob; Shanthraj, Pratheek; Raabe, Dierk
2018-03-01
The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To this end, basic balance and constitutive relations from non-equilibrium thermodynamics and continuum mixture theory are combined with a phase-field-based description of multicomponent solid phases and their interfaces. Solid phase modeling is based in particular on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields (e.g., related to chemical ordering, structural ordering, or defects), and local internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables. In this context, various phase interface models are considered. In the equilibrium limit, phase contrasts in composition and local deformation in the phase interface region are determined via bulk energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multicomponent, multiphase, generalization of existing two-phase binary alloy interface equilibrium conditions (e.g., KKS). On the mechanical side, the equilibrium limit of one interface model considered represents a multiphase generalization of Reuss-Sachs conditions from mechanical homogenization theory. Analogously, other interface models considered represent generalizations of interface equilibrium conditions consistent with laminate and sharp-interface theory. In the last part of the work, selected existing models are formulated within the current framework as special cases and discussed in detail.
The dynamics of the nuclear disassembly in a field-theoretical model at finite entropies
International Nuclear Information System (INIS)
Knoll, J.; Strack, B.
1984-10-01
The expansion phase of a hot nuclear system as created in an energetic heavy-ion collision is calculated and discussed by a selfconsistent field-theoretical model. Dynamical instabilities arising during the expansion from strong fluctuations of the one-body density are included explicitely. First multiplicity distributions and mass spectra resulting from a series of numerical runs in a 2+1 dimensional model world are presented. The dependence of break-up dynamics both on the properties of the binding force and possible correlations in the initially compressed hot state are discussed. (orig.)
International Nuclear Information System (INIS)
Yoshida, Makoto; Ohta, Hitoshi; Ito, Toshimitsu; Ajiro, Yoshitami
2006-01-01
We have performed high field and multi-frequency ESR measurements of finite length S=1 antiferromagnetic chains in Y 2 BaNi 0.96 Mg 0.04 O 5 . Owing to the high spectral resolution by high fields and high frequencies, observed ESR signals can be separated into the contributions of the finite chains with various chain lengths. Our results clearly show that the edge spins actually interact with each other through the quantum spin chain and the interaction depends on the chain length N. (author)
Dictionary of algebra, arithmetic, and trigonometry
Krantz, Steven G
2000-01-01
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geom...
Nonverbal arithmetic in humans: light from noise.
Cordes, Sara; Gallistel, C R; Gelman, Rochel; Latham, Peter
2007-10-01
Animal and human data suggest the existence of a cross-species system of analog number representation (e.g., Cordes, Gelman, Gallistel, & Whalen, 2001; Meeck & Church, 1983), which may mediate the computation of statistical regularities in the environment (Gallistel, Gelman, & Cordes, 2006). However, evidence of arithmetic manipulation of these nonverbal magnitude representations is sparse and lacking in depth. This study uses the analysis of variability as a tool for understanding properties of these combinatorial processes. Human subjects participated in tasks requiring responses dependent upon the addition, subtraction, or reproduction of nonverbal counts. Variance analyses revealed that the magnitude of both inputs and answer contributed to the variability in the arithmetic responses, with operand variability dominating. Other contributing factors to the observed variability and implications for logarithmic versus scalar models of magnitude representation are discussed in light of these results.
Hybrid content addressable memory MSD arithmetic
Li, Yao; Kim, Dai Hyun; Kostrzewski, Andrew A.; Eichmann, George
1990-07-01
The modified signed-digit (MSD) number system, because of its inherent weak interdigit dependance, has been suggested as a useful means for a fast and parallel digital arithmetic. To maintain a fast processing speed, a single-stage holographic optical content-addressable memory (CAM) based MSD algorithm was suggested. In this paper, a novel non-holographic opto-electronic CAM based fast MSD addition processing architecture is proposed. The proposed concept has been verified with our first-order proof-of-principle experiments. A figure of merit comparison of this and other existing approaches is also presented. Based on this key opto-electronic CAM element, implementation of more sophisticated I'VISD arithmetic, such as optical MSD subtraction and multiplication operations, are proposed.
Finite element calculation of fields around the end region of a turbine generator test rig
Energy Technology Data Exchange (ETDEWEB)
Eastham, J.F.; Rodger, D.; Lai, H.C.; Nouri, H. (Univ. of Bath (United Kingdom))
1993-03-01
Under transient conditions, most often caused by faults in the power system, unbalanced load is presented to a turbine generator. This gives rise to airgap fields which do not travel at the speed of the rotor, and cause induced currents which occur in the solid steel surface. This can cause high local heating. The current path is generally in the axial direction of the machine but the distribution in the end region is not so well known. Here, comparisons are drawn between the use of surface impedance elements and volume elements when modeling a test rig using the MEGA package. The test rig is representative of a turbine generator. The work is supported by practical measurements.
Coherent states, pseudodifferential analysis and arithmetic
Unterberger, André
2012-06-01
Basic questions regarding families of coherent states include describing some constructions of such and the way they can be applied to operator theory or partial differential equations. In both questions, pseudodifferential analysis is important. Recent developments indicate that they can contribute to methods in arithmetic, especially modular form theory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
A sorting network in bounded arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2011-01-01
Roč. 162, č. 4 (2011), s. 341-355 ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * sorting network * proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001272
Basak, Anup; Levitas, Valery I.
2018-04-01
A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.
W7-X vacuum and finite-β magnetic field structure resolved with the HINT 3D equilibrium code
International Nuclear Information System (INIS)
Hayashi, T.; Merkel, P.; Nuehrenberg, J.; Schwenn, U.
1994-01-01
The 3D equilibrium code HINT allows the direct investigation of finite-β effects on sizes and phases of islands in genuinely 3D configurations like the W7-X stellarator planned by the Max-Planck-Institut fuer Plasmaphysik in Germany. The code does not require the existence of nested flux surfaces. This, in contrast to the inverse formulation used in the VMEC code, leads to a considerably more complex computational goal. The HINT code combines some crucial features reducing the numerical problems and the computational effort to such an extent as to allow computation of 3D equilibria at finite-β with magnetic islands. The code is based on a two-step procedure: Starting from a given B and an initial pressure, the iteration technique for the pressure advancement is differencing in an artificial time with an explicit 4th order scheme, or - alternatively for resolving the island topology - field lines starting from all gridpoints are followed long enough to allow pressure equalization along these. B.∇p 0, for fixed B. In a second step, p is kept fixed and B is advanced with an artificial time for solving ∇p - jxB = 0 under the constraint of vanishing toroidal current J. The differential equations are discretized in space with 4th order difference approximations on an Eulerian grid spanned by a rectangular box whose toroidal rotation law follows the W7-X geometry. The two sub-iteration steps are repeated until the force balance is satisfied to an appropriate accuracy. The boundaries (where the boundary conditions are prescribed) are far enough away from the last closed magnetic surface, thus guaranteeing the motion of the plasma column not being constrained by the boundary conditions. Due to the stellarator symmetry in the toroidal direction only half of an equilibrium period is computed, using modified periodic boundary conditions guaranteeing the 4th order of the spatial discretization. (author) 5 refs., 4 figs
Arithmetic functions in torus and tree networks
Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.
2007-12-25
Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.
International Nuclear Information System (INIS)
Hua Jinsong; Lin Ping; Liu Chun; Wang Qi
2011-01-01
Highlights: → We study phase-field models for multi-phase flow computation. → We develop an energy-law preserving C0 FEM. → We show that the energy-law preserving method work better. → We overcome unphysical oscillation associated with the Cahn-Hilliard model. - Abstract: We use the idea in to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C 0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.
Brauer groups and obstruction problems moduli spaces and arithmetic
Hassett, Brendan; Várilly-Alvarado, Anthony; Viray, Bianca
2017-01-01
The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: · Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman...
Spherical conducting probes in finite Debye length plasmas and E x B fields
International Nuclear Information System (INIS)
Patacchini, Leonardo; Hutchinson, Ian H
2011-01-01
The particle-in-cell code SCEPTIC3D (Patacchini and Hutchinson 2010 Plasma Phys. Control. Fusion 52 035005) is used to calculate the interaction of a transversely flowing magnetized plasma with a negatively charged spherical conductor, in the entire range of magnetization and Debye length. The results allow the first fully self-consistent analysis of probe operation where neither the ion Larmor radius nor the Debye length are approximated by zero or infinity. An important transition in plasma structure occurs when the Debye length exceeds the average ion Larmor radius, as the sphere starts to shield the convective electric field driving the flow. A remarkable result is that in those conditions, the ion current can significantly exceed the unmagnetized orbital motion limit. When both the Debye length and the Larmor radius are small compared with the probe dimensions, however, their ratio does not affect the collection pattern significantly, and Mach-probe calibration methods derived in the context of quasineutral strongly magnetized plasmas (Patacchini and Hutchinson 2009 Phys. Rev. E 80 036403) hold for Debye lengths and ion Larmor radii smaller than about 10% of the probe radius.
Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field
Energy Technology Data Exchange (ETDEWEB)
Burinskaya, T. M., E-mail: tburinsk@iki.rssi.ru; Shevelev, M. M. [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2016-10-15
Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.
International Nuclear Information System (INIS)
Gelis, Francois
1998-12-01
The general framework of this work is thermal field theory, and more precisely the perturbative calculation of thermal Green's functions. In a first part, I consider the problems closely related to the formalism itself. After two introductory chapters devoted to set up the framework and the notations used afterwards, a chapter is dedicated to a clarification of certain aspects of the justification of the Feynman rules of the real time formalism. Then, I consider in the chapter 4 the problem of cutting rules in the real time formalisms. In particular, after solving a controversy on this subject, I generalize these cutting rules to the 'retarded-advanced' version of this formalism. Finally, the last problem considered in this part is that of the pion decay into two photons in a thermal bath. I show that the discrepancies found in the literature are due to peculiarities of the analytical properties of the thermal Green's functions. The second part deals with the calculations of the photons or dilepton (virtual photon) production rate by a quark gluon plasma. The framework of this study is the effective theory based on the resummation of hard thermal loops. The first aspects of this study is related to the production of virtual photons, where we show that important contributions arise at two loops, completing the result already known at one loop. In the case of real photon production, we show that extremely strong collinear singularities make two loop contributions dominant compared to one loop ones. In both cases, the importance of two loop contributions can be interpreted as weaknesses of the hard thermal loop approximation. (author)
Aldakheel, Fadi; Wriggers, Peter; Miehe, Christian
2017-12-01
The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2-15, 1977). Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486-522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation. It combines modified structures of Gurson-Tvergaard-Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157-169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1-17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit-Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup-cone failure mechanism.
International Nuclear Information System (INIS)
Johnson, W.R.; Dzuba, V.A.; Safronova, U.I.; Safronova, M.S.
2004-01-01
A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C 3 for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory
Tao, Ran
2015-01-01
is aimed to accurately measure the displacement and strain fields at the fiber-matrix scale in a cross-ply composite. First, the theories of both local subset-based digital image correlation (DIC) and global finite-element based DIC are outlined. Second, in
Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field
Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.
2015-10-01
We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.
Keller, Trevor; Lindwall, Greta; Ghosh, Supriyo; Ma, Li; Lane, Brandon M; Zhang, Fan; Kattner, Ursula R; Lass, Eric A; Heigel, Jarred C; Idell, Yaakov; Williams, Maureen E; Allen, Andrew J; Guyer, Jonathan E; Levine, Lyle E
2017-10-15
Numerical simulations are used in this work to investigate aspects of microstructure and microseg-regation during rapid solidification of a Ni-based superalloy in a laser powder bed fusion additive manufacturing process. Thermal modeling by finite element analysis simulates the laser melt pool, with surface temperatures in agreement with in situ thermographic measurements on Inconel 625. Geometric and thermal features of the simulated melt pools are extracted and used in subsequent mesoscale simulations. Solidification in the melt pool is simulated on two length scales. For the multicomponent alloy Inconel 625, microsegregation between dendrite arms is calculated using the Scheil-Gulliver solidification model and DICTRA software. Phase-field simulations, using Ni-Nb as a binary analogue to Inconel 625, produced microstructures with primary cellular/dendritic arm spacings in agreement with measured spacings in experimentally observed microstructures and a lesser extent of microsegregation than predicted by DICTRA simulations. The composition profiles are used to compare thermodynamic driving forces for nucleation against experimentally observed precipitates identified by electron and X-ray diffraction analyses. Our analysis lists the precipitates that may form from FCC phase of enriched interdendritic compositions and compares these against experimentally observed phases from 1 h heat treatments at two temperatures: stress relief at 1143 K (870 °C) or homogenization at 1423 K (1150 °C).
Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.
1992-01-01
Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.
International Nuclear Information System (INIS)
Ranade, Kedar S.
2009-01-01
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
International Nuclear Information System (INIS)
Ting, Wang; Zhan-Zhong, Cui; Li-Xin, Xu
2009-01-01
The transient thermoelastic stress fields of GaN films is analyzed by the finite element method for the laser lift-off (LLO) technique. Stress distributions in GaN films irradiated by pulse laser with different energy densities as functions of time and depth are simulated. The results show that the high thermoelastic stress distributions in GaN films localize within about 1 μm below the GaN/Al 2 O 3 interface using proper laser parameters. It is also found that GaN films can avoid the thermal deformation because the maximum thermoelastic stress 4.28 GPa is much smaller than the yield strength of GaN 15GPa. The effects of laser beam dimension and the thickness of GaN films on stress distribution are also analyzed. The variation range of laser beam dimension as a function of the thickness of GaN films is simulated to keep the GaN films free of thermal deformation. LLO experiments are also carried out. GaN-based light-emitting diodes (LEDs) are separated from sapphire substrates using the parameters obtained from the simulation. Compared with devices before LLO, P–I–V measurements of GaN-based LEDs after LLO show that the electrical and optical characteristics improve greatly, indicating that no stress damage is brought to GaN films using proper parameters obtained by calculation during LLO
Sun, Jian
2011-08-06
In this paper, an extraordinary magnetoresistance (EMR) device made of an InSb/Au hybrid structure was investigated. Those devices have a large potential in becoming a new generation of highly sensitive and cheap magnetic micro sensors. A crucial factor for the performance is the interface between the InSb and Au, which suffers from a certain contact resistivity. The Finite Element Method (FEM) was employed to simulate the current redistribution in the device, under an applied magnetic field. Specifically, the influence of the contact resistivity between the InSb bulk and Au shunt was studied. In a device with optimized geometry and without contact resistivity between the layers of InSb and Au, the EMR effect and the sensitivity show values of 1.89 × 104% and 0.02%/(10-4 T), respectively, at 1 Tesla. For values of contact resistivity up to 10-8cm2 the EMR effect is almost constant, while for higher values the EMR effect decreases exponentially. However, the sensitivity of the device does not decrease until 5 × 10-6 cm2 of contact resistivity. Only beyond this value the sensitivity, which in most cases is associated with the performance of the device, will deteriorate. © Springer Science+Business Media, LLC 2011.
International Nuclear Information System (INIS)
Kwak, Chang-Seob; Kim, Hong-Kyu; Kim, Tae-Hoon; Lee, Se-Hee
2017-01-01
A systematic numerical method for analyzing a 3D moving vacuum arc was proposed and tested in this research by using a transverse magnetic field (TMF) contact. The analysis was carried out by employing the finite element method and the experimental energy equation defined by Gundlach's formula. In the literature, the vacuum interrupter has been widely applied to medium-voltage switching circuits. TMF-type contacts use the Lorentz force density to move a high-temperature arc so as to prevent the contacts from being melted and damaged. The material erosion caused by the arc on the electrode's surface is an important process that results in the interruptive capabilities of these vacuum interrupters. In a classical arc model, to move the vacuum arc, it is required that the magneto-hydrodynamics be analyzed in the arc region at each step. However, with this approach convergence is difficult, resulting in a very time-consuming. Therefore, we propose a new technique to predict the behaviors of vacuum arc between two electrodes. This new approach adopts the experimental arc voltage equation between two electrodes defined by Gundlach's formula. We verify our proposed model by comparing its results with the arcing behaviors obtained from earlier experiments.
Arithmetic differential equations on $GL_n$, I: differential cocycles
Buium, Alexandru; Dupuy, Taylor
2013-01-01
The theory of differential equations has an arithmetic analogue in which derivatives are replaced by Fermat quotients. One can then ask what is the arithmetic analogue of a linear differential equation. The study of usual linear differential equations is the same as the study of the differential cocycle from $GL_n$ into its Lie algebra given by the logarithmic derivative. However we prove here that there are no such cocycles in the context of arithmetic differential equations. In sequels of t...
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.
Martins, J. M. P.; Thuillier, S.; Andrade-Campos, A.
2018-05-01
The identification of material parameters, for a given constitutive model, can be seen as the first step before any practical application. In the last years, the field of material parameters identification received an important boost with the development of full-field measurement techniques, such as Digital Image Correlation. These techniques enable the use of heterogeneous displacement/strain fields, which contain more information than the classical homogeneous tests. Consequently, different techniques have been developed to extract material parameters from full-field measurements. In this study, two of these techniques are addressed, the Finite Element Model Updating (FEMU) and the Virtual Fields Method (VFM). The main idea behind FEMU is to update the parameters of a constitutive model implemented in a finite element model until both numerical and experimental results match, whereas VFM makes use of the Principle of Virtual Work and does not require any finite element simulation. Though both techniques proved their feasibility in linear and non-linear constitutive models, it is rather difficult to rank their robustness in plasticity. The purpose of this work is to perform a comparative study in the case of elasto-plastic models. Details concerning the implementation of each strategy are presented. Moreover, a dedicated code for VFM within a large strain framework is developed. The reconstruction of the stress field is performed through a user subroutine. A heterogeneous tensile test is considered to compare FEMU and VFM strategies.
Using fuzzy arithmetic in containment event trees
International Nuclear Information System (INIS)
Rivera, S.S.; Baron, Jorge H.
2000-01-01
The use of fuzzy arithmetic is proposed for the evaluation of containment event trees. Concepts such as improbable, very improbable, and so on, which are subjective by nature, are represented by fuzzy numbers. The quantitative evaluation of containment event trees is based on the extension principle, by which operations on real numbers are extended to operations on fuzzy numbers. Expert knowledge is considered as state of the base variable with a normal distribution, which is considered to represent the membership function. Finally, this paper presents results of an example calculation of a containment event tree for the CAREM-25 nuclear power plant, presently under detailed design stage at Argentina. (author)
The Structure of Models of Peano Arithmetic
Kossak, Roman
2006-01-01
Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to HaimGaifman, and some of the results are classical but have never been published in a book form before.
Modeling Brain Responses in an Arithmetic Working Memory Task
Hamid, Aini Ismafairus Abd; Yusoff, Ahmad Nazlim; Mukari, Siti Zamratol-Mai Sarah; Mohamad, Mazlyfarina; Manan, Hanani Abdul; Hamid, Khairiah Abdul
2010-07-01
Functional magnetic resonance imaging (fMRI) was used to investigate brain responses due to arithmetic working memory. Nine healthy young male subjects were given simple addition and subtraction instructions in noise and in quiet. The general linear model (GLM) and random field theory (RFT) were implemented in modelling the activation. The results showed that addition and subtraction evoked bilateral activation in Heschl's gyrus (HG), superior temporal gyrus (STG), inferior frontal gyrus (IFG), supramarginal gyrus (SG) and precentral gyrus (PCG). The HG, STG, SG and PCG activate higher number of voxels in noise as compared to in quiet for addition and subtraction except for IFG that showed otherwise. The percentage of signal change (PSC) in all areas is higher in quiet as compared to in noise. Surprisingly addition (not subtraction) exhibits stronger activation.
Sabiniarz, Patrick; Kropp, Wolfgang
2010-07-01
Although tyre/road noise has been a research subject for more than three decades, there is still no consensus in the literature as to which waves on a tyre are mainly responsible for the radiation of sound during rolling. Even the free vibrational behaviour of a stationary (non-rotating) tyre, not in contact with the ground, is still not well understood in the mid- and high-frequency ranges. Thus, gaining an improved understanding of this behaviour is a natural first step towards illuminating the question of which waves on a rolling tyre contribute to sound radiation. This is the topic of the present paper, in which a model based on the waveguide finite element method (WFEM) is used to study free wave propagation, on a stationary tyre, in the range 0-1500 Hz. In the low-frequency region (0-300 Hz), wave propagation is found to be rather straightforward, with two main wave-types present. Both have cross-section modes involving a nearly rigid motion of the belt. For higher frequencies (300-1500 Hz) the behaviour is more complex, including phenomena such as 'curve veering' and waves for which the phase speed and group speed have opposite signs. Wave-types identified in this region include (i) waves involving mainly sidewall deformation, (ii) belt bending waves, (iii) a wave with significant extensional deformation of the central belt region and (iv) a wave with a 'breathing' cross-section mode. The phase speed corresponding to found waves is computed and their radiation efficiency is discussed, assuming free-field conditions. In a future publication, the tyre model will be used in conjunction with a contact model and a radiation model to investigate the contribution of these waves to radiated sound during rolling.
García, E.; Oliver, A.; Diaz, O.; Diez, Y.; Gubern-Mérida, A.; Martí, R.; Martí, J.
2017-03-01
Patient-specific finite element (FE) models of the breast have received increasing attention due to the potential capability of fusing images from different modalities. During the Magnetic Resonance Imaging (MRI) to X-ray mammography registration procedure, the FE model is compressed mimicking the mammographic acquisition. Subsequently, suspicious lesions in the MRI volume can be projected into the 2D mammographic space. However, most registration algorithms do not provide the reverse information, avoiding to obtain the 3D geometrical information from the lesions localized in the mammograms. In this work we introduce a fast method to localize the 3D position of the lesion within the MRI, using both cranio-caudal (CC) and medio-lateral oblique (MLO) mammographic projections, indexing the tetrahedral elements of the biomechanical model by means of an uniform grid. For each marked lesion in the Full-Field Digital Mammogram (FFDM), the X-ray path from source to the marker is calculated. Barycentric coordinates are computed in the tetrahedrons traversed by the ray. The list of elements and coordinates allows to localize two curves within the MRI and the closest point between both curves is taken as the 3D position of the lesion. The registration errors obtained in the mammographic space are 9.89 +/- 3.72 mm in CC- and 8.04 +/- 4.68 mm in MLO-projection and the error in the 3D MRI space is equal to 10.29 +/- 3.99 mm. Regarding the uniform grid, it is computed spending between 0.1 and 0.7 seconds. The average time spent to compute the 3D location of a lesion is about 8 ms.
International Nuclear Information System (INIS)
Aurenche, P.; Becherrawy, T.
1991-07-01
The predictions of the real-time and the imaginary-time formalisms of Finite Temperature Field Theory is compared. Retarded and advanced amplitudes are constructed in the real-time formalism which are linear combinations of the usual time-ordered thermo-field dynamics amplitudes. These amplitudes can be easily compared to the various analytically continued amplitudes of the imaginary-time formalism. Explicit calculation of the 2,3 and 4-point Green's functions in φ 3 field theory is done in the one and two-loop approximations, and the compatibility of the two formalisms is shown. (author) 17 refs., 12 figs
Children's Acquisition of Arithmetic Principles: The Role of Experience
Prather, Richard; Alibali, Martha W.
2011-01-01
The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
Indian Academy of Sciences (India)
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over C C . Let be a nodal curve of arithmetic genus one defined over R R , with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism ...
Arithmetic Training Does Not Improve Approximate Number System Acuity
Directory of Open Access Journals (Sweden)
Marcus Lindskog
2016-10-01
Full Text Available The Approximate Number System (ANS is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-minute training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences the ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.
Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces
Directory of Open Access Journals (Sweden)
M. Dehghani
2014-03-01
Full Text Available We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.
A novel chaotic encryption scheme based on arithmetic coding
International Nuclear Information System (INIS)
Mi Bo; Liao Xiaofeng; Chen Yong
2008-01-01
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Supersymmetric theories and finiteness
International Nuclear Information System (INIS)
Helayel-Neto, J.A.
1989-01-01
We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)
Frege, Dedekind, and Peano on the foundations of arithmetic
Gillies, Donald
2013-01-01
First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop
Assessing flood forecast uncertainty with fuzzy arithmetic
Directory of Open Access Journals (Sweden)
de Bruyn Bertrand
2016-01-01
Full Text Available Providing forecasts for flow rates and water levels during floods have to be associated with uncertainty estimates. The forecast sources of uncertainty are plural. For hydrological forecasts (rainfall-runoff performed using a deterministic hydrological model with basic physics, two main sources can be identified. The first obvious source is the forcing data: rainfall forecast data are supplied in real time by meteorological forecasting services to the Flood Forecasting Service within a range between a lowest and a highest predicted discharge. These two values define an uncertainty interval for the rainfall variable provided on a given watershed. The second source of uncertainty is related to the complexity of the modeled system (the catchment impacted by the hydro-meteorological phenomenon, the number of variables that may describe the problem and their spatial and time variability. The model simplifies the system by reducing the number of variables to a few parameters. Thus it contains an intrinsic uncertainty. This model uncertainty is assessed by comparing simulated and observed rates for a large number of hydro-meteorological events. We propose a method based on fuzzy arithmetic to estimate the possible range of flow rates (and levels of water making a forecast based on possible rainfalls provided by forcing and uncertainty model. The model uncertainty is here expressed as a range of possible values. Both rainfall and model uncertainties are combined with fuzzy arithmetic. This method allows to evaluate the prediction uncertainty range. The Flood Forecasting Service of Oise and Aisne rivers, in particular, monitors the upstream watershed of the Oise at Hirson. This watershed’s area is 310 km2. Its response time is about 10 hours. Several hydrological models are calibrated for flood forecasting in this watershed and use the rainfall forecast. This method presents the advantage to be easily implemented. Moreover, it permits to be carried out
International Nuclear Information System (INIS)
Yang, Sun Ho
2001-01-01
The detection of axial cracks using conventional MFL pig is a significant challenge in the gas pipeline inspection. In this study, a technique using interaction of circumferentially induced torrents with axial stress corrosion crack is presented. The feasibility of this technique is investigated using finite element modeling. Finite element analysis of such interaction is a difficult problem in terms of both computation time and memory requirements. The challenges arise due to the nonlinearity of material properties, the small sire of tight cracks relative to that of the magnetizer, and also time stepping involved in modeling velocity effects. This paper presents an approach based on perturbation methods. The overall analysis procedure is divided into 4 simple steps that can be performed sequentially. Modeling results show that this technique can effectively detect colonies of SCC as well as single SCC
3D adaptive finite element method for a phase field model for the moving contact line problems
Shi, Yi
2013-08-01
In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [18]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm. It is well known that the phase variable decays much faster away from the interface than the velocity variables. There- fore we use an adaptive strategy that will take into account of such difference. Numerical experiments show that our algorithm is both efficient and reliable. © 2013 American Institute of Mathematical Sciences.
Stolz, Claude
2010-12-01
The equilibrium solution of a damaged zone in finite elasticity is given for a class of hyperelastic materials which does not suffer tension when a critical stretching value is reached. The study is made for a crack in anti-plane shear loading condition. The prescribed loading is that of linearized elastostatics conditions at infinity. The geometry of the damaged zone is found and the stationary propagation is discussed when the inertia terms can be neglected.
Abe, M.; Prasannaa, V. S.; Das, B. P.
2018-03-01
Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (e EDM ), in order to explore physics beyond the standard model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite-field coupled-cluster (FFCC) approach. This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of e EDM searches. We used relativistic FFCC to calculate molecular properties of interest to e EDM experiments, that is, the effective electric field (Eeff) and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline-earth monofluorides (AEMs), the mercury monohalides (Hg X ), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to e EDM searches. We also report the calculation of the properties using a relativistic finite-field coupled-cluster approach with single, double, and partial triples' excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from our choice of basis sets, and higher-order correlation effects.
RAID-6 reed-solomon codes with asymptotically optimal arithmetic complexities
Lin, Sian-Jheng
2016-12-24
In computer storage, RAID 6 is a level of RAID that can tolerate two failed drives. When RAID-6 is implemented by Reed-Solomon (RS) codes, the penalty of the writing performance is on the field multiplications in the second parity. In this paper, we present a configuration of the factors of the second-parity formula, such that the arithmetic complexity can reach the optimal complexity bound when the code length approaches infinity. In the proposed approach, the intermediate data used for the first parity is also utilized to calculate the second parity. To the best of our knowledge, this is the first approach supporting the RAID-6 RS codes to approach the optimal arithmetic complexity.
Arithmetical aspects of the large sieve inequality
2009-01-01
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is square...
The Duality Principle in Teaching Arithmetic and Geometric Series
Yeshurun, Shraga
1978-01-01
The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)
Arithmetic convergent sequence space defined by modulus function
Directory of Open Access Journals (Sweden)
Taja Yaying
2019-10-01
Full Text Available The aim of this article is to introduce the sequence spaces $AC(f$ and $AS(f$ using arithmetic convergence and modulus function, and study algebraic and topological properties of this space, and certain inclusion results.
Some studies on arithmetical chaos in classical and quantum mechanics
International Nuclear Information System (INIS)
Bolte, J.
1993-04-01
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)
Investigation of an American Arithmetic Text Book (I)
植村, 憲治; UEMURA, Kenji
2006-01-01
The teaching method of mathematics and/or arithmetic essentially does not depend on language or culture. In this paper we introduce and investigate an American arithmetic text book and teacher's book of kindergarten, named "Mathematics" published by McGraw-Hill Company. And we point out the difference of Japanese teaching methods from those of the U.S. especially from the point of the Problem Solving Method which is still not taught in Japan as a system.
Demerdash, N. A.; Wang, R.; Secunde, R.
1992-01-01
A 3D finite element (FE) approach was developed and implemented for computation of global magnetic fields in a 14.3 kVA modified Lundell alternator. The essence of the new method is the combined use of magnetic vector and scalar potential formulations in 3D FEs. This approach makes it practical, using state of the art supercomputer resources, to globally analyze magnetic fields and operating performances of rotating machines which have truly 3D magnetic flux patterns. The 3D FE-computed fields and machine inductances as well as various machine performance simulations of the 14.3 kVA machine are presented in this paper and its two companion papers.
Schuler, Michael; Whitsitt, Seth; Henry, Louis-Paul; Sachdev, Subir; Läuchli, Andreas M
2016-11-18
The low-energy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2+1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z_{2} topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
Tao, Ran
2015-05-01
Laminated composites are materials with complex architecture made of continuous fibers embedded within a polymeric resin. The properties of the raw materials can vary from one point to another due to different local processing conditions or complex geometrical features for example. A first step towards the identification of these spatially varying material parameters is to image with precision the displacement fields in this complex microstructure when subjected to mechanical loading. This thesis is aimed to accurately measure the displacement and strain fields at the fiber-matrix scale in a cross-ply composite. First, the theories of both local subset-based digital image correlation (DIC) and global finite-element based DIC are outlined. Second, in-situ secondary electron tensile images obtained by scanning electron microscopy (SEM) are post-processed by both DIC techniques. Finally, it is shown that when global DIC is applied with a conformal mesh, it can capture more accurately sharp local variations in the strain fields as it takes into account the underlying microstructure. In comparison to subset-based local DIC, finite-element based global DIC is better suited for capturing gradients across the fiber-matrix interfaces.
Directory of Open Access Journals (Sweden)
Daniel Marcsa
2015-01-01
Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.
Yoshikawa, Masanobu; Kosaka, Kenichi; Seki, Hirohumi; Kimoto, Tsunenobu
2016-07-01
We measured the depolarized and polarized Raman spectra of a 4H-SiC metal-oxide-semiconductor field-effect transistor (MOSFET) and found that compressive stress of approximately 20 MPa occurs under the source and gate electrodes and tensile stress of approximately 10 MPa occurs between the source and gate electrodes. The experimental result was in close agreement with the result obtained by calculation using the finite element method (FEM). A combination of Raman spectroscopy and FEM provides much data on the stresses in 4H-SiC MOSFET. © The Author(s) 2016.
Pini, M. G.; Rettori, A.; Bogani, L.; Lascialfari, A.; Mariani, M.; Caneschi, A.; Sessoli, R.
2011-09-01
The static and dynamic properties of the single-chain molecular magnet Co(hfac)2NITPhOMe (CoPhOMe) (hfac = hexafluoroacetylacetonate, NITPhOMe = 4'-methoxy-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) are investigated in the framework of the Ising model with Glauber dynamics, in order to take into account both the effect of an applied magnetic field and a finite size of the chains. For static fields of moderate intensity and short chain lengths, the approximation of a monoexponential decay of the magnetization fluctuations is found to be valid at low temperatures; for strong fields and long chains, a multiexponential decay should rather be assumed. The effect of an oscillating magnetic field, with intensity much smaller than that of the static one, is included in the theory in order to obtain the dynamic susceptibility χ(ω). We find that, for an open chain with N spins, χ(ω) can be written as a weighted sum of N frequency contributions, with a sum rule relating the frequency weights to the static susceptibility of the chain. Very good agreement is found between the theoretical dynamic susceptibility and the ac susceptibility measured in moderate static fields (Hdc≤2 kOe), where the approximation of a single dominating frequency for each segment length turns out to be valid. For static fields in this range, data for the relaxation time, τ versus Hdc, of the magnetization of CoPhOMe at low temperature are also qualitatively reproduced by theory, provided that finite-size effects are included.
Advanced topics in the arithmetic of elliptic curves
Silverman, Joseph H
1994-01-01
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1983-01-01
Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)
Individual differences in children's understanding of inversion and arithmetical skill.
Gilmore, Camilla K; Bryant, Peter
2006-06-01
Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.
Chkhetiani, O G; Jurcisinova, E; Jurcisin, M; Mazzino, A; Repasan, M
2005-01-01
The advection of a passive scalar quantity by incompressible helical turbulent flow has been investigated in the framework of an extended Kraichnan model. Statistical fluctuations of the velocity field are assumed to have the Gaussian distribution with zero mean and defined noise with finite-time correlation. Actual calculations have been done up to two-loop approximation in the framework of the field-theoretic renormalization group approach. It turned out that the space parity violation (helicity) of a stochastic environment does not affect anomalous scaling which is the peculiar attribute of a corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, and the effective diffusivity strongly depend on the amount of helicity.
Cipora, Krzysztof; Nuerk, Hans-Christoph
2013-01-01
The SNARC (spatial-numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsignificant. Possible reasons for this nonsignificance could be that in previous studies (a) very small samples were used, (b) there were too few repetitions producing too little power and, consequently, reliabilities that were too small to reach conventional significance levels for the descriptive skill differences in the SNARC, and (c) general mathematical ability was assessed by the field of study of students, while individual arithmetic skills were not examined. Therefore we used a much bigger sample, a lot more repetitions, and direct assessment of arithmetic skills to explore relations between the SNARC effect and arithmetic skills. Nevertheless, a difference in SNARC effect between arithmetically skilled and nonskilled participants was not obtained. Bayesian analysis showed positive evidence of a true null effect, not just a power problem. Hence we conclude that the idea that arithmetically skilled and nonskilled participants generally differ in the SNARC effect is not warranted by our data.
Training of Attention in Children With Low Arithmetical Achievement
Directory of Open Access Journals (Sweden)
Maria Guarnera
2014-05-01
Full Text Available This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabilities (ALD assigned to experimental and control conditions. The numerical comprehension and calculation processes were assessed using the ABCA battery (Lucangeli, Tressoldi, & Fiore, 1998. Attentional abilities were evaluated using a multitask computerized assessment battery Attenzione e Concentrazione (Di Nuovo, 2000. WM abilities were evaluated by Listening span task, Digit span backward, Making verbal trails and Making colour trails. The results showed that intensive computerized attention training increased basic attentive skills and arithmetical performances with respect to numeric system in children with ALD. No effect on working memory abilities was found. Results are also important from a clinical perspective, since they may suggest strategies for planning individualized training programs.
Perceiving fingers in single-digit arithmetic problems
Directory of Open Access Journals (Sweden)
Ilaria eBerteletti
2015-03-01
Full Text Available In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.
Perceiving fingers in single-digit arithmetic problems.
Berteletti, Ilaria; Booth, James R
2015-01-01
In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.
Patterns of problem-solving in children's literacy and arithmetic.
Farrington-Flint, Lee; Vanuxem-Cotterill, Sophie; Stiller, James
2009-11-01
Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years I and 2 on the arithmetic (addition and subtraction) than literacy-based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural-based strategies, which included phonological strategies for reading and spelling and counting-all and finger modellingfor addition and subtraction, to more efficient retrieval methods from Years I to 2. Distinct patterns in children's problem-solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem-solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different-aged children show flexibility in their use of problem-solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem-solving skill across different educational contexts.
Number processing and arithmetic skills in children with cochlear implants
Directory of Open Access Journals (Sweden)
Silvia ePixner
2014-12-01
Full Text Available Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.
Algebra and Arithmetic of Modular Forms
DEFF Research Database (Denmark)
Rustom, Nadim
In [Rus14b] and [Rus14a], we study graded rings of modular forms over congruence subgroups, with coefficients in subrings A of C, and determine bounds of the weights of modular forms constituting a minimal set of generators, as well as on the degree of the generators of the ideal of relations...... between them. We give an algorithm that computes the structures of these rings, and formulate conjectures on the minimal generating weight for modular forms with coefficients in Z. We discuss questions of finiteness of systems of Hecke eigenvalues modulo pm, for a prime p and an integer m ≥ 2, in analogy...
International Nuclear Information System (INIS)
Fukushima, Toshio
2017-01-01
In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitational acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.
Energy Technology Data Exchange (ETDEWEB)
Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp [National Astronomical Observatory/SOKENDAI, Ohsawa, Mitaka, Tokyo 181-8588 (Japan)
2017-10-01
In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitational acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.
International Nuclear Information System (INIS)
Cheng, Tai-Min; Ma, Yan-Ming; Ge, Chong-Yuan; Sun, Shu-Sheng; Jia, Wei-Ye; Li, Qing-Yun; Shi, Xiao-Fei; Li, Lin; Zhu, Lin
2013-01-01
The elementary excitation spectra of a one-dimensional ferrimagnetic diamond chain in the spin-1/2 XY model at low temperatures have been calculated by using an invariant eigen-operator (IEO) method, the energies of elementary excitations in different specific cases are discussed, and the analytic solutions of three critical magnetic field intensities (H C1 , H C2 , and H peak ) are given. The magnetization versus external magnetic field curve displays a 1/3 magnetization plateau at low temperatures, in which H C1 is the critical magnetic field intensity from the disappearance of the 1/3 magnetization plateau to spin-flop states, H C2 is the critical magnetic field intensity from spin-flop states to the saturation magnetization, and H peak is the critical magnetic field intensity when the temperature magnetization shows a peak in the external magnetic field. The temperature dependences of the magnetic susceptibility and the specific heat show a double peak structure. The entropy and the magnetic susceptibility versus external magnetic field curves also exhibit a double peak structure, and the positions of the two peaks correspond to H C1 and H C2 , respectively. This derives from the competition among different types of energies: the temperature-dependent thermal disorder energy, the potential energy of the spin magnetic moment, the ferromagnetic exchange interaction energy, and the anti-ferromagnetic exchange interaction energy. However at low temperatures, the specific heat as a function of external magnetic field curve exhibits minima at the above two critical points (H C1 and H C2 ). The origins of the above phenomena are discussed in detail.
Thunes, James R.; Pal, Siladitya; Fortunato, Ronald N.; Phillippi, Julie A.; Gleason, Thomas G.; Vorp, David A.; Maiti, Spandan
2016-01-01
Incorporation of collagen structural information into the study of biomechanical behavior of ascending thoracic aortic (ATA) wall tissue should provide better insight into the pathophysiology of ATA. Structurally motivated constitutive models that include fiber dispersion and recruitment can successfully capture overall mechanical response of the arterial wall tissue. However, these models cannot examine local microarchitectural features of the collagen network, such as the effect of fiber disruptions and interaction between fibrous and non-fibrous components, which may influence emergent biomechanical properties of the tissue. Motivated by this need, we developed a finite element based three-dimensional structural model of the lamellar units of the ATA media that directly incorporates the collagen fiber microarchitecture. The fiber architecture was computer generated utilizing network features, namely fiber orientation distribution, intersection density and areal concentration, obtained from image analysis of multiphoton microscopy images taken from human aneurysmal ascending thoracic aortic media specimens with bicuspid aortic valve (BAV) phenotype. Our model reproduces the typical J-shaped constitutive response of the aortic wall tissue. We found that the stress state in the non-fibrous matrix was homogeneous until the collagen fibers were recruited, but became highly heterogeneous after that event. The degree of heterogeneity was dependent upon local network architecture with high stresses observed near disrupted fibers. The magnitude of non-fibrous matrix stress at higher stretch levels was negatively correlated with local fiber density. The localized stress concentrations, elucidated by this model, may be a factor in the degenerative changes in aneurysmal ATA tissue. PMID:27113538
Meyer, Frans J C; Davidson, David B; Jakobus, Ulrich; Stuchly, Maria A
2003-02-01
A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.
Higher arithmetic an algorithmic introduction to number theory
Edwards, Harold M
2008-01-01
Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to m...
Lossless Image Compression Based on Multiple-Tables Arithmetic Coding
Directory of Open Access Journals (Sweden)
Rung-Ching Chen
2009-01-01
Full Text Available This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC method to encode a gray-level image f. First, the MTAC method employs a median edge detector (MED to reduce the entropy rate of f. The gray levels of two adjacent pixels in an image are usually similar. A base-switching transformation approach is then used to reduce the spatial redundancy of the image. The gray levels of some pixels in an image are more common than those of others. Finally, the arithmetic encoding method is applied to reduce the coding redundancy of the image. To promote high performance of the arithmetic encoding method, the MTAC method first classifies the data and then encodes each cluster of data using a distinct code table. The experimental results show that, in most cases, the MTAC method provides a higher efficiency in use of storage space than the lossless JPEG2000 does.
Optimized 4-bit Quantum Reversible Arithmetic Logic Unit
Ayyoub, Slimani; Achour, Benslama
2017-08-01
Reversible logic has received a great attention in the recent years due to its ability to reduce the power dissipation. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. The arithmetic logic unit (ALU) is an important part of central processing unit (CPU) as the execution unit. This paper presents a complete design of a new reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The proposed ALU based on a reversible low power control unit and small performance parameters full adder named double Peres gates. The presented ALU can produce the largest number (28) of arithmetic and logic functions and have the smallest number of quantum cost and delay compared with existing designs.
Energy Technology Data Exchange (ETDEWEB)
Cavalcanti, E.; Castro, E.; Malbouisson, A.P.C. [Centro Brasileiro de Pesquisas Fisicas/MCTI, Rio de Janeiro, RJ (Brazil); Linhares, C.A. [Universidade do Estado do Rio de Janeiro, Instituto de Fisica, Rio de Janeiro, RJ (Brazil)
2017-10-15
A scalar model is built, as a quantum field theory defined on a toroidal topology, to describe a phase transition in films subjected to periodic boundary conditions and influenced by an external and constant magnetic field. Criticality is studied and the relations between the critical temperature, the film thickness, the magnetic field strength and the chemical potential are investigated. Since the model describes a second-order phase transition a comparison with the Ginzburg-Landau theory is made. (orig.)
Chowdhury, Amor; Sarjaš, Andrej
2016-09-15
The presented paper describes accurate distance measurement for a field-sensed magnetic suspension system. The proximity measurement is based on a Hall effect sensor. The proximity sensor is installed directly on the lower surface of the electro-magnet, which means that it is very sensitive to external magnetic influences and disturbances. External disturbances interfere with the information signal and reduce the usability and reliability of the proximity measurements and, consequently, the whole application operation. A sensor fusion algorithm is deployed for the aforementioned reasons. The sensor fusion algorithm is based on the Unscented Kalman Filter, where a nonlinear dynamic model was derived with the Finite Element Modelling approach. The advantage of such modelling is a more accurate dynamic model parameter estimation, especially in the case when the real structure, materials and dimensions of the real-time application are known. The novelty of the paper is the design of a compact electro-magnetic actuator with a built-in low cost proximity sensor for accurate proximity measurement of the magnetic object. The paper successively presents a modelling procedure with the finite element method, design and parameter settings of a sensor fusion algorithm with Unscented Kalman Filter and, finally, the implementation procedure and results of real-time operation.
Modal analysis of wake fields and its application to elliptical pill-box cavity with finite aperture
International Nuclear Information System (INIS)
Kim, S.H.; Chen, K.W.; Yang, J.S.
1990-01-01
The potential of the wake-field produced by a bunch of relativistic charged particles passing through a pill-box cavity is expressed by using Floquet's theorem, and an obvious requirement that the energy gain over all acceleration cavity of many pill boxes must be proportional to the number of pill boxes, based on the previous modal approach (BWW theory). It is found that the wake-field is consisted of two classes of modes: the longitudinal modes which are independent of the aperture and the pill-box gap, the hybrid (pill-box) modes which are dependent of the pill-box gap. The wake field is predominated by the fundamental longitudinal mode whose wavelength is on the order of the effective diameter of the cavity, and its magnitude is inversely proportional to the cross sectional area of the cavity for practical cavities with small apertures. Both longitudinal and transverse wake fields due to the longitudinal modes in an elliptical pill box cavity are expressed analytically in a closed series form by solving exactly the longitudinal eigenmode equation in the elliptical cylindrical coordinates in terms of Mathieu functions. It is found that both longitudinal and transverse wake fields whose amplitudes per driving charge are greater than 100 MV/m/μC can be generated in an elliptical cavity
Directory of Open Access Journals (Sweden)
R. Pirjola
1998-11-01
Full Text Available The electromagnetic field due to ionospheric currents has to be known when evaluating space weather effects at the earth's surface. Forecasting methods of these effects, which include geomagnetically induced currents in technological systems, are being developed. Such applications are time-critical, so the calculation techniques of the electromagnetic field have to be fast but still accurate. The contribution of secondary sources induced within the earth leads to complicated integral formulas for the field at the earth's surface with a time-consuming computation. An approximate method of calculation based on replacing the earth contribution by an image source having mathematically a complex location results in closed-form expressions and in a much faster computation. In this paper we extend the complex image method (CIM to the case of a more realistic electrojet system consisting of a horizontal line current filament with vertical currents at its ends above a layered earth. To be able to utilize previous CIM results, we prove that the current system can be replaced by a purely horizontal current distribution which is equivalent regarding the total (=primary + induced magnetic field and the total horizontal electric field at the earth's surface. The latter result is new. Numerical calculations demonstrate that CIM is very accurate and several magnitudes faster than the exact conventional approach.Key words. Electromagnetic theory · Geomagnetic induction · Auroral ionosphere
International Nuclear Information System (INIS)
Liu, Shuanglong; Feng, Yuan Ping; Zhang, Chun
2013-01-01
We show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region
Should we naturalize mind, or should we arithmetize matter?
Directory of Open Access Journals (Sweden)
Marchal Bruno
2017-12-01
Full Text Available We provide an argument showing that once we assume the mechanist hypothesis in the cognitive science then we have to explain physics from intensional number theory and/or mathematical computer science alone. The proof is constructive. It shows how to derive the physical laws from elementary arithmetic. It makes the computationalist thesis empirically refutable, by comparing the physics extracted from numbers and the inferred physics from observation. The proof shows that if mechanism is true, we cannot naturalize the mind, and we have to arithmetize matter, or beliefs in matter, instead.
Bit-wise arithmetic coding for data compression
Kiely, A. B.
1994-01-01
This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.
Trinary signed-digit arithmetic using an efficient encoding scheme
Salim, W. Y.; Alam, M. S.; Fyath, R. S.; Ali, S. A.
2000-09-01
The trinary signed-digit (TSD) number system is of interest for ultrafast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.
File compression and encryption based on LLS and arithmetic coding
Yu, Changzhi; Li, Hengjian; Wang, Xiyu
2018-03-01
e propose a file compression model based on arithmetic coding. Firstly, the original symbols, to be encoded, are input to the encoder one by one, we produce a set of chaotic sequences by using the Logistic and sine chaos system(LLS), and the values of this chaotic sequences are randomly modified the Upper and lower limits of current symbols probability. In order to achieve the purpose of encryption, we modify the upper and lower limits of all character probabilities when encoding each symbols. Experimental results show that the proposed model can achieve the purpose of data encryption while achieving almost the same compression efficiency as the arithmetic coding.
Learning Extended Finite State Machines
Cassel, Sofia; Howar, Falk; Jonsson, Bengt; Steffen, Bernhard
2014-01-01
We present an active learning algorithm for inferring extended finite state machines (EFSM)s, combining data flow and control behavior. Key to our learning technique is a novel learning model based on so-called tree queries. The learning algorithm uses the tree queries to infer symbolic data constraints on parameters, e.g., sequence numbers, time stamps, identifiers, or even simple arithmetic. We describe sufficient conditions for the properties that the symbolic constraints provided by a tree query in general must have to be usable in our learning model. We have evaluated our algorithm in a black-box scenario, where tree queries are realized through (black-box) testing. Our case studies include connection establishment in TCP and a priority queue from the Java Class Library.
International Nuclear Information System (INIS)
Sakai, Takayuki; Soneda, Naoki
1994-01-01
In PWR plants, an automatic recognition system of Eddy Current Testing (ECT) signals of steam generator tubes are strongly required to reduce inspectors' labor and to improve the reliability of the testing. Although the neural-network technique is very promising for this kind of system, it is necessary to evaluate its applicability to ECT signals throughly, where a database of the relationship of the defects and ECT signals plays a very important role. In this paper, a three dimensional finite element analysis system of electromagnetic field, which consists of an FEM code and pre/post processor, is developed to generate a database of ECT signals. T-Ω method and the edge element are employed in the FEM code to reduce the required computer memory. The code is verified through some comparisons with experiments and other calculations. (author)
International Nuclear Information System (INIS)
Rund, H.
1984-01-01
A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the 4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a lagrangian be gauge-invariant, uniquely determines the structure of these equations. (author)
Yuan, Jian-guo; Zhou, Guang-xiang; Gao, Wen-chun; Wang, Yong; Lin, Jin-zhao; Pang, Yu
2016-01-01
According to the requirements of the increasing development for optical transmission systems, a novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on the subgroup of the finite field multiplicative group is proposed. Furthermore, this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction, easier implementation, lower encoding/decoding complexity, better girth properties and more flexible adjustment for the code length and code rate. The simulation results show that the error correction performance of the QC-LDPC(3 780,3 540) code with the code rate of 93.7% constructed by this proposed method is excellent, its net coding gain is respectively 0.3 dB, 0.55 dB, 1.4 dB and 1.98 dB higher than those of the QC-LDPC(5 334,4 962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group, the SCG-LDPC(3 969,3 720) code constructed by the systematically constructed Gallager (SCG) random construction method, the LDPC(32 640,30 592) code in ITU-T G.975.1 and the classic RS(255,239) code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate ( BER) of 10-7. Therefore, the constructed QC-LDPC(3 780,3 540) code is more suitable for optical transmission systems.
Deng, Zhi-De; Lisanby, Sarah H.; Peterchev, Angel V.
2011-02-01
We present the first computational study comparing the electric field induced by various electroconvulsive therapy (ECT) and magnetic seizure therapy (MST) paradigms. Four ECT electrode configurations (bilateral, bifrontal, right unilateral, and focal electrically administered seizure therapy) and three MST coil configurations (circular, cap, and double cone) were modeled. The model incorporated a modality-specific neural activation threshold. ECT (0.3 ms pulse width) and MST induced the maximum electric field of 2.1-2.5 V cm-1 and 1.1-2.2 V cm-1 in the brain, corresponding to 6.2-7.2 times and 1.2-2.3 times the neural activation threshold, respectively. The MST electric field is more confined to the superficial cortex compared to ECT. The brain volume stimulated was much larger with ECT (up to 100%) than with MST (up to 8.2%). MST with the double-cone coil was the most focal, and bilateral ECT was the least focal. Our results suggest a possible biophysical explanation of the reduced side effects of MST compared to ECT. Our results also indicate that the conventional ECT pulse amplitude (800-900 mA) is much higher than necessary for seizure induction. Reducing the ECT pulse amplitude should be explored as a potential means of diminishing side effects.
Zamani, A.; Setareh, F.; Azargoshasb, T.; Niknam, E.
2018-03-01
A wide variety of semiconductor nanostructures have been fabricated and studied experimentally and alongside theoretical investigations show the great role they have in new generation opto-electronic devices. However, mathematical modeling provide important information due to their definitive goal of predicting features and understanding of such structures' behavior under different circumstances. Hence, in the current work, the effects of applied magnetic field, temperature and dimensions of the structure on the electromagnetically induced transparency (EIT) of a GaAs quantum ring are studied while both Rashba and Dresselhaus spin-orbit interactions (SOI) are taken into account. The Schrödinger equation is solved in cylindrical coordinate with axial symmetry and in order to study the EIT, the imaginary (absorption) and real (refractive index) parts of susceptibility as well as the group velocity of the probe light pulse are investigated. The absorption and refractive index plots show that, for a specific frequency of probe field the absorption vanishes and refractive index becomes unity (known as EIT) while around such frequency the group index is positive (sub-luminal probe propagation) and for higher and lower frequencies it alters to negative (super-luminal probe propagation). The numerical results reveal that the EIT frequency, transparency window and sub(super)-luminal frequency intervals shift as we change applied magnetic field, temperature and also the structure dimensions.
Energy Technology Data Exchange (ETDEWEB)
Zhao, Jun; Luo, Shan-Ming; Li, Feng-Qiang; Xu, Chen-Bing [Xiamen University of Technology, Xiamen (China)
2017-07-15
Failure analysis shows that increased die temperature caused by severe plastic deformation of material and heat conduction between hot billet and cavity significantly affects the distortion of gear cavity in steel synchronizer ring forging process. The forging process of steel synchronizer ring and die temperature distribution under different forging conditions are analyzed through finite element method. Simulation results show that severe plastic deformation occurs in the gear cavity. The improvement of lubrication condition results in decreased die temperature. When the initial billet temperature is high, the die temperature is also high. Increasing forging speed in a certain range facilitates the die temperature decrease. The distribution of die temperature in synthetic forming technology is more reasonable than that of one step forging. The synthetic forming technology is adopted in production to reduce the effects of severe plastic deformation caused by die temperature. The ejection mechanism and control system of the double disc friction press are improved to reduce the contact time between the hot billet and cavity. Experimental results show that synthetic forming technology is reasonable, and that the die service life is prolonged.
International Nuclear Information System (INIS)
Zhao, Jun; Luo, Shan-Ming; Li, Feng-Qiang; Xu, Chen-Bing
2017-01-01
Failure analysis shows that increased die temperature caused by severe plastic deformation of material and heat conduction between hot billet and cavity significantly affects the distortion of gear cavity in steel synchronizer ring forging process. The forging process of steel synchronizer ring and die temperature distribution under different forging conditions are analyzed through finite element method. Simulation results show that severe plastic deformation occurs in the gear cavity. The improvement of lubrication condition results in decreased die temperature. When the initial billet temperature is high, the die temperature is also high. Increasing forging speed in a certain range facilitates the die temperature decrease. The distribution of die temperature in synthetic forming technology is more reasonable than that of one step forging. The synthetic forming technology is adopted in production to reduce the effects of severe plastic deformation caused by die temperature. The ejection mechanism and control system of the double disc friction press are improved to reduce the contact time between the hot billet and cavity. Experimental results show that synthetic forming technology is reasonable, and that the die service life is prolonged.
Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard
2018-03-01
A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.
A Non-Arithmetical Gödel Logic
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2005-01-01
Roč. 13, č. 4 (2005), s. 435-441 ISSN 1367-0751 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * Gödel logic * arithmetical hierarchy Subject RIV: BA - General Mathematics Impact factor: 0.382, year: 2005
Why Is Learning Fraction and Decimal Arithmetic so Difficult?
Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.
2015-01-01
Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…
Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.
Marshall, Sandra P.
This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…
Bit-Wise Arithmetic Coding For Compression Of Data
Kiely, Aaron
1996-01-01
Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.
A wild model of linear arithmetic and discretely ordered modules
Czech Academy of Sciences Publication Activity Database
Glivický, Petr; Pudlák, Pavel
2017-01-01
Roč. 63, č. 6 (2017), s. 501-508 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : linear arithmetics Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016
Simple arithmetic: not so simple for highly math anxious individuals.
Chang, Hyesang; Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G
2017-12-01
Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. © The Author (2017). Published by Oxford University Press.
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
0011-0030.Data Representation amp Computer Arithmetic6 IEEE ...
Indian Academy of Sciences (India)
Home; public; Volumes; reso; 021; 01; 0011-0030.Data Representation amp Computer Arithmetic6 IEEE Standard Double Precision FormatIn.pdf. 404! error. The page your are looking for can not be found! Please check the link or use the navigation bar at the top. YouTube; Twitter; Facebook; Blog. Academy News.
Numbers in action: individual differences and interactivity in mental arithmetic.
Guthrie, Lisa G; Vallée-Tourangeau, Frédéric
2018-02-03
Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.
Partial sums of arithmetical functions with absolutely convergent ...
Indian Academy of Sciences (India)
For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the ∑ n ≤ N f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan's totient functions.
Dutton, Andrew William
1993-12-01
A combined numerical and experimental system for tissue heat transfer analysis was developed. The goal was to develop an integrated set of tools for studying the problem of providing accurate temperature estimation for use in hyperthermia treatment planning in a clinical environment. The completed system combines (1) Magnetic Resonance Angiography (MRA) to non-destructively measure the velocity field in situ, (2) the Streamwise Upwind Petrov-Galerkin finite element solution to the 3D steady state convective energy equation (CEE), (3) a medical image based automatic 3D mesh generator, and (4) a Gaussian type estimator to determine unknown thermal model parameters such as thermal conductivity, blood perfusion, and blood velocities from measured temperature data. The system was capable of using any combination of three thermal models (1) the Convective Energy Equation (CEE), (2) the Bioheat Transfer Equation (BHTE), and (3) the Effective Thermal Conductivity Equation (ETCE) Incorporation of the theoretically correct CEE was a significant theoretical advance over approximate models made possible by the use of MRA to directly measure the 3D velocity field in situ. Experiments were carried out in a perfused alcohol fixed canine liver with hyperthermia induced through scanned focused ultrasound Velocity fields were measured using Phase Contrast Angiography. The complete system was then used to (1) develop a 3D finite element model based upon user traced outlines over a series of MR images of the liver and (2) simulate temperatures at steady state using the CEE, BHTE, and ETCE thermal models in conjunction with the gauss estimator. Results of using the system on an in vitro liver preparation indicate the need for improved accuracy in the MRA scans and accurate spatial registration between the thermocouple junctions, the measured velocity field, and the scanned ultrasound power No individual thermal model was able to meet the desired accuracy of 0.5 deg C, the resolution
Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic
Directory of Open Access Journals (Sweden)
Federico Aschieri
2012-10-01
Full Text Available We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result – which shows that the Excluded Middle principle can be used to eliminate Skolem functions – has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.
International Nuclear Information System (INIS)
Zhang, Lijun; Stratmann, Matthias; Du, Yong; Sundman, Bo; Steinbach, Ingo
2015-01-01
A new approach to incorporate the sublattice models in the CALPHAD (CALculation of PHAse Diagram) formalism directly into the phase-field formalism is developed. In binary alloys, the sublattice models can be classified into two types (i.e., “Type I” and “Type II”), depending on whether a direct one-to-one relation between the element site fraction in the CALPHAD database and the phase concentration in the phase-field model exists (Type I), or not (Type II). For “Type II” sublattice models, the specific site fractions, corresponding to a given mole fraction, have to be established via internal relaxation between different sublattices. Internal minimization of sublattice occupancy and solute evolution during microstructure transformation leads, in general, to a solution superior to the separate solution of the individual problems. The present coupling technique is validated for Fe–C and Ni–Al alloys. Finally, the model is extended into multicomponent alloys and applied to simulate the nucleation process of VC monocarbide from austenite matrix in a steel containing vanadium
Matrix inequalities for the difference between arithmetic mean and harmonic mean
Liao, Wenshi; Wu, Junliang
2015-01-01
Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.
Digital speech processing arithmetic and its realization on ADSP-2191 system
International Nuclear Information System (INIS)
Zhang Wansheng; Wang Yonggang
2005-01-01
The paper reports the realization of LPC arithmetic in fixed-point DSP system. First we introduce the theory of LPC arithmetic and describe the chip (ADSP-2191)'s structure and function relating to the LPC arithmetic; emphasized on the realization process of LPC in ADSP-2191 and its result. (authors)
Rooijen, M. van; Verhoeven, L.T.W.; Steenbergen, B.
2015-01-01
Children with cerebral palsy (CP) are generally delayed in arithmetic compared to their peers. The development of early numeracy performance in children with CP is not yet evident, nor have the factors associated with change over time been identified. Therefore, we examined the development of
Education Development Center, Inc., Newton, MA.
This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being…
Directory of Open Access Journals (Sweden)
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Directory of Open Access Journals (Sweden)
Yifei Yan
2016-01-01
Full Text Available A novel optimised back analysis method is proposed in this paper. The in situ stress field of an underground gas storage (UGS reservoir in a Turkey salt cavern is analysed by the basic theory of elastic mechanics. A finite element method is implemented to optimise and approximate the objective function by systematically adjusting boundary loads. Optimising calculation is performed based on a novel method to reduce the error between measurement and calculation as much as possible. Compared with common back analysis methods such as regression method, the method proposed can further improve the calculation precision. By constructing a large circular geometric model, the effect of stress concentration is eliminated and a minimum difference between computed and measured stress can be guaranteed in the rectangular objective region. The efficiency of the proposed method is investigated and confirmed by its capability on restoring in situ stress field, which agrees well with experimental results. The characteristics of stress distribution of chosen UGS wells are obtained based on the back analysis results and by applying the corresponding fracture criterion, the shaft walls are proven safe.
Wang, Ren H.
1991-01-01
A method of combined use of magnetic vector potential (MVP) based finite element (FE) formulations and magnetic scalar potential (MSP) based FE formulations for computation of three-dimensional (3D) magnetostatic fields is developed. This combined MVP-MSP 3D-FE method leads to considerable reduction by nearly a factor of 3 in the number of unknowns in comparison to the number of unknowns which must be computed in global MVP based FE solutions. This method allows one to incorporate portions of iron cores sandwiched in between coils (conductors) in current-carrying regions. Thus, it greatly simplifies the geometries of current carrying regions (in comparison with the exclusive MSP based methods) in electric machinery applications. A unique feature of this approach is that the global MSP solution is single valued in nature, that is, no branch cut is needed. This is again a superiority over the exclusive MSP based methods. A Newton-Raphson procedure with a concept of an adaptive relaxation factor was developed and successfully used in solving the 3D-FE problem with magnetic material anisotropy and nonlinearity. Accordingly, this combined MVP-MSP 3D-FE method is most suited for solution of large scale global type magnetic field computations in rotating electric machinery with very complex magnetic circuit geometries, as well as nonlinear and anisotropic material properties.
Mi, Yan; Rui, Shaoqin; Li, Chengxiang; Yao, Chenguo; Xu, Jin; Bian, Changhao; Tang, Xuefeng
2017-07-01
High-frequency nanosecond-pulsed electric fields were recently introduced for tumor or abnormal tissue ablation to solve some problems of conventional electroporation. However, it is necessary to study the thermal effects of high-field-intensity nanosecond pulses inside tissues. The multi-parametric analysis performed here is based on a finite element model of liver tissue with a tumor that has been punctured by a pair of needle electrodes. The pulse voltage used in this study ranges from 1 to 4 kV, the pulse width ranges from 50 to 500 ns, and the repetition frequency is between 100 kHz and 1 MHz. The total pulse length is 100 μs, and the pulse burst repetition frequency is 1 Hz. Blood flow and metabolic heat generation have also been considered. Results indicate that the maximum instantaneous temperature at 100 µs can reach 49 °C, with a maximum instantaneous temperature at 1 s of 40 °C, and will not cause thermal damage during single pulse bursts. By parameter fitting, we can obtain maximum instantaneous temperature at 100 µs and 1 s for any parameter values. However, higher temperatures will be achieved and may cause thermal damage when multiple pulse bursts are applied. These results provide theoretical basis of pulse parameter selection for future experimental researches.
Directory of Open Access Journals (Sweden)
Krvavica Nino
2017-03-01
Full Text Available A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Q-scheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor λi was chosen correctly, the agreement between numerical results and field observations was satisfactory.
International Nuclear Information System (INIS)
Kato, A.; Nakamura, Y.; Wakatani, M.
1990-07-01
L = 2 torsatrons are studied to improve the high energy trapped particle confinement with additional l = 1 and/or l = 3 helical coils. The winding laws are selected in two ways. One is to realize 'σ - optimization' by the additional helical coils, but this approach loses magnetic well region. The other selection is to produce or deepen the magnetic well by the additional helical coils. L=3 helical coils are usable to this end. In this case the improvement of the trapped particle confinement depends on magnetic axis position. Radial electric field producing sheared rotational motion is also considered to improve the trapped particle confinement in a standard l = 2 torsatron. By excluding cancellation between E x B and ΔB drift motion occurred for the parabolic potential profiles, all deeply trapped particles can be confined in the central region. Degradation of the trapped particle confinement by the Shafranov shift is mitigated by shifting the magnetic axis inside in the vacuum configuration. (author)
Zurek, B.; Burnett, W. A.; deMartin, B.
2017-12-01
Ground motion models (GMMs) have historically been used as input in the development of probabilistic seismic hazard analysis (PSHA) and as an engineering tool to assess risk in building design. Generally these equations are developed from empirical analysis of observations that come from fairly complete catalogs of seismic events. One of the challenges when doing a PSHA analysis in a region where earthquakes are anthropogenically induced is that the catalog of observations is not complete enough to come up with a set of equations to cover all expected outcomes. For example, PSHA analysis at the Groningen gas field, an area of known induced seismicity, requires estimates of ground motions from tremors up to a maximum magnitude of 6.5 ML. Of the roughly 1300 recordable earthquakes the maximum observed magnitude to date has been 3.6ML. This paper is part of a broader study where we use a deterministic finite-difference wave-form modeling tool to compliment the traditional development of GMMs. Of particular interest is the sensitivity of the GMM's to uncertainty in the rupture process and how this scales to larger magnitude events that have not been observed. A kinematic fault rupture model is introduced to our waveform simulations to test the sensitivity of the GMMs to variability in the fault rupture process that is physically consistent with observations. These tests will aid in constraining the degree of variability in modeled ground motions due to a realistic range of fault parameters and properties. From this study it is our conclusion that in order to properly capture the uncertainty of the GMMs with magnitude up-scaling one needs to address the impact of uncertainty in the near field (risk. Further, by investigating and constraining the range of fault rupture scenarios and earthquake magnitudes on ground motion models, hazard and risk analysis in regions with incomplete earthquake catalogs, such as the Groningen gas field, can be better understood.
Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
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Sanjay Mehrotra
2010-07-01
Full Text Available The algorithm of Lenstra, Lenstra, and Lovász (LLL transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n0.5.
An efficient adaptive arithmetic coding image compression technology
International Nuclear Information System (INIS)
Wang Xing-Yuan; Yun Jiao-Jiao; Zhang Yong-Lei
2011-01-01
This paper proposes an efficient lossless image compression scheme for still images based on an adaptive arithmetic coding compression algorithm. The algorithm increases the image coding compression rate and ensures the quality of the decoded image combined with the adaptive probability model and predictive coding. The use of adaptive models for each encoded image block dynamically estimates the probability of the relevant image block. The decoded image block can accurately recover the encoded image according to the code book information. We adopt an adaptive arithmetic coding algorithm for image compression that greatly improves the image compression rate. The results show that it is an effective compression technology. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
A Learning Trajectory for Teaching Social Arithmetic using RME Approach
Fauzan, A.; Armiati, A.; Ceria, C.
2018-04-01
This paper discusses the role of a learning trajectory (LT) in promoting students’ reasoning when they learn social arithmetic using Realistic Mathematics Education (RME) approach. In our LT, we built the intertwining of the concepts such as profit, loss, percentage, discount, and interest rate, so that the students understand the relations among them. The LT was developed through a design research that consisted of a cyclic process of preparing for the experiment, conducting the experiment, and retrospective analysis. The research’s subject was 32 students at grade 7 MTsN Sintoga, Pariaman, Indonesia. Data were collected through observations, interviews, checklist, videotaping, and analyzing the students' works. The results showed that the LT could help the students to reinvent the concepts in social arithmetic. The students had more confidence to use their own strategies in solving contextual problems. The most important thing, we discovered the growth in the students’ mathematical reasoning.
Photon propagators at finite temperature
International Nuclear Information System (INIS)
Yee, J.H.
1982-07-01
We have used the real time formalism to compute the one-loop finite temperature corrections to the photon self energies in spinor and scalar QED. We show that, for a real photon, only the transverse components develop the temperature-dependent masses, while, for an external static electromagnetic field applied to the finite temperature system, only the static electric field is screened by thermal fluctuations. After showing how to compute systematically the imaginary parts of the finite temperature Green functions, we have attempted to give a microscopic interpretation of the imaginary parts of the self energies. (author)
On the arithmetic of fractal dimension using hyperhelices
International Nuclear Information System (INIS)
Toledo-Suarez, Carlos D.
2009-01-01
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Alternating minima and maxima, Nash equilibria and bounded arithmetic
Czech Academy of Sciences Publication Activity Database
Pudlák, Pavel; Thapen, Neil
2012-01-01
Roč. 163, č. 5 (2012), s. 604-614 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * bounded arithmetic * search problems Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2012 http://www.sciencedirect.com/science/article/pii/S016800721100090X
An algorithm for the arithmetic classification of multilattices.
Indelicato, Giuliana
2013-01-01
A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.
General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2009-01-01
Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172
Bi-amalgamations subject to the arithmetical property
Kabbaj, S.; Mahdou, N.; Moutui, M. A. S.
2016-01-01
This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the arithmetical property, with applications on the weak global dimension and transfer of the semihereditary property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. All results are backed with new and illustrative examples arising as bi-amalgamations.
International Nuclear Information System (INIS)
Bissbort, Ulf; Hofstetter, Walter; Thomale, Ronny
2010-01-01
We discuss the stochastic mean-field theory (SMFT) method, which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and re-entrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [M. Pasienski, D. McKay, M. White, and B. DeMarco, e-print arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make connection to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.
Directory of Open Access Journals (Sweden)
Yu-chuan Yang
2016-01-01
Full Text Available The slope stability problem is an important issue for the safety of human beings and structures. The stability analysis of the three-dimensional (3D slope is essential to prevent landslides, but the most important and difficult problem is how to determine the 3D critical slip surface with the minimum factor of safety in earth slopes. Basing on the slope stress field with the finite element method, a stability analysis method is proposed to determine the critical slip surface and the corresponding safety factor of 3D soil slopes. Spherical and ellipsoidal slip surfaces are considered through the analysis. The moment equilibrium is used to compute the safety factor combined with the Mohr-Coulomb criteria and the limit equilibrium principle. Some assumptions are introduced to reduce the search range of center points and the radius of spheres or ellipsoids. The proposed method is validated by a classical 3D benchmark soil slope. Simulated results indicate that the safety factor of the benchmark slope is 2.14 using the spherical slip surface and 2.19 using the ellipsoidal slip surface, which is close to the results of previous methods. The simulated results indicate that the proposed method can be used for the stability analysis of a 3D soil slope.
Márquez, Andrés; Francés, Jorge; Martínez, Francisco J.; Gallego, Sergi; Álvarez, Mariela L.; Calzado, Eva M.; Pascual, Inmaculada; Beléndez, Augusto
2018-03-01
Simplified analytical models with predictive capability enable simpler and faster optimization of the performance in applications of complex photonic devices. We recently demonstrated the most simplified analytical model still showing predictive capability for parallel-aligned liquid crystal on silicon (PA-LCoS) devices, which provides the voltage-dependent retardance for a very wide range of incidence angles and any wavelength in the visible. We further show that the proposed model is not only phenomenological but also physically meaningful, since two of its parameters provide the correct values for important internal properties of these devices related to the birefringence, cell gap, and director profile. Therefore, the proposed model can be used as a means to inspect internal physical properties of the cell. As an innovation, we also show the applicability of the split-field finite-difference time-domain (SF-FDTD) technique for phase-shift and retardance evaluation of PA-LCoS devices under oblique incidence. As a simplified model for PA-LCoS devices, we also consider the exact description of homogeneous birefringent slabs. However, we show that, despite its higher degree of simplification, the proposed model is more robust, providing unambiguous and physically meaningful solutions when fitting its parameters.
Quantile arithmetic methodology for uncertainty propagation in fault trees
International Nuclear Information System (INIS)
Abdelhai, M.; Ragheb, M.
1986-01-01
A methodology based on quantile arithmetic, the probabilistic analog to interval analysis, is proposed for the computation of uncertainties propagation in fault tree analysis. The basic events' continuous probability density functions (pdf's) are represented by equivalent discrete distributions by dividing them into a number of quantiles N. Quantile arithmetic is then used to performthe binary arithmetical operations corresponding to the logical gates in the Boolean expression of the top event expression of a given fault tree. The computational advantage of the present methodology as compared with the widely used Monte Carlo method was demonstrated for the cases of summation of M normal variables through the efficiency ratio defined as the product of the labor and error ratios. The efficiency ratio values obtained by the suggested methodology for M = 2 were 2279 for N = 5, 445 for N = 25, and 66 for N = 45 when compared with the results for 19,200 Monte Carlo samples at the 40th percentile point. Another advantage of the approach is that the exact analytical value of the median is always obtained for the top event
Relational thinking: The bridge between arithmetic and algebra
Directory of Open Access Journals (Sweden)
Ayhan Kızıltoprak
2017-09-01
Full Text Available The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students by means of clinical interviews and teaching episodes. For observing the development of relational thinking, pre and post clinical interviews were also conducted before and after the eight-session teaching experiment. Qualitative analysis of the research data revealed that the relational thinking skills of all the students developed. It was also found that there was an interaction between the development of fundamental arithmetic concepts and relational thinking; that the students developed concepts related to arithmetical operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividend, divisor and quotient. Moreover, students were able to use these concepts effectivelyalthough they failed to provide formal explanations about the relations between them. In addition, the students perceived the equal sign not only finding a result but also as a symbol used to establish a relation between operations and expressions.
An Asynchronous IEEE Floating-Point Arithmetic Unit
Directory of Open Access Journals (Sweden)
Joel R. Noche
2007-12-01
Full Text Available An asynchronous floating-point arithmetic unit is designed and tested at the transistor level usingCadence software. It uses CMOS (complementary metal oxide semiconductor and DCVS (differentialcascode voltage switch logic in a 0.35 µm process using a 3.3 V supply voltage, with dual-rail data andsingle-rail control signals using four-phase handshaking.Using 17,085 transistors, the unit handles single-precision (32-bit addition/subtraction, multiplication,division, and remainder using the IEEE 754-1985 Standard for Binary Floating-Point Arithmetic, withrounding and other operations to be handled by separate hardware or software. Division and remainderare done using a restoring subtractive algorithm; multiplication uses an additive algorithm. Exceptionsare noted by flags (and not trap handlers and the output is in single-precision.Previous work on asynchronous floating-point arithmetic units have mostly focused on single operationssuch as division. This is the first work to the authors' knowledge that can perform floating-point addition,multiplication, division, and remainder using a common datapath.
International Nuclear Information System (INIS)
Dai, Yang; Borisov, Alexey B.; Boyer, Keith; Rhodes, Charles K.
2000-01-01
The construction of inverse states in a finite field F P α enables the organization of the mass scale with fundamental octets in an eight-dimensional index space that identifies particle states with residue class designations. Conformance with both CPT invariance and the concept of supersymmetry follows as a direct consequence of this formulation. Based on two parameters (P α and g α ) that are anchored on a concordance of physical data, this treatment leads to (1) a prospective mass for the muon neutrino of approximately27.68 meV, (2) a value of the unified strong-electroweak coupling constant α* = (34.26) -1 that is physically defined by the ratio of the electron neutrino and muon neutrino masses, and (3) a see-saw congruence connecting the Higgs, the electron neutrino, and the muon neutrino masses. Specific evaluation of the masses of the corresponding supersymmetric Higgs pair reveals that both particles are superheavy (> 10 18 GeV). No renormalization of the Higgs masses is introduced, since the calculational procedure yielding their magnitudes is intrinsically divergence-free. Further, the Higgs fulfills its conjectured role through the see-saw relation as the particle defining the origin of all particle masses, since the electron and muon neutrino systems, together with their supersymmetric partners, are the generators of the mass scale and establish the corresponding index space. Finally, since the computation of the Higgs masses is entirely determined by the modulus of the field P α , which is fully defined by the large-scale parameters of the universe through the value of the universal gravitational constant G and the requirement for perfect flatness (Omega = 1.0), the see-saw congruence fuses the concepts of mass and space and creates a new unified archetype
Berg, Derek H.; Hutchinson, Nancy L.
2010-01-01
This study investigated whether processing speed, short-term memory, and working memory accounted for the differential mental addition fluency between children typically achieving in arithmetic (TA) and children at-risk for failure in arithmetic (AR). Further, we drew attention to fluency differences in simple (e.g., 5 + 3) and complex (e.g., 16 +…
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Oliveira, M.W. de.
1986-01-01
The consequences of the incorporation of finite temperature effects in fields theories are investigated. Particularly, we consider the sypersymmetric non-linear sigma model, calculating the effective potencial in the large N limit. Initially, we present the 1/N expantion formalism and, for the O(N) model of scalar field, we show the impossibility of spontaneous symmetry breaking. Next, we study the same model at finite temperature and in the presence of conserved charges (the O(N) symmetry's generator). We conclude that these conserved charges explicitly break the symmetry. We introduce a calculation method for the thermodynamic potential of the theory in the presence of chemical potentials. We present an introduction to Supersymmetry in the aim of describing some important concepts for the treatment at T>0. We show that Suppersymmetry is broken for any T>0, in opposition to what one expects, by the solution of the Hierachy Problem. (author) [pt
$\\delta$-Expansion at Finite Temperature
Ramos, Rudnei O.
1996-01-01
We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Early but not late blindness leads to enhanced arithmetic and working memory abilities.
Dormal, Valérie; Crollen, Virginie; Baumans, Christine; Lepore, Franco; Collignon, Olivier
2016-10-01
Behavioural and neurophysiological evidence suggest that vision plays an important role in the emergence and development of arithmetic abilities. However, how visual deprivation impacts on the development of arithmetic processing remains poorly understood. We compared the performances of early (EB), late blind (LB) and sighted control (SC) individuals during various arithmetic tasks involving addition, subtraction and multiplication of various complexities. We also assessed working memory (WM) performances to determine if they relate to a blind person's arithmetic capacities. Results showed that EB participants performed better than LB and SC in arithmetic tasks, especially in conditions in which verbal routines and WM abilities are needed. Moreover, EB participants also showed higher WM abilities. Together, our findings demonstrate that the absence of developmental vision does not prevent the development of refined arithmetic skills and can even trigger the refinement of these abilities in specific tasks. Copyright © 2016 Elsevier Ltd. All rights reserved.
Optimal Design of Fixed-Point and Floating-Point Arithmetic Units for Scientific Applications
Pongyupinpanich, Surapong
2012-01-01
The challenge in designing a floating-point arithmetic co-processor/processor for scientific and engineering applications is to improve the performance, efficiency, and computational accuracy of the arithmetic unit. The arithmetic unit should efficiently support several mathematical functions corresponding to scientific and engineering computation demands. Moreover, the computations should be performed as fast as possible with a high degree of accuracy. Thus, this thesis proposes algorithm, d...
Reading instead of reasoning? Predictors of arithmetic skills in children with cochlear implants.
Huber, Maria; Kipman, Ulrike; Pletzer, Belinda
2014-07-01
The aim of the present study was to evaluate whether the arithmetic achievement of children with cochlear implants (CI) was lower or comparable to that of their normal hearing peers and to identify predictors of arithmetic achievement in children with CI. In particular we related the arithmetic achievement of children with CI to nonverbal IQ, reading skills and hearing variables. 23 children with CI (onset of hearing loss in the first 24 months, cochlear implantation in the first 60 months of life, atleast 3 years of hearing experience with the first CI) and 23 normal hearing peers matched by age, gender, and social background participated in this case control study. All attended grades two to four in primary schools. To assess their arithmetic achievement, all children completed the "Arithmetic Operations" part of the "Heidelberger Rechentest" (HRT), a German arithmetic test. To assess reading skills and nonverbal intelligence as potential predictors of arithmetic achievement, all children completed the "Salzburger Lesetest" (SLS), a German reading screening, and the Culture Fair Intelligence Test (CFIT), a nonverbal intelligence test. Children with CI did not differ significantly from hearing children in their arithmetic achievement. Correlation and regression analyses revealed that in children with CI, arithmetic achievement was significantly (positively) related to reading skills, but not to nonverbal IQ. Reading skills and nonverbal IQ were not related to each other. In normal hearing children, arithmetic achievement was significantly (positively) related to nonverbal IQ, but not to reading skills. Reading skills and nonverbal IQ were positively correlated. Hearing variables were not related to arithmetic achievement. Children with CI do not show lower performance in non-verbal arithmetic tasks, compared to normal hearing peers. Copyright © 2014. Published by Elsevier Ireland Ltd.