A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation

Directory of Open Access Journals (Sweden)

Li Yao

2013-01-01

Full Text Available Ji-Huan He systematically studied the inverse problem of calculus of variations. This note reveals that the semi-inverse method also works for a generalized KdV-mKdV equation with nonlinear terms of any orders.

Description and biological notes of the first species of Xenos (Strepsiptera:Stylopidae) parasitic in Polistes carnifex F. (Hymenoptera:Vespidae) in Mexico

DEFF Research Database (Denmark)

Kathirithamby, J.; Hughes, David P.

2006-01-01

A description and biological notes on the first species of Xenos (X. hamiltoni) (Strepsiptera: Stylopidae) parasitic in Polistes carnifex F. from Mexico is given. A list of Strepsiptera and their hosts from Mexico is provided....

Self-consistent description of the SHFB equations for 112Sn

Science.gov (United States)

Ghafouri, M.; Sadeghi, H.; Torkiha, M.

2018-03-01

The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

A note on a nonlinear equation arising in discussions of the steady fall of a resistive, viscous, isothermal fluid across a magnetic field

Energy Technology Data Exchange (ETDEWEB)

Tautz, R. C., E-mail: robert.c.tautz@gmail.com [Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin (Germany); Lerche, I., E-mail: lercheian@yahoo.com [Institut für Geowissenschaften, Naturwissenschaftliche Fakultät III, Martin-Luther-Universität Halle, D-06099 Halle (Germany)

2015-11-15

This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are of use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

Science.gov (United States)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

Science.gov (United States)

Radhakrishnan, Krishnan; Hindmarsh, Alan C.

1993-01-01

LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

A model-independent description of few-body system with strong interaction

International Nuclear Information System (INIS)

Simenog, I.V.

1985-01-01

In this contribution, the authors discuss the formulation of equations that provide model-independent description of systems of three and more nucleons irrespective of the details of the interaction, substantiate the approach, estimate the correction terms with respect to the force range, and give basic qualitative results obtained by means of the model-independent procedure. They consider three nucleons in the doublet state (spin S=I/2) taking into account only S-interaction. The elastic nd-scattering amplitude may be found from the model-independent equations that follow from the Faddeev equations in the short-range-force limit. They note that the solutions of several model-independent equations and basic results obtained with the use of this approach may serve both as a standard solution and starting point in the discussion of various conceptions concerning the details of nuclear interactions

A modified van der Pol equation with delay in a description of the heart action

Directory of Open Access Journals (Sweden)

Zduniak Beata

2014-12-01

Full Text Available In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff-Parkinson-White syndrome.

Technical note: Use of a simplified equation for estimating glomerular filtration rate in beef cattle.

Science.gov (United States)

Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K

2013-11-01

This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

Lectures on partial differential equations

CERN Document Server

Petrovsky, I G

1992-01-01

Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

A note on the super AKNS equations

International Nuclear Information System (INIS)

Li Yishen; Zhang Lining.

1986-10-01

We find some relationships between the usual AKNS scheme with the super one, when its elements take value from the Grassmann algebra on a two-dimensional vector space. The solutions of these super AKNS equations are discussed. (author)

Wave equations for pulse propagation

International Nuclear Information System (INIS)

Shore, B.W.

1987-01-01

Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

A note on the three dimensional sine--Gordon equation

OpenAIRE

Shariati, Ahmad

1996-01-01

Using a simple ansatz for the solutions of the three dimensional generalization of the sine--Gordon and Toda model introduced by Konopelchenko and Rogers, a class of solutions is found by elementary methods. It is also shown that these equations are not evolution equations in the sense that solution to the initial value problem is not unique.

Lecture Notes and Exercises for Course 21240 (Basic Analytical Chemistry)

DEFF Research Database (Denmark)

1999-01-01

The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years.......The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years....

Lecture Notes and Exercises for Course 21240 (Basic Analytical Chemistry)

DEFF Research Database (Denmark)

1998-01-01

The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years.......The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years....

Notes on Well-Posed, Ensemble Averaged Conservation Equations for Multiphase, Multi-Component, and Multi-Material Flows

International Nuclear Information System (INIS)

Ray A. Berry

2005-01-01

ensemble averaging can also be used to produce the governing equation systems. In fact volume and time averaging can be viewed as special cases of ensemble averaging. Ensemble averaging is beginning to gain some notice, for example the general-purpose multi-material flow simulation code CFDLib under continuing developed at the Los Alamos National Laboratory [Kashiwa and Rauenzahn 1994] is based on an ensemble averaged formulation. The purpose of this short note is to give an introduction to the ensemble averaging methodology and to show how ensemble averaged balance equations and entropy inequality can be obtained from the microscopic balances. It then details some seven-equation, two-pressure, two-velocity hyperbolic, well-posed models for two-phase flows. Lastly, a simple example is presented of a model in which the flow consists of two barotropic fluids with no phase change in which an equilibrium pressure equation is obtained in the spirit of pressure-based methods of computational fluid dynamics

A note on Verhulst's logistic equation and related logistic maps

International Nuclear Information System (INIS)

Gutierrez, M Ranferi; Reyes, M A; Rosu, H C

2010-01-01

We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map x n+1 = rx n (1 - x n ) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map x n+1 - x n = rx n (1 - x n+1 ) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.

Reduced kinetic equations: An influence functional approach

International Nuclear Information System (INIS)

Wio, H.S.

1985-01-01

The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed

A Note on Unsteady Temperature Equation For Gravity Flow of A ...

African Journals Online (AJOL)

We present an analytical study of unsteady temperature energy equation for gravity of a fluid with non – Newtonian behaviour through a porous medium. For the case of radial axisymmetric flow, the governing partial differential equation is transformed into an ordinary differential equation through similarity variables.

A Note on the Field-Theoretical Description of Superfluids

CERN Document Server

Andrianopoli, L; Grassi, P A; Trigiante, M

2014-01-01

Recently, a Lagrangian description of superfluids attracted some interest from the fluid/gravity-correspondence viewpoint. In this respect, the work of Dubovksy et al. has proposed a new field theoretical description of fluids, which has several interesting aspects. On another side, we have provided in arXiv:1304.2206 a supersymmetric extension of the original works. In the analysis of the Lagrangian structures a new invariant appeared which, although related to known invariants, provides, in our opinion, a better parametrisation of the fluid dynamics in order to describe the fluid/superfluid phases.

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

International Nuclear Information System (INIS)

Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

2014-01-01

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

Energy Technology Data Exchange (ETDEWEB)

Harko, Tiberiu [University College London, Department of Mathematics, London (United Kingdom); Leung, Chun Sing [Polytechnic University, Department of Applied Mathematics, Hong Kong (China); Mocanu, Gabriela [Babes-Bolyai University, Faculty of Physics, Cluj-Napoca (Romania)

2014-05-15

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

Science.gov (United States)

Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

2014-05-01

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

Lecture notes on ideal magnetohydrodynamics

International Nuclear Information System (INIS)

Goedbloed, J.P.

1983-03-01

Notes, prepared for a course of lectures held at the Instituto de Fisica, Universidade Estadual de Campinas, Brazil (June-August 1978). An extensive theoretical treatment of the behaviour of hot plasmas caught in equations and mathematical models is presented in 12 chapters

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

Science.gov (United States)

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

Writing a technical note.

Science.gov (United States)

Ng, K H; Peh, W C G

2010-02-01

A technical note is a short article giving a brief description of a specific development, technique or procedure, or it may describe a modification of an existing technique, procedure or device applicable to medicine. The technique, procedure or device described should have practical value and should contribute to clinical diagnosis or management. It could also present a software tool, or an experimental or computational method. Technical notes are variously referred to as technical innovations or technical developments. The main criteria for publication will be the novelty of concepts involved, the validity of the technique and its potential for clinical applications.

A Note on Iterative Refinement for Seminormal Equations

Czech Academy of Sciences Publication Activity Database

Rozložník, Miroslav; Smoktunowicz, A.; Kopal, J.

2014-01-01

Roč. 75, January (2014), s. 167-174 ISSN 0168-9274 R&D Projects: GA ČR(CZ) GAP108/11/0853 Grant - others:TUL(CZ) SGS 7822/115 Institutional support: RVO:67985807 Keywords : condition number * numerical stability * normal equations Subject RIV: BA - General Mathematics Impact factor: 1.221, year: 2014

Self-Consistent System of Equations for a Kinetic Description of the Low-Pressure Discharges Accounting for the Nonlocal and Collisionless Electron Dynamics

International Nuclear Information System (INIS)

Kaganovich, Igor D.; Polomarov, Oleg

2003-01-01

In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated

Improving operation notes to meet British Orthopaedic Association guidelines.

Science.gov (United States)

Morgan, David; Fisher, Noel; Ahmad, Aman; Alam, Fazle

2009-04-01

Operation notes are an important part of medical records for clinical, academic and medicolegal reasons. This study audited the quality of operative note keeping for total knee replacements against the standards set by the British Orthopaedic Association (BOA). A prospective review of all patients undergoing total knee replacement at a district general hospital over 8 months. Data recorded were compared with those required by the BOA good-practice guidelines. Change in practice was implemented and the audit cycle completed. Data were statistically analysed. A total of 129 operation notes were reviewed. There was a significant improvement in the mean number of data points recorded from 9.6 to 13.1. The least well recorded data were diagnosis, description of findings, alignment and postoperative flexion range. All had a significant improvement except description of findings. The operating surgeon writing the note improved from 56% to 67%. Detailed postoperative instructions also improved in quality. Surgeon education and the use of a checklist produce better quality total knee replacement operation notes in line with BOA guidelines. Further improvements may be made by making the data points part of the operation note itself.

A Note about the General Meromorphic Solutions of the Fisher Equation

Directory of Open Access Journals (Sweden)

Jian-ming Qi

2014-01-01

Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

Quantum Gross-Pitaevskii Equation

Directory of Open Access Journals (Sweden)

Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

2017-07-01

Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

Notes on spectrum and exponential decay in nonautonomous evolutionary equations

Directory of Open Access Journals (Sweden)

Christian Pötzsche

2016-08-01

Full Text Available We first determine the dichotomy (Sacker-Sell spectrum for certain nonautonomous linear evolutionary equations induced by a class of parabolic PDE systems. Having this information at hand, we underline the applicability of our second result: If the widths of the gaps in the dichotomy spectrum are bounded away from $0$, then one can rule out the existence of super-exponentially decaying (i.e. slow solutions of semi-linear evolutionary equations.

Taxonomic notes on some Polyglyptini: descriptions of new genus and new species (Homoptera, Membracidae, Smiliinae

Directory of Open Access Journals (Sweden)

Albino M. Sakakibara

1996-01-01

Full Text Available Taxonomic notes on some Polyglyptini; descriptions of new genus and new species (Homoptera, Membracidae, Smiliinae. The genera Hemiptycha Germar, Metheisa Fowler, Maturnaria Metcalf, Aphetea Fowler, Dioclophara Kirkaldy, and Phormophora Stål, are redescribed; Creonus, gen.n. (type species: Maturna lloydi Funkhouser, 1914, and Aphetea robustula, sp.n. (from Bolivia, are described. Some nomenclatural changes are introduced, as follow: - Hemiptycha Germar, 1833 = Polyrhyssa Stål, 1869, syn.n.: - Hemiptycha cultrata (Coquebert, 1801, comb.n., = Polyglyptodes flavocostatus Haviland, 1925, syn.n., = Polyrhyssa cultrata maculata Fonseca, 1942, syn.n. - Hemiptycha obtecta (Fabricius, 1803 = Hille herbicola Haviland, 1925, syn.n. - Maturnaria ephippigera (Fairmaire, 1846 = Publilia tumulata Buckton, 1903, syn.n., = Metheisa fowleri Funkhouser, 1927, syn.n. - Creonus lloydi (Funkhouser, 1914, comb.n. - Aphetea parvula (Fabricius, 1803, comb.n., = Aphetea affinis Haviland, 1925, syn.n. - Dioclophara Kirkaldy, 1904 = lncolea Goding, 1926, syn.n. - Dioclophara viridula (Fairmaire, 1846 = Maturna multilineata Fonseca, 1942, syn.n. - Dioclophara variegata (Goding, 1926, comb.n. = lncolea viridis Goding, 1926, syn.n. - Phormophora maura (Fabricius, 1803 = Darnis dorsata Fabricius, 1803, syn.n.

Invariant imbedding equations for linear scattering problems

International Nuclear Information System (INIS)

Apresyan, L.

1988-01-01

A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation

Notes on Japanese Rhizocephala, with description of two new species

NARCIS (Netherlands)

Boschma, H.

1935-01-01

The following notes are based upon material of parasites on two Crustaceans from Japan, viz., Pachygrapsus crassipes Randall and Petrolisthes japonicus de Haan 1). Each of these two species may be infested by two different species of Rhizocephala: on Pachygrapsus crassipes occur the parasites

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

Science.gov (United States)

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

Unified description of astrophysical properties of neutron stars independent of the equation of state

Science.gov (United States)

Pappas, George

2015-12-01

In recent years, a lot of work was done that has revealed some very interesting properties of neutron stars. One can relate the first few multipole moments of a neutron star, or quantities that can be derived from them, with relations that are independent of the equation of state (EoS). This is a very significant result that has great implications for the description of neutron stars and in particular for the description of the spacetime around them. Additionally, it was recently shown that there is a four-parameter analytic spacetime, known as the two-soliton spacetime, which can accurately capture the properties of the geometry around neutron stars. This allows for the possibility of describing in a unified formalism the astrophysically relevant properties of the spacetime around a neutron star independently of the particulars of the EoS for the matter of the star. More precisely, the description of these astrophysical properties is done using an EoS omniscient spacetime that can describe the exterior of any neutron star. In the present work, we investigate properties such as the location of the innermost stable circular orbit RISCO (or the surface of the star when the latter overcomes the former), the various frequencies of perturbed circular equatorial geodesics, the efficiency of an accretion disc, its temperature distribution, and other properties associated with the emitted radiation from the disc, in a way that holds for all possible choices of a realistic EoS for the neutron star. Furthermore, we provide proof of principle that if one were to measure the right combinations of pairs of these properties, with the additional knowledge of the mass of the neutron star, one could determine the EoS of the star.

Lecture notes on diophantine analysis

CERN Document Server

Zannier, Umberto

2014-01-01

These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several Supplements, hinted exercises and an Appendix on recent work on heights.

A note on Verhulst's logistic equation and related logistic maps

Energy Technology Data Exchange (ETDEWEB)

Gutierrez, M Ranferi; Reyes, M A [Depto de Fisica, Universidad de Guanajuato, Apdo. Postal E143, 37150 Leon, Gto. (Mexico); Rosu, H C, E-mail: hcr@ipicyt.edu.m [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis PotosI (Mexico)

2010-05-21

We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map x{sub n+1} = rx{sub n}(1 - x{sub n}) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map x{sub n+1} - x{sub n} = rx{sub n}(1 - x{sub n+1}) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.

An introduction to differential equations and their applications

CERN Document Server

Farlow, Stanley J

2006-01-01

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

Science.gov (United States)

Pain, J.-Ch.

2011-12-01

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.

A study of actions in operative notes.

Science.gov (United States)

Wang, Yan; Pakhomov, Serguei; Burkart, Nora E; Ryan, James O; Melton, Genevieve B

2012-01-01

Operative notes contain rich information about techniques, instruments, and materials used in procedures. To assist development of effective information extraction (IE) techniques for operative notes, we investigated the sublanguage used to describe actions within the operative report 'procedure description' section. Deep parsing results of 362,310 operative notes with an expanded Stanford parser using the SPECIALIST Lexicon resulted in 200 verbs (92% coverage) including 147 action verbs. Nominal action predicates for each action verb were gathered from WordNet, SPECIALIST Lexicon, New Oxford American Dictionary and Stedman's Medical Dictionary. Coverage gaps were seen in existing lexical, domain, and semantic resources (Unified Medical Language System (UMLS) Metathesaurus, SPECIALIST Lexicon, WordNet and FrameNet). Our findings demonstrate the need to construct surgical domain-specific semantic resources for IE from operative notes.

The Kadomtsev-Petviashvili equations and fundamental string theory

International Nuclear Information System (INIS)

Gilbert, G.

1988-01-01

In this paper the infinite sequence of non-linear partial differential equations known as the Kadomtsev-Petviashvili equations is described in simple terms and possible applications to a fundamental description of interacting strings are addressed. Lines of research likely to prove useful in formulating a description of non-perturbative string configurations are indicated. (orig.)

Notes on TQFT wire models and coherence equations for SU(3) triangular cells

CERN Document Server

Coquereaux, R.; Schieber, G.

2010-01-01

After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.

Comparison of the Schrodinger and Salpeter equations

International Nuclear Information System (INIS)

Jacobs, S.; Olsson, M.G.

1985-01-01

A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

Legendre transformations and Clairaut-type equations

Energy Technology Data Exchange (ETDEWEB)

Lavrov, Peter M., E-mail: lavrov@tspu.edu.ru [Tomsk State Pedagogical University, Kievskaya St. 60, 634061 Tomsk (Russian Federation); National Research Tomsk State University, Lenin Av. 36, 634050 Tomsk (Russian Federation); Merzlikin, Boris S., E-mail: merzlikin@tspu.edu.ru [National Research Tomsk Polytechnic University, Lenin Av. 30, 634050 Tomsk (Russian Federation)

2016-05-10

It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.

Notes on black holes and three dimensional gravity

International Nuclear Information System (INIS)

Banados, Maximo

1999-01-01

In these notes we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody symmetry, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. A brief introduction to the classical and semiclassical aspects of black holes is also included. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and Yang-Mills theory

Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations

International Nuclear Information System (INIS)

Yannouleas, C.

1984-05-01

From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

Energy Technology Data Exchange (ETDEWEB)

Donchev, Veliko, E-mail: velikod@ie.bas.bg [Laboratory “Physical Problems of Electron and Ion Technologies,” Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia (Bulgaria)

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

From differential to difference equations for first order ODEs

Science.gov (United States)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Partial differential equations for scientists and engineers

CERN Document Server

Farlow, Stanley J

1993-01-01

Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

Some notes about the nuclear data libraries

International Nuclear Information System (INIS)

Panini, G.C.

1984-01-01

The paper gives a short description of the main nuclear data collections. The features which are particular of each source are enhanced and compared. Notes about the Nuclear Data Processing are also outlined. The paper is intended as a preliminary approach for people interested in the Nuclear Data management

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

International Nuclear Information System (INIS)

Davidson, R.C.; Chen, C.

1997-08-01

A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B sol (rvec x) is developed. The analysis is carried out for a thin beam with characteristic beam radius r b much-lt S, and directed axial momentum γ b mβ b c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f b (rvec x,rvec p,t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B z (z) = B 0 = const. and for the case of a periodic solenoidal focusing field B z (z + S) = B z (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field rvec B sol (rvec x) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria

A nonquasiclassical description of inhomogeneous superconductors

International Nuclear Information System (INIS)

Zaikin, A.D.; Panyukov, S.V.

1988-01-01

Exact microscopic equations are derived that make it possible to describe inhomogeneous superconductors when the quasi-classical approach is not suitable. These equations are simpler than the Gorkov equations. The authors generalize the derived equations for describing the nonequilibrium states of inhomogeneous superconductors. It is demonstrated that the derived equations (including the case of a nonequilibrium quasi particle distribution function) may be written in the form of linear differential equations for the simultaneous wave function μ, ν. The quasi-classical limit of such equations is examined. Effective boundary conditions are derived for the μ, ν functions that allow description of superconductors with a sharp change in parameters within the scope of the quasi-classical approach

Note on the hydrodynamic description of thin nematic films: Strong anchoring model

KAUST Repository

Lin, Te-Sheng; Cummings, Linda J.; Archer, Andrew J.; Kondic, Lou; Thiele, Uwe

2013-01-01

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion. © 2013 AIP Publishing LLC.

SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

Science.gov (United States)

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

A derivation of the beam equation

International Nuclear Information System (INIS)

Duque, Daniel

2016-01-01

The Euler–Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained. (paper)

A derivation of the beam equation

Science.gov (United States)

Duque, Daniel

2016-01-01

The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained.

Energy master equation

DEFF Research Database (Denmark)

Dyre, Jeppe

1995-01-01

energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model—the energy master equation...... (EME)—is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...

Note: Additionally refined new possibilities of plasma probe diagnostics

Science.gov (United States)

Riaby, V. A.; Savinov, V. P.; Masherov, P. E.; Yakunin, V. G.

2018-03-01

In two previous Notes published in this journal, a method of measuring probe sheath thickness and ion mass was described using Langmuir probe diagnostics in low pressure xenon plasma close to Maxwellian substance. According to the first Note, this method includes two stages: (i) in a special experiment with known ion mass, the Bohm and Child-Langmuir-Boguslavsky (CLB) equations for cylindrical Langmuir probes used in this xenon plasma were solved jointly to determine the probe sheath thicknesses and Bohm coefficient CBCyl ≈ 1.13; and (ii) in a general experiment, with known CBCyl, the same equations could be solved to obtain the probe sheath thicknesses and the mean ion mass. In the second Note, the (i) stage of this method was refined: the results of the CLB probe sheath model application, which were termed "evaluations," were corrected using the step-front probe sheath model, which was closer to reality in the special experiment with the xenon plasma. This process resulted in a Bohm coefficient of CBCyl ≈ 1.23 for the cylindrical probe. In the present Note, corrected xenon plasma parameters without the influence of the bare probe protective shield were used for the (i) stage of this diagnostic method. This action also refined the Bohm coefficient, lowering it to CBCyl ≈ 0.745 for cylindrical probes. This advance makes the new diagnostics method more objective and reliable.

Mysore study: A study of suicide notes.

Science.gov (United States)

Namratha, P; Kishor, M; Sathyanarayana Rao, T S; Raman, Rajesh

2015-01-01

Suicide is one of the leading causes of preventable deaths. Recent data suggest South India as one of the regions with highest suicide rates in the world. In 2013, 134,799 people committed suicide in India according to the statistics released by the National Crime Records Bureau. Suicide note is one of the most important sources to understand suicide, which may be beneficial in suicide prevention. Studies on suicidal notes from this part of the world are sparse. The aim was to study the themes in suicide notes that might be useful in prevention strategies. A descriptive study of all suicide notes of those individuals who committed suicide between 2010 and 2013 available with Police Department, Mysore district was obtained and analyzed. A total of 22 suicide note were available. A majority of suicide note was in age group of 16-40 years (86%) and most were men (59%). All suicide notes were handwritten, the majority (70%) in regional language Kannada. Length of notes varied from just few words to few pages. Contents of suicide notes included apology/shame/guilt (80%), love for those left behind (55%) and instruction regarding practical affairs (23%). Most have blamed none for the act (50%). 23% mentioned that they are committing suicide to prove their innocence. 32% mentioned a last wish. The majority of suicidal note contained "guilt" which is a strong indicator of possible depression in deceased. Creating awareness about suicide among public and ensuring access to professionals trained in suicide prevention is need of the hour in this part of the world.

A note on a degenerate elliptic equation with applications for lakes and seas

Directory of Open Access Journals (Sweden)

Didier Bresch

2004-03-01

Full Text Available In this paper, we give an intermediate regularity result on a degenerate elliptic equation with a weight blowing up on the boundary. This kind of equations is encountoured when modelling some phenomena linked to seas or lakes. We give some examples where such regularity is useful.

Partial differential equations II elements of the modern theory equations with constant coefficients

CERN Document Server

Shubin, M

1994-01-01

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

Wave equations in higher dimensions

CERN Document Server

Dong, Shi-Hai

2011-01-01

Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

The multiparton distribution equations in QCD

International Nuclear Information System (INIS)

Shelest, V.P.; Snigirev, A.M.; Zinovjev, G.M.

1982-01-01

The equations for multiparton distribution functions of deep-inelastic lepton-hadron scattering and fragmentation functions of e + e - annihilation are obtained by using parton interpretation of the leading logarithm diagrams of perturbative QCD theory. These equations have essentially different structute but the solutions are the same on the definite initial conditions and coincide with the jet calculus rules. The difference is crucial when these equations for hadron jets description are generalized [ru

Advanced functional evolution equations and inclusions

CERN Document Server

Benchohra, Mouffak

2015-01-01

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Analysis of medication adherence-related notes from a service-oriented community pharmacy.

Science.gov (United States)

Witry, Matthew; Parry, Rachel; McDonough, Randal; Deninger, Michael

2017-07-15

Medication nonadherence is a significant public health problem. Community pharmacists are positioned to intervene, however, the process is not well understood. To classify and quantify the reasons for nonadherence documented by community pharmacists. A retrospective content analysis of pharmacist notes related to nonadherence at a service oriented community pharmacy in the Midwest United States. Notes from the site's dispensing custom documentation software were obtained from September 1, 2014 through February 28, 2015 that were labeled "compliance", either prompted by proportion of days covered calculations or entered as a drug therapy problem. A code list was iterated for the notes based on the literature and by reading the notes and generating descriptive codes. A reliability analysis was calculated for two coders. Notes were coded, check-coded, and discrepancies were resolved using a consensus process. Frequencies were calculated for each code and representative text was selected. Pharmacists documented 3491 notes as part of their continuous medication monitoring process. Nineteen codes were developed. The reliability for the coders had a Cohen's Kappa of 0.749. The majority of notes (61.4%) documented the pharmacist evaluated the refill and had no concerns or would continue to follow. Also documented were specific reasons for out of range PDCs not indicative of a nonadherence problem. Only 2.2% of notes specifically documented a nonadherence problem, such as forgetfulness or cost. While pharmacists encountered many false positive nonadherence alerts, following up with patients led to hundreds of discussions and clarifications about how patients use their medications at home. These results suggest a small minority of late refills are judged by pharmacists as indicative of an adherence problem, contrary to the prevailing literature. Pharmacists may benefit from modifying their approach to nonadherence interviewing and documentation as they seek to address

Lecture Notes for the Course in Water Wave Mechanics

DEFF Research Database (Denmark)

Andersen, Thomas Lykke; Frigaard, Peter

knowledge. The course is at the same time an introduction to the course in coastal hydraulics on the 8th semester. The notes cover the following five lectures: 1. Definitions. Governing equations and boundary conditions. Derivation of velocity potential for linear waves. Dispersion relationship. 2. Particle...... paths, velocities, accelerations, pressure variation, deep and shallow water waves, wave energy and group velocity. 3. Shoaling, refraction, diffraction and wave breaking. 4. Irregular waves. Time domain analysis of waves. 5. Wave spectra. Frequency domain analysis of waves. The present notes are based...

Notes on Three Newly Naturalized Plants in Taiwan

Directory of Open Access Journals (Sweden)

Shih-Huei Chen

2005-03-01

Full Text Available Chloris divaricata R. Br. var. cynodontoides (Bal. Lazarides, Boerhavia coccinea Mill., and Hyptis pectinata (L. Poit. are recently found naturalized in Taiwan. The present study gives the taxonomic description and line drawings of the three species. In addition, their distribution and notes on ecology and taxonomy are provided.

Scattering of quantized solitary waves in the cubic Schrodinger equation

International Nuclear Information System (INIS)

Dolan, L.

1976-01-01

The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states

A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method

Directory of Open Access Journals (Sweden)

Amir Fallahzadeh

2014-07-01

Full Text Available In this paper, the convergence of Zakharov-Kuznetsov (ZK equation by homotopy analysis method (HAM is investigated. A theorem is proved to guarantee the convergence of HAMand to find the series solution of this equation via a reliable algorithm.

Notes on elementary particle physics

CERN Document Server

Muirhead, William Hugh

1972-01-01

Notes of Elementary Particle Physics is a seven-chapter text that conveys the ideas on the state of elementary particle physics. This book emerged from an introductory course of 30 lectures on the subject given to first-year graduate students at the University of Liverpool. The opening chapter deals with pertinent terminologies in elementary particle physics. The succeeding three chapters cover the concepts of transition amplitudes, probabilities, relativistic wave equations and fields, and the interaction amplitude. The discussion then shifts to tests of electromagnetic interactions, particul

An Eulerian description of the streaming process in the lattice Boltzmann equation

CERN Document Server

Lee Tae Hun

2003-01-01

This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...

Gazing into the multiparton distribution equations in QCD

International Nuclear Information System (INIS)

Shelest, V.P.; Sinigirev, A.M.; Zinovjev, G.M.

1982-01-01

Using a parton interpretation of the leading logarithm diagrams of perturbative QCD theory we obtain the equations for the multiparton distribution and fragmentation functions. These equations are not identical but the solutions are the same on the definite initial conditions and coincide with the jet calculus rules. The difference is crucial when we generalize these equations for a hardron-jet description. (orig.)

Hamiltonian field description of two-dimensional vortex fluids and guiding center plasmas

International Nuclear Information System (INIS)

Morrison, P.J.

1981-03-01

The equations that describe the motion of two-dimensional vortex fluids and guiding center plasmas are shown to possess underlying field Hamiltonian structure. A Poisson bracket which is given in terms of the vorticity, the physical although noncanonical dynamical variable, casts these equations into Heisenberg form. The Hamiltonian density is the kinetic energy density of the fluid. The well-known conserved quantities are seen to be in involution with respect to this Poisson bracket. Expanding the vorticity in terms of a Fourier-Dirac series transforms the field description given here into the usual canonical equations for discrete vortex motion. A Clebsch potential representation of the vorticity transforms the noncanonical field description into a canonical description

Incompressible Navier-Stokes equations. Theory and practice

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, T.

1996-12-31

This paper contains notes from a seminar presented at the Dept. of Mathematics in the University of Bergen, Norway, Oct. 1996. It first introduces the theory of existence and uniqueness of solutions to the incompressible Navier-Stokes equation and defines a well-posed initial-boundary value problem. It then discusses different methods for solving numerically the Navier-Stokes equations in velocity-pressure formulation. The emphasis is on pressure correction methods. 19 refs.

Solution of partial differential equations by agent-based simulation

International Nuclear Information System (INIS)

Szilagyi, Miklos N

2014-01-01

The purpose of this short note is to demonstrate that partial differential equations can be quickly solved by agent-based simulation with high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick determination of potential distributions and demonstration purposes in teaching electromagnetism. (letters and comments)

Description of the male of Eburella pinima Martins and notes on the geographical distribution of Eburodacrys aenigma Galileo & Martins and Eburodacrys lanei Zajciw (Coleoptera, Cerambycidae

Directory of Open Access Journals (Sweden)

Juan Pablo Botero

2013-12-01

Full Text Available Description of the male of Eburella pinima Martins and notes on the geographical distribution of Eburodacrys aenigma Galileo & Martins and Eburodacrys lanei Zajciw (Coleoptera, Cerambycidae. The male of Eburella pinima Martins, 1997 is described and illustrated for the first time. Information on Eburodacrys aenigma Galileo & Martins, 2006, previously known only from the female holotype, which lacked locality label, is herein complemented. This species is recorded from Brazil and the male is depicted for the first time. The geographical distribution of Eburodacrys lanei Zajciw, 1958 is further restricted here as some previous records are confirmed to result from misidentifications of E. aenigma.

A note on unique solvability of the absolute value equation

Directory of Open Access Journals (Sweden)

Taher Lotfi

2014-05-01

Full Text Available It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A+|B|]$‎, ‎we can create a new unique solvability condition for the absolute value equation $Ax+B|x|=b$‎, ‎since regularity of interval matrices implies unique solvability of their corresponding absolute value equation‎. ‎This condition is formulated in terms of positive definiteness of a certain point matrix‎. ‎Special case $B=-I$ is verified too as an application.

A Guide to Field Notes for Qualitative Research: Context and Conversation.

Science.gov (United States)

Phillippi, Julia; Lauderdale, Jana

2018-02-01

Field notes are widely recommended in qualitative research as a means of documenting needed contextual information. With growing use of data sharing, secondary analysis, and metasynthesis, field notes ensure rich context persists beyond the original research team. However, while widely regarded as essential, there is not a guide to field note collection within the literature to guide researchers. Using the qualitative literature and previous research experience, we provide a concise guide to collection, incorporation, and dissemination of field notes. We provide a description of field note content for contextualization of an entire study as well as individual interviews and focus groups. In addition, we provide two "sketch note" guides, one for study context and one for individual interviews or focus groups for use in the field. Our guides are congruent with many qualitative and mixed methodologies and ensure contextual information is collected, stored, and disseminated as an essential component of ethical, rigorous qualitative research.

Coupling and reduction of the HAWC equations

DEFF Research Database (Denmark)

Nim, E.

2001-01-01

This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system.......This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model...

Eight equation model for arbitrary shaped pipe conveying fluid

International Nuclear Information System (INIS)

Gale, J.; Tiselj, I.

2006-01-01

Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)

The unified description of kinetic and hydrodynamic processes in gases and plasmas

International Nuclear Information System (INIS)

Klimontovich, Yu.L.

1992-01-01

The unified description of kinetic and hydrodynamic processes in gases and plasmas for all values of the Knudsen number is proposed. The generalized kinetic equation consists of the additional dissipative term and is defined by the diffusion of the distribution function in the coordinate space. This equation is used for the description of nonequilibrium processes in passive and active media. (orig.)

Discontinuous Galerkin for the Radiative Transport Equation

KAUST Repository

Guermond, Jean-Luc

2013-10-11

This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

Discontinuous Galerkin for the Radiative Transport Equation

KAUST Repository

Guermond, Jean-Luc; Kanschat, Guido; Ragusa, Jean C.

2013-01-01

This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

Quality of outpatient clinical notes: a stakeholder definition derived through qualitative research

Directory of Open Access Journals (Sweden)

Hanson Janice L

2012-11-01

content. Conclusions Perspectives of these four stakeholder groups provide a comprehensive description of quality in outpatient clinical documentation. The resulting description of characteristics and content necessary for quality notes provides a research-based foundation for assessing the quality of clinical documentation in outpatient health care settings.

Quality of outpatient clinical notes: a stakeholder definition derived through qualitative research.

Science.gov (United States)

Hanson, Janice L; Stephens, Mark B; Pangaro, Louis N; Gimbel, Ronald W

2012-11-19

groups provide a comprehensive description of quality in outpatient clinical documentation. The resulting description of characteristics and content necessary for quality notes provides a research-based foundation for assessing the quality of clinical documentation in outpatient health care settings.

A note on Burgers' equation with time delay: Instability via finite-time blow-up

International Nuclear Information System (INIS)

Jordan, P.M.

2008-01-01

Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time

An introduction to stochastic differential equations

CERN Document Server

Evans, Lawrence C

2014-01-01

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. -Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. -George Papa

Crossing of the cosmological constant boundary-an equation of state description

International Nuclear Information System (INIS)

Stefancic, Hrvoje

2006-01-01

The phenomenon of the dark energy transition between the quintessence regime (w > -1) and the phantom regime (w < -1), also known as the cosmological constant boundary crossing, is analysed in terms of the dark energy equation of state. It is found that the dark energy equation of state in the dark energy models which exhibit the transition is implicitly defined. The generalizations of the models explicitly constructed to exhibit the transition are studied to gain insight into the mechanism of the transition. It is found that the cancellation of the terms corresponding to the cosmological constant boundary makes the transition possible

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Conserved quantities for generalized KdV equations

International Nuclear Information System (INIS)

Calogero, F.; Rome Univ.; Degasperis, A.; Rome Univ.

1980-01-01

It is noted that the nonlinear evolution equation usub(t) = α(t)usub(xxx) - 6ν(t) usub(x)u, u is identical to u(x,t), possesses three (and, in some cases, four) conserved quantities, that are explicitly displayed. These results are of course relevant only to the cases in which this evolution equation is not known to possess an infinite number of conserved quantities. Purpose and scope of this paper is to report three or four simple conservation laws possessed by the evolution equation usub(t) = α(t)usub(xxx) - 6ν(t)usub(x)u, u is identical to u(x,t). (author)

Microscopic description of nuclear reactions

International Nuclear Information System (INIS)

Gorbatov, A.M.

1992-01-01

The genealogical series method has been extended to the continuous spectrum of the many-body systems. New nonlinear integral equations have been formulated to perform the microscopical description of the nuclear reactions with arbitrary number of particles. The way to solve them numerically is demonstrated

Description of nuclear collective motion by Wigner function moments

International Nuclear Information System (INIS)

Balbutsev, E.B.

1996-01-01

The method is presented in which the collective motion is described by the dynamic equations for the nuclear integral characteristics. The 'macroscopic' dynamics is formulated starting from the equations of the microscopic theory. This is done by taking the phase space moments of the Wigner function equation. The theory is applied to the description of collective excitations with multipolarities up to λ=5. (author)

A note on the Stokes operator and its powers

KAUST Repository

Guermond, Jean-Luc; Salgado, Abner

2010-01-01

The so-called Stokes operator is an important tool in the analysis of the solutions of the Navier-Stokes equations and their numerical approximation. The aim of this note is to clarify certain properties of the fractional powers of this operator which are sometimes misused. © 2010 Korean Society for Computational and Applied Mathematics.

A note on the Stokes operator and its powers

KAUST Repository

Guermond, Jean-Luc

2010-04-28

The so-called Stokes operator is an important tool in the analysis of the solutions of the Navier-Stokes equations and their numerical approximation. The aim of this note is to clarify certain properties of the fractional powers of this operator which are sometimes misused. © 2010 Korean Society for Computational and Applied Mathematics.

Physical dynamics of quasi-particles in nonlinear wave equations

International Nuclear Information System (INIS)

Christov, Ivan; Christov, C.I.

2008-01-01

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field

Physical dynamics of quasi-particles in nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu

2008-02-04

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.

Monge-Ampere equations and characteristic connection functors

International Nuclear Information System (INIS)

Tunitskii, D V

2001-01-01

We investigate contact equivalence of Monge-Ampere equations. We define a category of Monge-Ampere equations and introduce the notion of a characteristic connection functor. This functor maps the category of Monge-Ampere equations to the category of affine connections. We give a constructive description of the characteristic connection functors corresponding to three subcategories, which include a large class of Monge-Ampere equations of elliptic and hyperbolic type. This essentially reduces the contact equivalence problem for Monge-Ampere equations in the cases under study to the equivalence problem for affine connections. Using E. Cartan's familiar theory, we are thus able to state and prove several criteria of contact equivalence for a large class of elliptic and hyperbolic Monge-Ampere equations

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

Science.gov (United States)

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

Gauges for the Ginzburg-Landau equations of superconductivity

International Nuclear Information System (INIS)

Fleckinger-Pelle, J.; Kaper, H.G.

1995-01-01

This note is concerned with gauge choices for the time-dependent Ginzburg-Landau equations of superconductivity. The requiations model the state of a superconducting sample in a magnetic field near the critical tempeature. Any two solutions related through a ''gauge transformation'' describe the same state and are physically indistinquishable. This ''gauge invariance'' can be exploited for analtyical and numerical purposes. A new gauge is proposed, which reduces the equations to a particularly attractive form

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Reparametrization invariance and the Schroedinger equation

International Nuclear Information System (INIS)

Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

1999-01-01

A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation

Finite difference evolution equations and quantum dynamical semigroups

International Nuclear Information System (INIS)

Ghirardi, G.C.; Weber, T.

1983-12-01

We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)

Effective equations for the quantum pendulum from momentous quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

2012-08-24

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Norsett, S.P.

2001-01-01

1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations

A new approach to the self-dual Yang-Mills equations

International Nuclear Information System (INIS)

Takasaki, K.

1984-01-01

Inspired by Sato's new theory for soliton equations, we find a new approach to the self-dual Yang-Mills equations. We first establish a correspondence of solutions between the self-dual Yang-Mills equations and a new system of equations with infinitely many unknown functions. It then turns out that the latter equations can be easily solved by a simple explicit procedure. This leads to an explicit description of a very broad class of solutions to the self-dual Yang-Mills equations, and also to a construction of transformations acting on these solutions. (orig.)

On the hierarchy of partially invariant submodels of differential equations

Energy Technology Data Exchange (ETDEWEB)

Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

2008-07-04

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

Science.gov (United States)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

International Nuclear Information System (INIS)

Golovin, Sergey V

2008-01-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

Equational theories of tropical sernirings

DEFF Research Database (Denmark)

Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna

2003-01-01

examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...

Soliton-like solutions to the GKdV equation by extended mapping method

International Nuclear Information System (INIS)

Wu Ranchao; Sun Jianhua

2007-01-01

In this note, many new exact solutions of the generalized KdV equation, such as rational solutions, periodic solutions like Jacobian elliptic and triangular functions, soliton-like solutions, are constructed by symbolic computation and the extended mapping method, with the auxiliary ordinary equation replaced by a more general one

Relativistic equations of state at finite temperature

International Nuclear Information System (INIS)

Santos, A.M.S.; Menezes, D.P.

2004-01-01

In this work we study the effects of temperature on the equations of state obtained within a relativistic model with and without β equilibrium, over a wide range of densities. We integrate the TOV equations. We also compare the results of the equation of state, effective mass and strangeness fraction from the TM1, NL3 and GL sets of parameters, as well as investigating the importance of antiparticles in the treatment. The have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars. (author)

Feynman path integral related to stochastic schroedinger equation

International Nuclear Information System (INIS)

Belavkin, V.P.; Smolyanov, O.G.

1998-01-01

The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru

Relativistic description of atomic nuclei

International Nuclear Information System (INIS)

Krutov, V.A.

1985-01-01

Papers on the relativistic description of nuclei are reviewed. The Brown and Rho ''small'' bag'' model is accepted for hardrons. Meson exchange potentials of the nucleon-nucleon interaction have been considered. Then the transition from a system of two interacting nucleons has been performed to the relativistic nucleus description as a multinucleon system on the basis of OBEP (one-boson exchange potential). The proboem of OPEP (one-pion-exchange potential) inclusion to a relativistic scheme is discussed. Simplicity of calculations and attractiveness of the Walecka model for specific computations and calculations was noted. The relativistic model of nucleons interacting through ''effective'' scalar and vector boson fields was used in the Walacka model for describing neutronaand nuclear mater matters

Macroscopic and microscopic description of HE-HI collisions; classical equations of motion calculations

International Nuclear Information System (INIS)

Bodmer, A.R.

1978-01-01

The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references

Variational characterization of generalized Jacobi equations

International Nuclear Information System (INIS)

Casciaro, B.

1995-09-01

A Lagrangian depending on derivatives of the fields up to a generic order is considered, together with a series development around a given section. The problem of extremality and stability of action for this system is then addressed. Higher-order variations in the Lagrangian, the Euler-Lagrange equation, the expansion of the action, the D-invariant decomposition of the Lagrangian, the Jacobi equation, and a unified description of the Euler-Lag range and Jacobi equations are discussed. As a conclusion of the work it is stated that the theory of second variations is worthy to be revisited and a comment on a recent paper by Taub is made. 10 refs

The Monge-Ampère equation

CERN Document Server

Gutiérrez, Cristian E

2016-01-01

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampère equation and a chapter on interior Hölder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampère-type equations and their diverse applications in th...

Notes on Mayer expansions and matrix models

International Nuclear Information System (INIS)

Bourgine, Jean-Emile

2014-01-01

Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of N=2 4d gauge theories. The associated canonical model involves coupled integrations that take the form of a generalized matrix model. It can be studied with the standard techniques of matrix models, in particular collective field theory and loop equations. In the first part of these notes, we explain how the results of collective field theory can be derived from the cluster expansion. The equalities between free energies at first orders is explained by the discrete Laplace transform relating canonical and grand canonical models. In a second part, we study the canonical loop equations and associate them with similar relations on the grand canonical side. It leads to relate the multi-point densities, fundamental objects of the matrix model, to the generating functions of multi-rooted clusters. Finally, a method is proposed to derive loop equations directly on the grand canonical model

The Use of Transformations in Solving Equations

Science.gov (United States)

Libeskind, Shlomo

2010-01-01

Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…

Notes on quantum groups

International Nuclear Information System (INIS)

Pressley, A.; Chari, V.; Tata Inst. of Fundamental Research, Bombay

1990-01-01

The authors presents an introduction to quantum groups defined as a deformation of the universal enveloping algebra of a Lie algebra. After the description of Hopf algebras with some examples the approach of Drinfel'd and Jimbo is described, where the quantization of a Lie algebra represents a Hopf algebra, defined over the algebra of formal power series in an indetermined h. The authors show that this approach arises from a r-matrix, which satisfies the classical Yang-Baxter equation. As example quantum sl 2 is considered. Furthermore the approaches of Manin and Woroniwicz and the R-matrix approach are described. (HSI)

On a Functional Equation for the Generating Function of the Logarithmic Series Distribution

OpenAIRE

Panaretos, John

1987-01-01

This note deals with finding the solution of a functional equation, where the function involved has the additional property of being a probability generating function. It turns out that the unique solution of this particular functional equation is the probability generating function of the logarithmic series distribution

Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

International Nuclear Information System (INIS)

Bettelheim, Eldad; Abanov, Alexander G; Wiegmann, Paul B

2008-01-01

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1-4] and provide vital tools for studying non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form. (fast track communication)

Equations for the stochastic cumulative multiplying chain

Energy Technology Data Exchange (ETDEWEB)

Lewins, J D [Cambridge Univ. (UK). Dept. of Engineering

1980-01-01

The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage.

Equations for the stochastic cumulative multiplying chain

International Nuclear Information System (INIS)

Lewins, J.D.

1980-01-01

The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage. (author)

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

Science.gov (United States)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

International Nuclear Information System (INIS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-01-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references

A consistent description of kinetics and hydrodynamics of quantum Bose-systems

Directory of Open Access Journals (Sweden)

P.A.Hlushak

2004-01-01

Full Text Available A consistent approach to the description of kinetics and hydrodynamics of many-Boson systems is proposed. The generalized transport equations for strongly and weakly nonequilibrium Bose systems are obtained. Here we use the method of nonequilibrium statistical operator by D.N. Zubarev. New equations for the time distribution function of the quantum Bose system with a separate contribution from both the kinetic and potential energies of particle interactions are obtained. The generalized transport coefficients are determined accounting for the consistent description of kinetic and hydrodynamic processes.

Description of regional blow-up in a porous-medium equation

Directory of Open Access Journals (Sweden)

Carmen Cortazar

2002-10-01

Full Text Available We describe the (finite-time blow-up phenomenon for a non-negative solution of a porous medium equation of the form $$ u_t = Delta u^m + u^m $$ in the entire space. Here $m>1$ and the initial condition is assumed compactly supported. Blow-up takes place exactly inside a finite number of balls with same radii and exhibiting the same self-similar profile.

Nonholonomic deformation of generalized KdV-type equations

International Nuclear Information System (INIS)

Guha, Partha

2009-01-01

Karasu-Kalkani et al (2008 J. Math. Phys. 49 073516) recently derived a new sixth-order wave equation KdV6, which was shown by Kupershmidt (2008 Phys. Lett. 372A 2634) to have an infinite commuting hierarchy with a common infinite set of conserved densities. Incidentally, this equation was written for the first time by Calogero and is included in the book by Calogero and Degasperis (1982 Lecture Notes in Computer Science vol 144 (Amsterdam: North-Holland) p 516). In this paper, we give a geometric insight into the KdV6 equation. Using Kirillov's theory of coadjoint representation of the Virasoro algebra, we show how to obtain a large class of KdV6-type equations equivalent to the original equation. Using a semidirect product extension of the Virasoro algebra, we propose the nonholonomic deformation of the Ito equation. We also show that the Adler-Kostant-Symes scheme provides a geometrical method for constructing nonholonomic deformed integrable systems. Applying the Adler-Kostant-Symes scheme to loop algebra, we construct a new nonholonomic deformation of the coupled KdV equation.

The Max-Plus Algebra of the Natural Numbers has no Finite Equational Basis

DEFF Research Database (Denmark)

Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna

2003-01-01

This paper shows that the collection of identities which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum is not finitely based. Moreover, it is proven that, for every n, the equations in at most n variables that hold in N do not form...... an equational basis. As a stepping stone in the proof of these facts, several results of independent interest are obtained. In particular, explicit descriptions of the free algebras in the variety generated by N are offered. Such descriptions are based upon a geometric characterization of the equations...

Holographic description of Kerr-Bolt-AdS-dS spacetimes

International Nuclear Information System (INIS)

Chen, B.; Ghezelbash, A.M.; Kamali, V.; Setare, M.R.

2011-01-01

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the 'near region', the wave equation in extremal limit could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL(2,R) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

Some issues linked to the description of systems in strong interaction

International Nuclear Information System (INIS)

Theussl, L.

2001-06-01

In the first part of this work we have dealt with some issues that are relevant in the area of nucleonic resonances within different constituent quark models. In this context we have concentrated on the theoretical description of Pi and Nu decays for N and Delta resonances. The results obtained point to the necessity of a more microscopic description of the dynamics which is at the same time responsible for the binding of quarks inside baryons and the decay of the latter ones. In the second part we have contributed to the study of crossed two-boson exchanges in the Bethe-Salpeter equation as well as to the investigation of different three-dimensional approaches that follow from the Bethe-Salpeter equation in a certain non-relativistic reduction scheme. These one include in particular an equation whose interaction depends on the total energy of the system. It was shown that such an equation is able to account for a certain number of properties of Bethe-Salpeter equation, in particular, that there also arise abnormal solutions in such an approach. (author)

A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method

Directory of Open Access Journals (Sweden)

Sandile S. Motsa

2012-01-01

Full Text Available We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations. Comparison with exact and other results in the literature shows that the method is accurate and effective in finding solutions of nonlinear equations with oscillatory solutions, nonlinear eigenvalue problems, and other nonlinear problems with bifurcations.

Poiseuille equation for steady flow of fractal fluid

Science.gov (United States)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

The second-order description of rotational non-equilibrium effects in polyatomic gases

Science.gov (United States)

Myong, Rho Shin

2017-11-01

The conventional description of gases is based on the physical laws of conservation (mass, momentum, and energy) in conjunction with the first-order constitutive laws, the two-century old so-called Navier-Stokes-Fourier (NSF) equation based on a critical assumption made by Stokes in 1845 that the bulk viscosity vanishes. While the Stokes' assumption is certainly legitimate in the case of dilute monatomic gases, ever increasing evidences, however, now indicate that such is not the case, in particular, in the case of polyatomic gases-like nitrogen and carbon dioxide-far-from local thermal equilibrium. It should be noted that, from room temperature acoustic attenuation data, the bulk viscosity for carbon dioxide is three orders of magnitude larger than its shear viscosity. In this study, this fundamental issue in compressible gas dynamics is revisited and the second-order constitutive laws are derived by starting from the Boltzmann-Curtiss kinetic equation. Then the topology of the second-order nonlinear coupled constitutive relations in phase space is investigated. Finally, the shock-vortex interaction problem where the strong interaction of two important thermal (translational and rotational) non-equilibrium phenomena occurs is considered in order to highlight the rotational non-equilibrium effects in polyatomic gases. This work was supported by the National Research Foundation of South Korea (NRF 2017-R1A2B2-007634).

Statistical analysis of the description accuracy of dependence of flow stresses upon the deformation rate in the state of superplasticity by phenomenological equations

International Nuclear Information System (INIS)

Bojtsov, V.V.; Tsepin, M.A.; Karpilyanskij, N.N.; Ershov, A.N.

1982-01-01

Results of statistical analysis of the description accuracy of superplasticity S-form curve by different analytic expressions, suggested on the basis of phenomenological and metallophysical concepts about the nature of superplastic deformation, are given. Experimental investigations into the dependence of flow stresses on the deformation rate were conducted on VT3-1 two-phase titanium alloy. Test samples were cut out of a rod, 30 mm in diameter, produced by lengthwise rolling in α+#betta#-region. Optimal temperature of superplasticity manifestation was determined by the method of stress relaxation from a relaxation time value to a given stress. It was established that the Smirnov phemonemological equation describes in the best way the rate dependence of flow stress of superplastic material. This equation can be used for solution of problems of studying mechanism, physical nature of superplastic deformation, analysing strain-stress state and the structure of deformation zone during the processes of pressure shaping of superplastic materials, when considerably wide range (in the limits of 7-8 orders) of deformation rate variation takes place

On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

International Nuclear Information System (INIS)

Dietrich, K.; Vautherin, D.

1985-01-01

We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

Note Taking and Note Sharing While Browsing Campaign Information

DEFF Research Database (Denmark)

Robertson, Scott P.; Vatrapu, Ravi; Abraham, George

2009-01-01

Participants were observed while searching and browsing the internet for campaign information in a mock-voting situation in three online note-taking conditions: No Notes, Private Notes, and Shared Notes. Note taking significantly influenced the manner in which participants browsed for information...

Note by Note: a New Revolution in Cooking

OpenAIRE

Burke, Roisin; Danaher, Pauline

2016-01-01

Note by note cooking is an application of Molecular Gastronomy. It was first proposed by French Physical Chemist and Molecular Gastronomy Co-founder, Hervé This. Note by Note dishes are being created as part of Ph.D. research in the Dublin Institute of Technology, Cathal Brugha Street.

Using voice to create hospital progress notes: Description of a mobile application and supporting system integrated with a commercial electronic health record.

Science.gov (United States)

Payne, Thomas H; Alonso, W David; Markiel, J Andrew; Lybarger, Kevin; White, Andrew A

2018-01-01

We describe the development and design of a smartphone app-based system to create inpatient progress notes using voice, commercial automatic speech recognition software, with text processing to recognize spoken voice commands and format the note, and integration with a commercial EHR. This new system fits hospital rounding workflow and was used to support a randomized clinical trial testing whether use of voice to create notes improves timeliness of note availability, note quality, and physician satisfaction with the note creation process. The system was used to create 709 notes which were placed in the corresponding patient's EHR record. The median time from pressing the Send button to appearance of the formatted note in the Inbox was 8.8 min. It was generally very reliable, accepted by physician users, and secure. This approach provides an alternative to use of keyboard and templates to create progress notes and may appeal to physicians who prefer voice to typing. Copyright © 2017 Elsevier Inc. All rights reserved.

Algebraic resolution of the Burgers equation with a forcing term

Indian Academy of Sciences (India)

2017-04-07

Apr 7, 2017 ... stochastic processes, dispersive water waves, gas dyna- mics, heat conduction ... as the adhesion model [14], vehicular traffic [13], the study of directed polymers in ... ing to note that Burgers equation also appears naturally.

Rate equation description of quantum noise in nanolasers with few emitters

DEFF Research Database (Denmark)

Mørk, Jesper; Lippi, G. L.

2018-01-01

Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2...

A note on numerical solution of a parabolic-Schrödinger equation

Science.gov (United States)

Ozdemir, Yildirim; Alp, Mustafa

2016-08-01

In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.

Time-course window estimator for ordinary differential equations linear in the parameters

NARCIS (Netherlands)

Vujacic, Ivan; Dattner, Itai; Gonzalez, Javier; Wit, Ernst

In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may

Power Series Solution to the Pendulum Equation

Science.gov (United States)

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

CORECOOL, model description of the programme

International Nuclear Information System (INIS)

Andersen, J.G.M.; Abel-Larsen, H.

1978-11-01

CORECOOL, Convection and Radiation Emergency Cooling, is a model for the two-phase flow and heat transfer in a fuel element during the core heat-up phase following a loss of coolant accident. The model for the two-phase flow is based on a solution of the conservation equations with a separate description of the two phases and thermodynamic non-equilibrium. The flow-regimes considered are drop flow and film flow. The heat transfer consists of convection, sputtering and radiation heat transfer. The documentation of CORECOOL consists of four parts: I) model description, II) programme description (COMMERCIAL), III) users guide (COMMERCIAL) IV) verification (COMMERCIAL). CORECOOL is a joint project between Risoe National Laboratory Denmark and General Electric Company, San Jose, USA. (author)

Construction and accuracy of partial differential equation approximations to the chemical master equation.

Science.gov (United States)

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Kinetic equation for spin-polarized plasmas

International Nuclear Information System (INIS)

Cowley, S.C.; Kulsrud, R.M.; Valeo, E.

1984-07-01

The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10 -4 S -1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

Microscopic descriptions of high-energy heavy-ion collisions

International Nuclear Information System (INIS)

Bodmer, A.R.

1977-01-01

The essentials of the equation-of-motion (EOM) approach are given and some of its significant and interesting results are described. A framework for the theoretical description of high-energy heavy-ion (HE-HI) collisions is presented; specifically included are a critical assessment of various approaches--EOM calculations, Boltzmann equations/cascade calculations, and hydrodynamics--their relationships and their respective domains of applicability, if any, to HE-HI collisions. 11 figures, 3 tables

Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation

International Nuclear Information System (INIS)

Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul

2009-01-01

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

Science.gov (United States)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Numerical Solution of Differential Algebraic Equations and Applications

DEFF Research Database (Denmark)

Thomsen, Per Grove

2005-01-01

These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...

An appraisal of computational techniques for transient heat conduction equation

International Nuclear Information System (INIS)

Kant, T.

1983-01-01

A semi-discretization procedure in which the ''space'' dimension is discretized by the finite element method is emphasized for transient problems. This standard methodology transforms the space-time partial differential equation (PDE) system into a set of ordinary differential equations (ODE) in time. Existing methods for transient heat conduction calculations are then reviewed. Existence of two general classes of time integration schemes- implicit and explicit is noted. Numerical stability characteristics of these two methods are elucidated. Implicit methods are noted to be numerically stable, permitting large time steps, but the cost per step is high. On the otherhand, explicit schemes are noted to be inexpensive per step, but small step size is required. Low computational cost of the explicit schemes make it very attractive for nonlinear problems. However, numerical stability considerations requiring use of very small time steps come in the way of its general adoption. Effectiveness of the fourth-order Runge-Kutta-Gill explicit integrator is then numerically evaluated. Finally we discuss some very recent works on development of computational algorithms which not only achieve unconditional stability, high accuracy and convergence but involve computations on matrix equations of elements only. This development is considered to be very significant in the light of our experience gained for simple heat conduction calculations. We conclude that such algorithms have the potential for further developments leading to development of economical methods for general transient analysis of complex physical systems. (orig.)

Calculation notes that support accident scenario and consequence determination of a waste tank criticality

International Nuclear Information System (INIS)

Marusich, R.M. Westinghouse Hanford

1996-01-01

The purpose of this calculation note is to provide the basis for criticality consequences for the Tank Farm Safety Analysis Report (FSAR). Criticality scenario is developed and details and description of the analysis methods are provided

Particle Systems and Partial Differential Equations I

CERN Document Server

Gonçalves, Patricia

2014-01-01

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012.  The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory, and to stimulate discussions and possibly new collaborations among researchers with different backgrounds.  The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navie...

Bare and effective fluid description in brane world cosmology

Energy Technology Data Exchange (ETDEWEB)

Cruz, Norman [Universidad de Santiago, Departamento de Fisica, Facultad de Ciencia, Casilla 307, Santiago (Chile); Lepe, Samuel; Saavedra, Joel [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Casilla 4950, Valparaiso (Chile); Pena, Francisco [Universidad de La Frontera, Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Avda. Francisco Salazar 01145, Casilla 54-D, Temuco (Chile)

2010-03-15

An effective fluid description, for a brane world model in five dimensions, is discussed for both signs of the brane tension. We found several cosmological scenarios where the effective equation differs widely from the bare equation of state. For universes with negative brane tension, with a bare fluid satisfying the strong energy condition, the effective fluid can cross the barrier {omega} {sub eff}=-1. (orig.)

A unified BFKL/DGLAP description of deep inelastic scattering

International Nuclear Information System (INIS)

Kwiecinski, J.; Stasto, A. M.; Martin, A. D.

1997-01-01

We introduce a coupled pair of evolution equations for the unintegrated gluon distribution and the sea quark distribution which incorporate both the resummed leading ln(1/x) BFKL contributions and the resummed leading ln(Q 2 ) DGLAP contributions. We solve these unified equations in the perturbative QCD domain. With only two physically motivated parameters we obtain an excellent description of the HERA F 2 data

SU(4) properties of the Dirac equation

International Nuclear Information System (INIS)

Linhares, C.A.; Mignaco, J.A.

1988-01-01

The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequente properties are displayed in the continuum as well as in the lattice description. (author) [pt

SU(4) proprerties of the Dirac equation

International Nuclear Information System (INIS)

Linhares, C.A.; Mignaco, J.A.

1985-09-01

The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequent properties are displayed in the continuum as well as in the lattice description [pt

Microscopic description of fission dynamics: Toward a 3D computation of the time dependent GCM equation

Directory of Open Access Journals (Sweden)

Regnier D.

2017-01-01

Full Text Available Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization in nuclear energy. The need for a predictive theory applicable where no data is available, together with the variety of potential applications, is an incentive to develop a fully microscopic approach to fission dynamics. One of the most promising theoretical frameworks is the time dependent generator coordinate method (TDGCM applied under the Gaussian overlap approximation (GOA. However, the computational cost of this method makes it difficult to perform calculations with more than two collective degree of freedom. Meanwhile, it is well-known from both semi-phenomenological and fully microscopic approaches that at least four or five dimensions may play a role in the dynamics of fission. To overcome this limitation, we develop the code FELIX aiming to solve the TDGCM+GOA equation for an arbitrary number of collective variables. In this talk, we report the recent progress toward this enriched description of fission dynamics. We will briefly present the numerical methods adopted as well as the status of the latest version of FELIX. Finally, we will discuss fragments yields obtained within this approach for the low energy fission of major actinides.

Microscopic description of fission dynamics: Toward a 3D computation of the time dependent GCM equation

Science.gov (United States)

Regnier, D.; Dubray, N.; Schunck, N.; Verrière, M.

2017-09-01

Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization in nuclear energy. The need for a predictive theory applicable where no data is available, together with the variety of potential applications, is an incentive to develop a fully microscopic approach to fission dynamics. One of the most promising theoretical frameworks is the time dependent generator coordinate method (TDGCM) applied under the Gaussian overlap approximation (GOA). However, the computational cost of this method makes it difficult to perform calculations with more than two collective degree of freedom. Meanwhile, it is well-known from both semi-phenomenological and fully microscopic approaches that at least four or five dimensions may play a role in the dynamics of fission. To overcome this limitation, we develop the code FELIX aiming to solve the TDGCM+GOA equation for an arbitrary number of collective variables. In this talk, we report the recent progress toward this enriched description of fission dynamics. We will briefly present the numerical methods adopted as well as the status of the latest version of FELIX. Finally, we will discuss fragments yields obtained within this approach for the low energy fission of major actinides.

Field Equations for Lovelock Gravity: An Alternative Route

Directory of Open Access Journals (Sweden)

Sumanta Chakraborty

2018-01-01

Full Text Available We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

Energy Technology Data Exchange (ETDEWEB)

Seif, Dariush, E-mail: dariush.seif@iwm-extern.fraunhofer.de [Fraunhofer Institut für Werkstoffmechanik, Freiburg 79108 (Germany); Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095-1597 (United States); Ghoniem, Nasr M. [Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095-1597 (United States)

2014-12-15

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô’s calculus, rate equations for the first five moments of the size distribution in helium–vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium–vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

Science.gov (United States)

Seif, Dariush; Ghoniem, Nasr M.

2014-12-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô's calculus, rate equations for the first five moments of the size distribution in helium-vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium-vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

International Nuclear Information System (INIS)

Seif, Dariush; Ghoniem, Nasr M.

2014-01-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô’s calculus, rate equations for the first five moments of the size distribution in helium–vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium–vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

The respiratory system in equations

CERN Document Server

Maury, Bertrand

2013-01-01

The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

Microscopic description of magnetized plasma: quasiparticle concept

International Nuclear Information System (INIS)

Sosenko, P.P.; Decyk, V.K.

1993-01-01

A quasiparticle concept is developed systematically, from first principles, within the context of microscopic description of magnetized plasma. It is argued that the zeroth velocity-gyroangle harmonic of the microscopic particle distribution function under the gyrokinetic change of variables can be taken as a microscopic quasi-particle density in a reduced phase space. The nature of quasiparticles is discussed and equations of their motion are derived within both exact and reduced microscopic descriptions. The reduced one employs explicitly the separation of interesting time scales. (orig.)

Holographic description of Kerr-Bolt-AdS-dS spacetimes

Energy Technology Data Exchange (ETDEWEB)

Chen, B., E-mail: bchen01@pku.edu.c [Department of Physics, and State Key Laboratory of Nuclear Physics and Technology, and Center for High Energy Physics, Peking University, Beijing 100871 (China); Ghezelbash, A.M., E-mail: masoud.ghezelbash@usask.c [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada); Kamali, V., E-mail: vkamali1362@gmail.co [Department of Campus of Bijar, Kurdistan University, Bijar (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.i [Department of Campus of Bijar, Kurdistan University, Bijar (Iran, Islamic Republic of)

2011-07-01

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the 'near region', the wave equation in extremal limit could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL(2,R) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

High-precision numerical integration of equations in dynamics

Science.gov (United States)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.

Numerical Solution of Parabolic Equations

DEFF Research Database (Denmark)

Østerby, Ole

These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...... expense. Problems in two space dimensions are effectively handled using the Alternating Direction Implicit (ADI) technique. We present a systematic way of incorporating inhomogeneous terms and derivative boundary conditions in ADI methods as well as mixed derivative terms....

Nonlinear elliptic equations and nonassociative algebras

CERN Document Server

Nadirashvili, Nikolai; Vlăduţ, Serge

2014-01-01

This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

Twistor theory and the Einstein equations

International Nuclear Information System (INIS)

Law, P.R.

1985-01-01

R. Penrose has argued that the goal of twistor theory with regard to the vacuum Einstein equations ought to consist of some kind of unification of twistor-theoretic description of anti-self-dual (a.s.d.) and self-dual (s.d.) space-times. S.d. space-times currently possess a description only in terms of dual twistor space, however, rather than twistor space. In this paper, suggestions due to Penrose for providing a purely twistor space description of s.d. space-times are investigated. It is shown how the points of certain s.d. space-times define mappings on twistor space and the geometry of these mappings is studied. The families of mappings for two particular s.d. space-times are presented explicitly. (author)

Khokhlov Zabolotskaya Kuznetsov type equation: nonlinear acoustics in heterogeneous media

Science.gov (United States)

Kostin, Ilya; Panasenko, Grigory

2006-04-01

The KZK type equation introduced in this Note differs from the traditional form of the KZK model known in acoustics by the assumptions on the nonlinear term. For this modified form, a global existence and uniqueness result is established for the case of non-constant coefficients. Afterwards the asymptotic behaviour of the solution of the KZK type equation with rapidly oscillating coefficients is studied. To cite this article: I. Kostin, G. Panasenko, C. R. Mecanique 334 (2006).

Chemical and physical FET-based sensors or variations on an equation

NARCIS (Netherlands)

Olthuis, Wouter

2005-01-01

This paper exposes the continuous thread of Bergveld’s work: the model equation of the field-effect transistor (FET) derived and repeated in the theoretical section. Zooming in on some of the variables of this equation leads us to several of his important projects. A short description and typical

"Quod Erat Demonstrandum": Understanding and Explaining Equations in Physics Teacher Education

Science.gov (United States)

Karam, Ricardo; Krey, Olaf

2015-01-01

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this…

Profiling Chilean Suicide Note-Writers through Content Analysis

Directory of Open Access Journals (Sweden)

Francisco Ceballos-Espinoza

2016-09-01

Full Text Available Suicides account for 2000 deaths in Chile each year. With a suicide rate of 11.3, it is classified as a country with high suicide risk. Aims: to identify personality and cognitive characteristics of the group of Chilean suicides that left suicide notes, through a content analysis. Methods: descriptive field study with an ex post facto design. All suicides registered between 2010 and 2012 by the Investigations Police of Chile were analyzed, obtaining 203 suicide notes from 96 cases. The Darbonne categories for content analysis were used with the inter-judge method. Results: The mean age of the suicides was 44.2 (SD = 18.53. Most of the notes were addressed to family members (51.7%. The most expressed reasons were marital- or interpersonal-related (24.6%; another 23.6% expressed a lack of purpose or hopelessness (including depression, wish to die, low self-esteem. The most frequent content expressed were instructions (about money, children, and funeral. All of the notes showed logical thinking and were written with coherence and clarity. Notably 42% of the notes were marked by affections of fondness, love or dependence of others. Regarding attitudes, the most common were of escape or farewell (42.4%, followed by fatalism, hopelessness, frustration or tiredness (40%. 24 statistically significant differences were found throughout the categories of analysis, according to cohorts of age, marital status and sex. Conclusions: the findings contribute to the profiling of Chilean suicides and to the implementation of suicide prevention programs

Solution of the Burgers Equation in the Time Domain

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M. Bednařík

2002-01-01

Full Text Available This paper deals with a theoretical description of the propagation of a finite amplitude acoustic waves. The theory based on the homogeneous Burgers equation of the second order of accuracy is presented here. This equation takes into account both nonlinear effects and dissipation. The method for solving this equation, using the well-known Cole-Hopf transformation, is presented. Two methods for numerical solution of these equations in the time domain are presented. The first is based on the simple Simpson method, which is suitable for smaller Goldberg numbers. The second uses the more advanced saddle point method, and is appropriate for large Goldberg numbers.

GeneNotes – A novel information management software for biologists

Directory of Open Access Journals (Sweden)

Wong Wing H

2005-02-01

Full Text Available Abstract Background Collecting and managing information is a challenging task in a genome-wide profiling research project. Most databases and online computational tools require a direct human involvement. Information and computational results are presented in various multimedia formats (e.g., text, image, PDF, word files, etc., many of which cannot be automatically processed by computers in biologically meaningful ways. In addition, the quality of computational results is far from perfect and requires nontrivial manual examination. The timely selection, integration and interpretation of heterogeneous biological information still heavily rely on the sensibility of biologists. Biologists often feel overwhelmed by the huge amount of and the great diversity of distributed heterogeneous biological information. Description We developed an information management application called GeneNotes. GeneNotes is the first application that allows users to collect and manage multimedia biological information about genes/ESTs. GeneNotes provides an integrated environment for users to surf the Internet, collect notes for genes/ESTs, and retrieve notes. GeneNotes is supported by a server that integrates gene annotations from many major databases (e.g., HGNC, MGI, etc.. GeneNotes uses the integrated gene annotations to (a identify genes given various types of gene IDs (e.g., RefSeq ID, GenBank ID, etc., and (b provide quick views of genes. GeneNotes is free for academic usage. The program and the tutorials are available at: http://bayes.fas.harvard.edu/genenotes/. Conclusions GeneNotes provides a novel human-computer interface to assist researchers to collect and manage biological information. It also provides a platform for studying how users behave when they manipulate biological information. The results of such study can lead to innovation of more intelligent human-computer interfaces that greatly shorten the cycle of biology research.

CHEMICAL REACTIONS ON ADSORBING SURFACE: KINETIC LEVEL OF DESCRIPTION

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P.P.Kostrobii

2003-01-01

Full Text Available Based on the effective Hubbard model we suggest a statistical description of reaction-diffusion processes for bimolecular chemical reactions of gas particles adsorbed on the metallic surface. The system of transport equations for description of particles diffusion as well as reactions is obtained. We carry out the analysis of the contributions of all physical processes to the formation of diffusion coefficients and chemical reactions constants.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

Science.gov (United States)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS

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Giorgio Gubbiotti

2016-06-01

Full Text Available In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.

Hamiltonian field description of the one-dimensional Poisson-Vlasov equations

International Nuclear Information System (INIS)

Morrison, P.J.

1981-07-01

The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained

Description of the approach to equilibrium in the Boltzmann equation

Energy Technology Data Exchange (ETDEWEB)

Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

1985-06-01

An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

On the Controllability of a Differential Equation with Delayed and Advanced Arguments

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Raúl Manzanilla

2010-01-01

Full Text Available A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.

The Spectral/hp-Finite Element Method for Partial Differential Equations

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2009-01-01

dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...

Final state dipole showers and the DGLAP equation

International Nuclear Information System (INIS)

Nagy, Zoltan; Soper, Davison E.

2009-01-01

We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a recent paper of Dokshitzer and Marchesini that raised troubling issues about whether a dipole based shower could give the DGLAP equation for the quark energy distribution.

On the evolution equations, solvable through the inverse scattering method

International Nuclear Information System (INIS)

Gerdjikov, V.S.; Khristov, E.Kh.

1979-01-01

The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation

Description of deeply inelastic collisions in terms of a transport equation

International Nuclear Information System (INIS)

Weidenmueller, H.A.

1977-01-01

A transport equation for deeply inelastic collisions is derived from a random-matrix model for the form factors for inelastic scattering and transfer reactions. The parametrization of these form factors is discussed. Results in one dimension indicate the importance of quantum fluctuations, and limitations of other approaches to the same problem. Results of three dimensions are compared with the data

Notes on two species of Processa (Decapoda: Processidae from the Mexican Pacific

Directory of Open Access Journals (Sweden)

Manuel Ayón-Parente

Full Text Available Material belonging to the genus Processa, held in the Regional Marine Invertebrates Collection in Mazatlán, Mexico, is revised including specimens of the widely distributed P. peruviana, and the scarcely collected P. hawaiensis. For comparative purposes with the specimens from Hawaii and other localities, a detailed description of a male of P. hawaiensis collected in continental Mexico is provided, including illustrations of all appendages. Small differences are noted with previous description and partial redescriptions of this species, including proportion between propodus and dactylus of the fourth pereopod, and between merus and carpus of the right cheliped. In addition, the shape and setation of the first pair of pleopods in the Mexican material differs from the description of P. hawaiensis based on African material.

Students’ difficulties in solving linear equation problems

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Visualising magnetic fields numerical equation solvers in action

CERN Document Server

Beeteson, John Stuart

2001-01-01

Visualizing Magnetic Fields: Numerical Equation Solvers in Action provides a complete description of the theory behind a new technique, a detailed discussion of the ways of solving the equations (including a software visualization of the solution algorithms), the application software itself, and the full source code. Most importantly, there is a succinct, easy-to-follow description of each procedure in the code.The physicist Michael Faraday said that the study of magnetic lines of force was greatly influential in leading him to formulate many of those concepts that are now so fundamental to our modern world, proving to him their "great utility as well as fertility." Michael Faraday could only visualize these lines in his mind's eye and, even with modern computers to help us, it has been very expensive and time consuming to plot lines of force in magnetic fields

Hydrogen equation in spaces of arbitrary dimensions

International Nuclear Information System (INIS)

Amusia, M Ya

2015-01-01

We note that presenting Hydrogen atom Schrodinger equation in the case of arbitrary dimensions require simultaneous modification of the Coulomb potential that only in three dimensions has the form Z / r. This was not done in a number of relatively recent papers (see [1] and references therein). Therefore, some results obtained in [1] seem to be doubtful. Several required considerations in the area are mentioned. (paper)

A Note on the Invariance Properties and Conservation Laws of the Kadomstev—Petviashvili Equation with Power Law Nonlinearity

International Nuclear Information System (INIS)

Bokhari A H; Zaman F D; Fakhar K; Kara A H

2011-01-01

First, we studied the invariance properties of the Kadomstev—Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows. (general)

Notes on solving Maxwell equations, part 2, Green's function for stratified media

OpenAIRE

Rook, R.

2011-01-01

In the previous report (part 1), the problem and its governing equations are described and is discarded in this report. The finite element method in part 1, or any other method for that matter, determines the fields in and close to the scatterer (near-field) that is used to construct the fields in the far-field. The goal of part 2 is to find far-field expressions formulated as total fields or the Radar Cross Section (RCS) of the scattered fields. The far-field is calculated from the scatterer...

Recursive approach for non-Markovian time-convolutionless master equations

Science.gov (United States)

Gasbarri, G.; Ferialdi, L.

2018-02-01

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.

On the relativistic Vlasov equation in guiding-center coordinates

International Nuclear Information System (INIS)

Salimullah, M.; Chaudhry, M.B.; Hassan, M.H.A.

1989-11-01

The relativistic Vlasov equation has been expressed in terms of the guiding-center coordinates in a hot magnetized plasma. It is noted that the relativistic effect reduces the cyclotron resonance frequency for electrostatic and electromagnetic waves propagating transverse to the direction of the static magnetic field in the plasma. (author). 4 refs

Patched based methods for adaptive mesh refinement solutions of partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Saltzman, J.

1997-09-02

This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.

FORSIM, Solution of Ordinary or Partial Differential Equation with Initial Conditions

International Nuclear Information System (INIS)

Carver, M.B.

1985-01-01

1 - Description of problem or function: FORSIM is a FORTRAN oriented simulation program which automates the continuous transient solution of systems of ordinary and/or partial differential equations. The user writes his equations in a FORTRAN subroutine, following prescribed rules, and loads this routine along with the executive routines. The executive routines then read in initial data supplied by the user and proceed with the integration. 2 - Method of solution: Partial differential equations are converted to coupled ordinary differential equations by suitable discretization formulae. Integration is done by variable order, variable step-size error controlled algorithms. 3 - Restrictions on the complexity of the problem - Maximum of: 1000 ordinary differential equations

Descriptive Topology in Selected Topics of Functional Analysis

CERN Document Server

Kakol, J; Pellicer, Manuel Lopez

2011-01-01

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set

Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows

Science.gov (United States)

Minier, Jean-Pierre; Profeta, Christophe

2015-11-01

This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Zp=(xp,Up) and is represented by its PDF p (t ;yp,Vp) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Zp=(xp,Up,Us) , and, consequently, handles an extended PDF p (t ;yp,Vp,Vs) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to describe physical systems

Van der Waals equation of state revisited: importance of the dispersion correction.

Science.gov (United States)

de Visser, Sam P

2011-04-28

One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

Quasisymmetry equations for conventional stellarators

International Nuclear Information System (INIS)

Pustovitov, V.D.

1994-11-01

General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)

Linearised collective Schroedinger equation for nuclear quadrupole surface vibrations

International Nuclear Information System (INIS)

Greiner, M.; Heumann, D.; Scheid, W.

1990-11-01

The linearisation of the Schroedinger equation for nuclear quadrupole surface vibrations yields a new spin degree of freedom, which is called collective spin and has a value of 3/2. With the introduction of collective spin dependent potentials, this linearised Schroedinger equation is then used for the description of low energy spectra and electromagnetic transition probabilities of some even-odd Xe, Ir and Au nuclei which have a spin 3/2 in their groundstate. (orig.)

Topological soliton solutions for some nonlinear evolution equations

Directory of Open Access Journals (Sweden)

Ahmet Bekir

2014-03-01

Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.

Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

KAUST Repository

Bonito, Andrea

2013-12-01

This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients. © 2013 Elsevier Ltd.

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

International Nuclear Information System (INIS)

Misguich, J.H.

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

Energy Technology Data Exchange (ETDEWEB)

Misguich, J.H

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

New diffusion-like solutions of one-speed transport equations in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.

1988-01-01

Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ψ(r, μ) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted. (author)

Approximate solutions for the two-dimensional integral transport equation. The critically mixed methods of resolution

International Nuclear Information System (INIS)

Sanchez, Richard.

1980-11-01

This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr

Immigrant fertility in Sweden, 2000-2011: A descriptive note

Directory of Open Access Journals (Sweden)

Lotta Persson

2014-03-01

Full Text Available Background: Modern Scandinavian population registers provide excellent data sources that allow a user to quickly gain an impression of the level of fertility and its structure across subpopulations. This may also allow the analyst to check a feature of the much-cited disruption hypothesis, at least in part. Objective: The purpose of this note is to exploit this potential to give an overview of the structure of recent total fertility after immigration to Sweden from various groups of sending countries, separately for males and females. In the process we demonstrate to what extent the post-migration fertility compensation which is part of the fertility disruption hypothesis is fulfilled in our study population. Due to the nature of our data we have refrained from studying fertility before migration. Methods: Based on data from a combination of two Swedish administrative registers (the Historic Population Register and the Multi-Generation Register that cover both men and women in the entire population for the years 2000-2011, we compute and plot TFR-like age-cumulated fertility levels, specific for years since immigration, for six groups of sending countries, separately for men and women. Results: We find that the post-migration fertility compensation specified as part of the fertility disruption hypothesis is visibly confirmed in our Swedish study population for female European immigrants from non-EU countries and for female immigrants from non-European countries with a low or medium UN Human Development Index, but not so for other female immigrants, i.e. not for those who come from a Nordic country or from a non-Nordic EU country, and not for female immigrants from a non-European country with a high Human Development Index, including the United States. We find mild but less conclusive evidence for the same feature for males. Conclusions: This shows that at least as far as post-migration fertility compensation is concerned, the disruption

FORSIM-6, Automatic Solution of Coupled Differential Equation System

International Nuclear Information System (INIS)

Carver, M.B.; Stewart, D.G.; Blair, J.M.; Selander, W.N.

1983-01-01

1 - Description of problem or function: The FORSIM program is a versatile package which automates the solution of coupled differential equation systems. The independent variables are time, and up to three space coordinates, and the equations may be any mixture of partial and/or ordinary differential equations. The philosophy of the program is to provide a tool which will solve a system of differential equations for a user who has basic but unspecialized knowledge of numerical analysis and FORTRAN. The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single FORTRAN subroutine, although he may write a number of routines if this is more suitable. These are then loaded with the control routines, which perform the solution and any requested input and output. 2 - Method of solution: Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms

An acoustic eikonal equation for attenuating VTI media

KAUST Repository

Hao, Qi

2016-09-06

We present an acoustic eikonal equation governing the complex-valued travel time of P-waves in attenuating, transversely isotropic media with a vertical symmetry axis (VTI). This equation is based on the assumption that the Pwave complex-valued travel time is independent of the Swave velocity parameter v in Thomsen\\'s notation and the attenuation coefficient A in the Thomsen-type notation for attenuating VTI media. We combine perturbation theory and Shanks transform to develop practical approximations to the attenuating acoustic eikonal equation, capable of admitting analytical description of the attenuation in homogeneous media. For a horizontal, attenuating VTI layer, we also derive non-hyperbolic approximations for the real and imaginary parts of the complex-valued reflection travel time.

Calculation notes that support accident scenario and consequence of the in-tank fuel fire/deflageration

International Nuclear Information System (INIS)

Crowe, R.D. Westinghouse Hanford

1996-01-01

The purpose of this calculation note is to provide the basis for In-Tank Fuel fire/Deflageration consequence for the Tank Farm Safety Analysis Report (FSAR). Tank Fuel Fire/Deflageration scenario is developed and details and description of the analysis methods are provided

Calculation notes that support accident scenario and consequence of the in-tank fuel fire/deflagration

Energy Technology Data Exchange (ETDEWEB)

Crowe, R.D.

1996-09-27

The purpose of this calculation note is to provide the basis for In-Tank Fuel Fire/Deflageration consequence for the Tank Farm Safety Analysis Report (FSAR). Tank Fuel Fire/Deflageration scenario is developed and details and description of the analysis methods are provided.

Coarse-grained description of cosmic structure from Szekeres models

International Nuclear Information System (INIS)

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos

2016-01-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities of structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research

Breeding description for fast reactors and symbiotic reactor systems

International Nuclear Information System (INIS)

Hanan, N.A.

1979-01-01

A mathematical model was developed to provide a breeding description for fast reactors and symbiotic reactor systems by means of figures of merit type quantities. The model was used to investigate the effect of several parameters and different fuel usage strategies on the figures of merit which provide the breeding description. The integrated fuel cycle model for a single-reactor is reviewed. The excess discharge is automatically used to fuel identical reactors. The resulting model describes the accumulation of fuel in a system of identical reactors. Finite burnup and out-of-pile delays and losses are treated in the model. The model is then extended from fast breeder park to symbiotic reactor systems. The asymptotic behavior of the fuel accumulation is analyzed. The asymptotic growth rate appears as the largest eigenvalue in the solution of the characteristic equations of the time dependent differential balance equations for the system. The eigenvector corresponding to the growth rate is the core equilibrium composition. The analogy of the long-term fuel cycle equations, in the framework of this model, and the neutron balance equations is explored. An eigenvalue problem adjoint to the one generated by the characteristic equations of the system is defined. The eigenvector corresponding to the largest eigenvalue, i.e. to the growth rate, represents the ''isotopic breeding worths.'' Analogously to the neutron adjoint flux it is shown that the isotopic breeding worths represent the importance of an isotope for breeding, i.e. for the growth rate of a system

Integration of Lax and Zakharov-Schabat equations by means of algebraic geometry's methods

International Nuclear Information System (INIS)

Gozman, N.Ja.; Latyshev, A.V.; Savostjanov, M.V.; Lebedev, D.R.

1982-01-01

The solutions of nonlinear partial differential equations of Lax and Zakharov-Schabat types are obtained with the help of algebro-geometric method. The Krichever-Drinfeld bimodule for rational curve with cusp point is constructed. It is noted that rational solutions of Zakharov-Schabat equations can be found by means of constructed bimodule in the case of rank 1 only. The evolution of the poles of these solutions is investigated

Lecture note on neutron and photon transport calculation with MCNP

International Nuclear Information System (INIS)

Sakurai, Kiyoshi

2003-01-01

This paper is a lecture note on the continuous energy Monte Carlo method. The contents are as follows; history of the Monte Carlo study, continuous energy Monte Carlo codes, libraries, evaluation method for calculation results, integral emergent particle density equation, pseudorandom number, random walk, variance reduction techniques, MCNP weight window method, MCNP weight window generator, exponential transform, estimators, criticality problem and research subjects. This paper is a textbook for beginners on the Monte Carlo calculation. (author)

MINPACK-1, Subroutine Library for Nonlinear Equation System

International Nuclear Information System (INIS)

Garbow, Burton S.

1984-01-01

1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

Solution of a general pexiderized permanental functional equation

Indian Academy of Sciences (India)

49

and the result follows by equating these last two relations. We return now to the proof of the lemma. Note from C9) that T is completely deter- mined if we know the values of T on the unit circle. Consider any two points on the unit circle (α, β) = (cos γ, sin γ), (x, y) = (cos θ, sin θ) with angles γ, θ oriented counterclock- wise.

Conditions for the existence of control functions in nonseparable simultaneous equations models

OpenAIRE

Blundell, Richard; Matzkin, Rosa L.

2010-01-01

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this note, we define a new property of functions called control function s...

Neutronics equations: Positiveness; compactness; spectral theory; time asymptotic behavior

International Nuclear Information System (INIS)

Mokhtar-Kharroubi, M.

1987-12-01

Neutronics equations are studied: the continuous model (with and without delayed neutrons) and the multigroup model. Asymptotic descriptions of these equations (t→+∞) are obtained, either by the Dunford method or by using semigroup perturbation techniques, after deriving the spectral theory for the equations. Compactness problems are reviewed, and a general theory of compact injection in neutronic functional space is derived. The effects of positiveness in neutronics are analyzed: the irreducibility of the transport semigroup, and the properties of the main eigenvalue (existence, nonexistence, frame, strict dominance, strict monotony in relation to all the parameters). A class of transport operators whose real spectrum can be completely described is shown [fr

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Notes on Mathematical Language: Development Strings, Development Patterns, String Theory and Conditions Language

CERN Document Server

Struck, James T

2003-01-01

Mathematics, according to Lancelot Hogben, is the language of size, shape, and order. This note adds two words to the language of mathematics. First, a verb, develop or develops, is introduced to describe a development pattern or development string. These are patterns of development with examples from fibrillation, spread of electric changes in muscles and nerves, and matter changing into energy. The relevance of this idea to the idea in physics called String Theory is discussed. A critical comment on the use of the String, rather than other objects like circles, boxes, or spheres is made. Second, an adjective or adverb called conditions language is introduced. Equations like E=mc2, Coulomb's law, Newton's law of Gravitation, the equation for the definition of pie and the path to peace and war are discussed with relevance to the idea of conditions language. Conditions language is nothing more than including the relevant conditions where the equation works or when it applies in parentheses with the equation. V...

Evaluation of Maryland abutment scour equation through selected threshold velocity methods

Science.gov (United States)

Benedict, S.T.

2010-01-01

The U.S. Geological Survey, in cooperation with the Maryland State Highway Administration, used field measurements of scour to evaluate the sensitivity of the Maryland abutment scour equation to the critical (or threshold) velocity variable. Four selected methods for estimating threshold velocity were applied to the Maryland abutment scour equation, and the predicted scour to the field measurements were compared. Results indicated that performance of the Maryland abutment scour equation was sensitive to the threshold velocity with some threshold velocity methods producing better estimates of predicted scour than did others. In addition, results indicated that regional stream characteristics can affect the performance of the Maryland abutment scour equation with moderate-gradient streams performing differently from low-gradient streams. On the basis of the findings of the investigation, guidance for selecting threshold velocity methods for application to the Maryland abutment scour equation are provided, and limitations are noted.

Geometry of Kaluza-Klein theory. II. Field equations

International Nuclear Information System (INIS)

Maia, M.D.

1985-01-01

In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group

The action principle for a system of differential equations

International Nuclear Information System (INIS)

Gitman, D M; Kupriyanov, V G

2007-01-01

We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of constructing the action principle are presented. From simple consideration, we derive the necessary and sufficient conditions for the existence of a multiplier matrix which can endow a prescribed set of second-order differential equations with the structure of the Euler-Lagrange equations. An explicit form of the action is constructed if such a multiplier exists. If a given set of differential equations cannot be derived from an action principle, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The general procedure is illustrated by several examples

The action principle for a system of differential equations

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Instituto de FIsica, Universidade de Sao Paulo (Brazil); Kupriyanov, V G [Instituto de FIsica, Universidade de Sao Paulo (Brazil)

2007-08-17

We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of constructing the action principle are presented. From simple consideration, we derive the necessary and sufficient conditions for the existence of a multiplier matrix which can endow a prescribed set of second-order differential equations with the structure of the Euler-Lagrange equations. An explicit form of the action is constructed if such a multiplier exists. If a given set of differential equations cannot be derived from an action principle, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The general procedure is illustrated by several examples.

Lecture Notes for the Course in Water Wave Mechanics

DEFF Research Database (Denmark)

Andersen, Thomas Lykke; Frigaard, Peter; Burcharth, Hans F.

knowledge. The course is at the same time an introduction to the course in coastal hydraulics on the 8th semester. The notes cover the first four lectures of the course: • Definitions. Governing equations and boundary conditions. • Derivation of velocity potential for linear waves. Dispersion relationship...... Particle velocities and accelerations. • Particle paths, pressure variation, deep and shallow water waves, wave energy and group velocity. • Shoaling, refraction, diffraction and wave breaking. The last part of the course is on analysis of irregular waves and was included in the first two editions...

TINTE. Nuclear calculation theory description report

Energy Technology Data Exchange (ETDEWEB)

Gerwin, H.; Scherer, W.; Lauer, A. [Forschungszentrum Juelich GmbH (DE). Institut fuer Energieforschung (IEF), Sicherheitsforschung und Reaktortechnik (IEF-6); Clifford, I. [Pebble Bed Modular Reactor (Pty) Ltd. (South Africa)

2010-01-15

The Time Dependent Neutronics and Temperatures (TINTE) code system deals with the nuclear and the thermal transient behaviour of the primary circuit of the High-temperature Gas-cooled Reactor (HTGR), taking into consideration the mutual feedback effects in twodimensional axisymmetric geometry. This document contains a complete description of the theoretical basis of the TINTE nuclear calculation, including the equations solved, solution methods and the nuclear data used in the solution. (orig.)

Trajectory description of the quantum–classical transition for wave packet interference

Energy Technology Data Exchange (ETDEWEB)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-08-15

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.

Hamiltonian Description of Convective-cell Generation

International Nuclear Information System (INIS)

Krommes, J.A.; Kolesnikov, R.A.

2004-01-01

The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted

The Multigroup Neutron Diffusion Equations/1 Space Dimension

Energy Technology Data Exchange (ETDEWEB)

Linde, Sven

1960-06-15

A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix.

The Multigroup Neutron Diffusion Equations/1 Space Dimension

International Nuclear Information System (INIS)

Linde, Sven

1960-06-01

A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix

Structure preserving transformations for Newtonian Lie-admissible equations

International Nuclear Information System (INIS)

Cantrijn, F.

1979-01-01

Recently, a new formulation of non-conservative mechanics has been presented in terms of Hamilton-admissible equations which constitute a generalization of the conventional Hamilton equations. The algebraic structure entering the Hamilton-admissible description of a non-conservative system is that of a Lie-admissible algebra. The corresponding geometrical treatment is related to the existence of a so-called symplectic-admissible form. The transformation theory for Hamilton-admissible systems is currently investigated. The purpose of this paper is to describe one aspect of this theory by identifying the class of transformations which preserve the structure of Hamilton-admissible equations. Necessary and sufficient conditions are established for a transformation to be structure preserving. Some particular cases are discussed and an example is worked out

Description of group-theoretical model of developed turbulence

International Nuclear Information System (INIS)

Saveliev, V L; Gorokhovski, M A

2008-01-01

We propose to associate the phenomenon of stationary turbulence with the special self-similar solutions of the Euler equations. These solutions represent the linear superposition of eigenfields of spatial symmetry subgroup generators and imply their dependence on time through the parameter of the symmetry transformation only. From this model, it follows that for developed turbulent process, changing the scale of averaging (filtering) of the velocity field is equivalent to composition of scaling, translation and rotation transformations. We call this property a renormalization-group invariance of filtered turbulent fields. The renormalization group invariance provides an opportunity to transform the averaged Navier-Stokes equation over a small scale (inner threshold of the turbulence) to larger scales by simple scaling. From the methodological point of view, it is significant to note that the turbulent viscosity term appeared not as a result of averaging of the nonlinear term in the Navier-Stokes equation, but from the molecular viscosity term with the help of renormalization group transformation.

Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2012-01-01

Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

Radial solutions to semilinear elliptic equations via linearized operators

Directory of Open Access Journals (Sweden)

Phuong Le

2017-04-01

Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

Science.gov (United States)

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

International Nuclear Information System (INIS)

Hackbusch, W.

1983-01-01

1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

Parquet equations for numerical self-consistent-field theory

International Nuclear Information System (INIS)

Bickers, N.E.

1991-01-01

In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail. (author). 14 refs, 9 figs

Stochastic differential equations and a biological system

DEFF Research Database (Denmark)

Wang, Chunyan

1994-01-01

The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have...... description. In order to identify the parameters, a Maximum likelihood estimation method is used together with a simplified truncated second order filter. Because of the continuity feature of the predictor equation, two numerical integration methods, called the Odeint and the Discretization method...

Complex Riccati equations as a link between different approaches for the description of dissipative and irreversible systems

International Nuclear Information System (INIS)

Schuch, Dieter

2012-01-01

Quantum mechanics is essentially described in terms of complex quantities like wave functions. The interesting point is that phase and amplitude of the complex wave function are not independent of each other, but coupled by some kind of conservation law. This coupling exists in time-independent quantum mechanics and has a counterpart in its time-dependent form. It can be traced back to a reformulation of quantum mechanics in terms of nonlinear real Ermakov equations or equivalent complex nonlinear Riccati equations, where the quadratic term in the latter equation explains the origin of the phase-amplitude coupling. Since realistic physical systems are always in contact with some kind of environment this aspect is also taken into account. In this context, different approaches for describing open quantum systems, particularly effective ones, are discussed and compared. Certain kinds of nonlinear modifications of the Schrödinger equation are discussed as well as their interrelations and their relations to linear approaches via non-unitary transformations. The modifications of the aforementioned Ermakov and Riccati equations when environmental effects are included can be determined in the time-dependent case. From formal similarities conclusions can be drawn how the equations of time-independent quantum mechanics can be modified to also incluce the enviromental aspects.

Fluid description of multi-component solar partially ionized plasma

International Nuclear Information System (INIS)

Khomenko, E.; Collados, M.; Vitas, N.; Díaz, A.

2014-01-01

We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the radiation field. All approximations and assumptions are carefully considered. Generalized Ohm's law is derived for the single-fluid and two-fluid formalism. Our approach is analytical with some order-of-magnitude support calculations. After general equations are developed, we particularize to some frequently considered cases as for the interaction of matter and radiation

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

International Nuclear Information System (INIS)

Lind, R.C.

1973-01-01

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation

International Nuclear Information System (INIS)

Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.

1989-01-01

The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs

T-4 handbook of material properties data bases. Volume 1c. Equations of state

International Nuclear Information System (INIS)

Holian, K.S.

1984-11-01

This manual is a compilation of descriptions of the equations of state (EOS) in the T-4 computerized library of material properties tables. The introduction gives a brief descriptions of the library and of the physics theories and models which were used to calculate the equations of state. Then each EOS is described in detail. First, various physical parameters of each theoretical EOS are tabulated and compared with experiments when available. Then the method of generating the EOS is briefly described. Finally, the tabels are plotted in terms of pressure and energy vs density along line of constant temperature

Ophthalmology patients' interest in online access to clinic notes at three US clinics.

Science.gov (United States)

Lee, Bryan S; Oster, Natalia V; Chen, Galen Y; Ding, Leona L; Walker, Janice D; Elmore, Joann G

2017-07-01

This study aimed to understand patients' perceptions about potential benefits and harms of accessing their own ophthalmology clinic notes via an electronic patient portal as part of the OpenNotes initiative. The authors conducted a cross-sectional, in-person survey of ophthalmology patients at three US eye clinics. The paper survey was self-administered or administered with assistance from study staff before or after patients' clinical visits. The authors used descriptive statistics to summarise patient characteristics and patient attitudes about accessing their ophthalmology notes online. Chi-square and t-tests were performed to assess differences in patient responses between clinic locations. Four hundred and fifty-one patients responded (response rate 65%). Most patients thought that accessing doctors' notes online was a good idea (95%), wanted to view their clinic notes online (94%), and agreed online access would increase their understanding of their eye problems (95%) and help them better remember their care plan (94%); 14% said online access would increase their worry; 43% had privacy concerns; and 96% indicated they would show or discuss their notes with at least one other person. Non-white patients were more likely than white patients to perceive online clinic notes as a useful tool, but they were also more likely to worry and to express greater privacy concerns. Patients at three US eye clinics were strongly in favour of online access to ophthalmology notes and were optimistic this access would improve their understanding and self-care. Ophthalmologists should consider offering online access to their notes to enhance doctor-patient communication and improve clinical outcomes. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.

Monopoles and rational maps: A note on a theorem of Donaldson

International Nuclear Information System (INIS)

Hurtubise, J.

1985-01-01

In a recent paper, Donaldson gave a description of the moduli space of SU(2) monopoles in terms of rational maps; this was done indirectly, via the associated solution of Nahm's equations. We give here an interpretation of these rational maps in terms of the monopole's spectral curve, and then as ''scattering data'' for the monopole itself. (orig.)

Instabilities and chaos in a kinetic equation for active nematics

International Nuclear Information System (INIS)

Shi, Xia-qing; Ma, Yu-qiang; Chaté, Hugues

2014-01-01

We study dry active nematics at the kinetic equation level, stressing the differences with the well-known Doi theory for non-active rods near thermal equilibrium. By deriving hydrodynamic equations from the kinetic equation, we show analytically that these two description levels share the same qualitative phase diagram, as defined by the linear instability limits of spatially-homogeneous solutions. In particular, we show that the ordered, homogeneous state is unstable in a region bordering the linear onset of nematic order, and is only linearly stable deeper in the ordered phase. Direct simulations of the kinetic equation reveal that its solutions are chaotic in the region of linear instability of the ordered homogeneous state. The local mechanisms for this large-scale chaos are discussed. (paper)

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

Science.gov (United States)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first

Note Taking on Trial: A Legal Application of Note-Taking Research

Science.gov (United States)

Kiewra, Kenneth A.

2016-01-01

This article is about note taking, but it is not an exhaustive review of note-taking literature. Instead, it portrays the application of note-taking research to an unusual and important area of practice--the law. I was hired to serve as an expert witness on note taking in a legal case that hinged, in part, on the completeness and accuracy of…

Lecture background notes on transient sodium boiling and voiding in fast reactors

International Nuclear Information System (INIS)

Okrent, D.; Fauske, H.K.

1972-01-01

This set of lecture background notes includes the following: (1) Introductory remarks on fast reactor safety, which are intended to provide some perspective on the role played by sodium boiling. (2) A discussion of superheat which reviews the experimental data and nucleation models with emphasis on the pressure-temperature history effect on radius of active cavity sites, including the role played by inert gas. (3) A discussion of the growth and collapse of spherical bubbles. (4) A historical description of the development of computer codes to describe voiding and a detailed description of the analytical formulation of typical models for calculating voiding due to boiling, fission gas release, and molten fuel-coolant interaction. (U.S.)

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

Science.gov (United States)

Blossey, R.; Maggs, A. C.; Podgornik, R.

2017-06-01

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

Note on the End Game in Homotopy Zero Curve Tracking

OpenAIRE

Sosonkina, Masha; Watson, Layne T.; Stewart, David E.

1995-01-01

Homotopy algorithms to solve a nonlinear system of equations f(x)=0 involve tracking the zero curve of a homotopy map p(a,theta,x) from theta=0 until theta=1. When the algorithm nears or crosses the hyperplane theta=1, an "end game" phase is begun to compute the solution x(bar) satisfying p(a,theta,x(bar))=f(x(bar))=0. This note compares several end game strategies, including the one implemented in the normal flow code FIXPNF in the homotopy software package HOMPACK.

Oscillation criteria for third order nonlinear delay differential equations with damping

Directory of Open Access Journals (Sweden)

Said R. Grace

2015-01-01

Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

Operations involving momentum variables in non-Hamiltonian evolution equations

International Nuclear Information System (INIS)

Benatti, F.; Ghirardi, G.C.; Rimini, A.; Weber, T.

1988-02-01

Non-Hamiltonian evolution equations have been recently considered for the description of various physical processes. Among this type of equations the class which has been more extensively studied is the one usually referred to as Quantum Dynamical Semigroup equations (QDS). In particular an equation of the QDS type has been considered as the basis for a model, called Quantum Mechanics with Spontaneous Localization (QMSL), which has been shown to exhibit some very interesting features allowing to overcome most of the conceptual difficulties of standard quantum theory, QMSL assumes a modification of the pure Schroedinger evolution by assuming the occurrence, at random times, of stochastic processes for the wave function corresponding formally to approximate position measurements. In this paper, we investigate the consequences of modifying and/or enlarging the class of the considered stochastic processes, by considering the spontaeous occurrence of approximate momentum and of simultaneous position and momentum measurements. It is shown that the considered changes in the elementary processes have unacceptable consequences. In particular they either lead to drastic modifications in the dynamics of microsystems or are completely useless from the point of view of the conceptual advantages that one was trying to get from QMSL. The present work supports therefore the idea that QMSL, as originally formulated, can be taken as the basic scheme for the generalizations which are still necessary in order to make it appropriate for the description of systems of identical particles and to meet relativistic requirements. (author). 14 refs

Operations involving momentum variables in non-Hamiltonian evolution equation

International Nuclear Information System (INIS)

Benatti, F.; Ghirardi, G.C.; Weber, T.; Rimini, A.

1988-01-01

Non-Hamiltonian evolution equations have been recently considered for the description of various physical processes. Among these types of equations the class which has been more extensively studied is the one usually referred to as quantum-dynamical semi-group equations (QDS). In particular an equation of the QDS type has been considered as the basis for a model, called quantum mechanics with spontaneous localization (QMSL), which has been shown to exhibit some very interesting features allowing us to overcome most of the conceptual difficulties of standard quantum theory. QMSL assumes a modification of the pure Schroedinger evolution by assuming the occurrence, at random times, of stochastic processes for the wave function corresponding formally to approximate position measurements. In this paper the consequences of modifying and/or enlarging the class of the considered stochastic processes, by considering the spontaneous occurrence of approximate momentum and of simultaneous position and momentum measurements, are investigated. It is shown that the considered changes in the elementary processes have unacceptable consequences. In particular they either lead to drastic modification in the dynamics of microsystems or are completely useless from the point of view of the conceptual advantages that one was trying to get from QMSL. The present work supports therefore the idea that QMSL, as originally formulated, can be taken as the basic scheme for the generalizations which are still necessary in order to make it appropriate for the description of systems of identical particles and to meet relativistic requirements

Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

International Nuclear Information System (INIS)

Goreac, D.

2009-01-01

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case

Geometric description of a discrete power function associated with the sixth Painlevé equation.

Science.gov (United States)

Joshi, Nalini; Kajiwara, Kenji; Masuda, Tetsu; Nakazono, Nobutaka; Shi, Yang

2017-11-01

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with [Formula: see text] symmetry. By constructing the action of [Formula: see text] as a subgroup of [Formula: see text], i.e. the symmetry group of P VI , we show how to relate [Formula: see text] to the symmetry group of the lattice. Moreover, by using translations in [Formula: see text], we explain the odd-even structure appearing in previously known explicit formulae in terms of the τ function.

Limit Properties of Solutions of Singular Second-Order Differential Equations

Directory of Open Access Journals (Sweden)

Weinmüller Ewa

2009-01-01

Full Text Available We discuss the properties of the differential equation , a.e. on , where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is given. We also describe the structure of boundary conditions which are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.

MixedNotes

DEFF Research Database (Denmark)

Jokela, Tero; Lucero, Andrés

2014-01-01

Affinity Diagramming is a technique to organize and make sense of qualitative data. It is commonly used in Contextual Design and HCI research. However, preparing notes for and building an Affinity Diagram remains a laborious process, with a wide variety of different approaches and practices....... In this paper, we present MixedNotes, a novel technique to prepare physical paper notes for Affinity Diagramming, and a software tool to support this technique. The technique has been tested with large real-life Affinity Diagrams with overall positive results....

Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces

Directory of Open Access Journals (Sweden)

E. Hanebaly

2000-03-01

Full Text Available It is known that for $omega$-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ${Bbb R}^+$ is equivalent to the existence of an omega-periodic solution (see Haraux [5] and Hanebaly [7, 10]. It is also known that if the Banach space is strictly convex and the equation is almost periodic and of monotonous type, then the existence of a continuous solution with a precompact range is equivalent to the existence of an almost periodic solution (see Hanebaly [8]. In this note we want to generalize the results above for multi-valued differential equations.

VMOMS: a computer code for finding moment solutions to the Grad-Shafranov equation

International Nuclear Information System (INIS)

Lao, L.L.; Wieland, R.M.; Houlberg, W.A.; Hirshman, S.P.

1982-02-01

A code VMOMS is described which finds approximate solutions to the Grad-Shafranov equation describing scalar pressure-balance equilibria for axisymmetric tokamak plasmas. A Fourier series expansion of the flux surface coordinates (R,Z) is made in terms of two new coordinates (rho, theta), and the resulting equation is conveniently reduced to a system of ordinary differential equations (ODE's) using a variational principle. The solution of these simple equations with pressure and current as driving functions, yields, in principle, a complete description of the equilibrium. Complete axisymmetry is assumed, as well as up-down symmetry about the toroidal midplane

Measurement theory and the Schroedinger equation

International Nuclear Information System (INIS)

Schwarz, A.S.; Tyupkin, Yu.S.

1987-01-01

The paper is an analysis of the measuring process in quantum mechanics based on the Schroedinger equation. The arguments employed use an assumption reflecting, to some extent, the statistical properties of the vacuum. A description is given of the cases in which different incoherent superpositions of pure states in quantum mechanics are physically equivalent. The fundamental difference between quantum and classical mechanics as explained by the existence of unobservable variables is discussed. (U.K.)

The Effectiveness of Note-Taking on Reading Comprehension of Iranian EFL Learners

Directory of Open Access Journals (Sweden)

Farnoush Bahrami

2017-10-01

Full Text Available By taking notes students could save time for reading all textbooks for their exams or for their representations. Taking notes increases attention of students to read or heard materials, and this increases their comprehension. Thus, the present study is important because note-taking could help them to remember what they learnt, absolutely important information. The method used in this research was survey. The 40 Persian EFL learners were selected from a language institute in Karaj to participate in the present study. These learners were divided into two groups; one of them is experimental group (N=20 and the other one is control group (N=20. Pretest and post test were two instruments that were used to carry out this study, a pretest about skill of note-taking of passages of the lessons was used for both experimental and control group. This test consisted of 4 passages. The same test was administrated again as the post test for both groups by the end of the course to see the different conclusion between taking note of experimental group and control group. Reliability between 4 texts is in oscillation from 0.6 to 0.81 (from 0.6 upwards. Therefore this reliability was an acceptable one. To analyze data descriptive statistics (that was contained percentage, frequency and mean score and also inferential statistics (that was contained ANOVA, Pearson correlation, independent sample t-test, multivariate’s test, regression were carried out by using SPSS16 soft ware. The findings confirmed that note taking is effective in reading comprehension.

Computer local construction of a general solution for the Chew-Low equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1980-01-01

General solution of the dynamic form of the Chew-Low equations in the vicinity of the restpoint is considered. A method for calculating coefficients of series being members of such solution is suggested. The results of calculations, coefficients of power series and expansions carried out by means of the SCHOONSCHIP and SYMBAL systems are given. It is noted that the suggested procedure of the Chew-Low equation solutions basing on using an electronic computer as an instrument for analytical calculations permits to obtain detail information on the local structure of general solution

Revising Lecture Notes: How Revision, Pauses, and Partners Affect Note Taking and Achievement

Science.gov (United States)

Luo, Linlin; Kiewra, Kenneth A.; Samuelson, Lydia

2016-01-01

Note taking has been categorized as a two-stage process: the recording of notes and the review of notes. We contend that note taking might best involve a three-stage process where the missing stage is revision. This study investigated the benefits of revising lecture notes and addressed two questions: First, is revision more effective than…

Description of width and spectra of two relativistic fermions bound states

International Nuclear Information System (INIS)

Sidorov, A.V.; Skachkov, N.B.

1979-01-01

The formalism for relativistic description of two particles with spin 1/2 is constructed. Used is the two-particle three-dimensional equation, obtained by quasipotential approach. Quasipotential equation in the relativistic configurational space with OBEP potential is reduced to the system of partial equations which is the analog of nonrelativistic Hamada-Jonston system. WKB approach is used to calculate mass spectra and leptonic width of mesons in quark model. The results of the study can be applied to the calculation of mass spectra and widths of electromagnetic decays of systems of e + e - , μ + μ - , c anti c, b anti b, N anti N type

Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

CERN Document Server

Meleshko, Sergey V

2005-01-01

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Heavy meson observables and Dyson-Schwinger equations

International Nuclear Information System (INIS)

Ivanov, M. A.

1998-01-01

Dyson-Schwinger equation (DSE) studies show that the b-quark mass-function is approximately constant, and that this is true to a lesser extent for the c-quark. This observation provides the basis for a study of the leptonic and semileptonic decays of heavy pseudoscalar mesons using a ''heavy-quark'' limit of the DSES, which, when exact, reduces the number of independent form factors. Semileptonic decays with light mesons in the final state are also accessible because the DSES provide a description of light-quark propagation characteristics and light-meson structure. A description of B-meson decays is straightforward, however, the study of decays involving the D-meson indicates that c-quark mass-corrections are quantitatively important

Effective quadrature formula in solving linear integro-differential equations of order two

Science.gov (United States)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

Linearized gyro-kinetic equation

International Nuclear Information System (INIS)

Catto, P.J.; Tsang, K.T.

1976-01-01

An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated

Discrete variational derivative method a structure-preserving numerical method for partial differential equations

CERN Document Server

Furihata, Daisuke

2010-01-01

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

The multidensity integral equation approach in the theory of complex liquids

International Nuclear Information System (INIS)

Holovko, M.F.

2001-01-01

Recent development of the multi-density integral equation approach and its application to the statistical mechanical modelling of a different type of association and clusterization in liquids and solutions are reviewed. The effects of dimerization, polymerization and network formation are discussed. The numerical and analytical solutions of the integral equations in the multi-density formalism for pair correlation functions are used for the description of structural and thermodynamical properties of ionic solutions, polymers and network forming fluids

Resource description and access 2013 revision

CERN Document Server

2013-01-01

This e-book contains the 2013 Revision of RDA: Resource Description and Access, and includes the July 2013 Update. This e-book offers links within the RDA text and the capability of running rudimentary searches of RDA, but please note that this e-book does not have the full range of content or functionality provided by the subscription product RDA Toolkit. Included: A full accumulation of RDA- the revision contains a full set of all current RDA instructions. It replaces the previous version of RDA Print as opposed to being an update packet to that version. RDA has gone through many changes sin

EPICS release 3.11.6 specific documentation -- Release notes for EPICS 3.11.6

International Nuclear Information System (INIS)

1994-01-01

These notes cover the following: (1) directions for switching to production APS release R3.11.6; (2) unbundling of channel access clients; (3) access security; (4) channel access additions; synchronous time support; and (5) description of major differences between R3.11.3 and R3.11.6 Also included is a list of new and/or updated documentation for the program

Research Note:

DEFF Research Database (Denmark)

Behuria, Pritish; Buur, Lars; Gray, Hazel

2017-01-01

its core conceptual and methodological features. This Research Note starts by setting out our understanding of political settlements and provides an overview of existing political settlements literature on African countries. The note then explores how the key concept of ‘holding power’ has been...

Consistent dynamical and statistical description of fission and comparison

Energy Technology Data Exchange (ETDEWEB)

Shunuan, Wang [Chinese Nuclear Data Center, Beijing, BJ (China)

1996-06-01

The research survey of consistent dynamical and statistical description of fission is briefly introduced. The channel theory of fission with diffusive dynamics based on Bohr channel theory of fission and Fokker-Planck equation and Kramers-modified Bohr-Wheeler expression according to Strutinsky method given by P.Frobrich et al. are compared and analyzed. (2 figs.).

Properties of wavelet discretization of Black-Scholes equation

Science.gov (United States)

Finěk, Václav

2017-07-01

Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.

The Maxwell-Stefan description of mixture diffusion in nanoporous crystalline materials

NARCIS (Netherlands)

Krishna, R.

2014-01-01

The efficacy of nanoporous crystalline materials in separation applications is often influenced to a significant extent by diffusion of guest molecules within the pores of the structural frameworks. The Maxwell-Stefan (M-S) equations provide a fundamental and convenient description of mixture

Dissipative behavior of some fully non-linear KdV-type equations

Science.gov (United States)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Equations of motion for a radiating charged particle in electromagnetic fields on curved spacetime

International Nuclear Information System (INIS)

Prasanna, A.R.

1982-11-01

In this note we present the equations of motion for a radiating charged particle in the framework of general relativity and give a formal procedure of solving the system numerically using iterations, when the motion is confined to the equatorial plane. (author)

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

Science.gov (United States)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

A model for the stochastic origins of Schrodinger's equation

OpenAIRE

Davidson, Mark P.

2001-01-01

A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.

Use of state variables in the description of irradiation creep and deformation of metals

International Nuclear Information System (INIS)

Hart, E.W.; Li, C.Y.

1976-01-01

The understanding of the effects of irradiation on metal creep and deformation are not yet satisfactory, owing in part to the limitations on experimentation in radiation environment. Because of such limitations, theoretical considerations must play a strong role. Virtually all of the theoretical considerations currently employed are based on micro-mechanical models for the deformation behavior. The recent theoretical and experimental development of a plastic equation of state for metal deformation has led to the identification of some of the principal micro-mechanisms in phenomenological terms. The role of the individual mechanisms can be related to the state variables of the description, and those variables are directly accessible measurable quantities. This paper explores how irradiation might affect this description. It is shown that the radiation flux and the radiation fluence are expected to affect different components of the equation of state. The resultant description makes considerable use of the information developed in radiation-free environment. 5 fig

Numerical solution of integral equations, describing mass spectrum of vector mesons

International Nuclear Information System (INIS)

Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.

1988-01-01

The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data

A note on notes: note taking and containment.

Science.gov (United States)

Levine, Howard B

2007-07-01

In extreme situations of massive projective identification, both the analyst and the patient may come to share a fantasy or belief that his or her own psychic reality will be annihilated if the psychic reality of the other is accepted or adopted (Britton 1998). In the example of' Dr. M and his patient, the paradoxical dilemma around note taking had highly specific transference meanings; it was not simply an instance of the generalized human response of distracted attention that Freud (1912) had spoken of, nor was it the destabilization of analytic functioning that I tried to describe in my work with Mr. L. Whether such meanings will always exist in these situations remains a matter to be determined by further clinical experience. In reopening a dialogue about note taking during sessions, I have attempted to move the discussion away from categorical injunctions about what analysis should or should not do, and instead to foster a more nuanced, dynamic, and pair-specific consideration of the analyst's functioning in the immediate context of the analytic relationship. There is, of course, a wide variety of listening styles among analysts, and each analyst's mental functioning may be affected differently by each patient whom the analyst sees. I have raised many questions in the hopes of stimulating an expanded discussion that will allow us to share our experiences and perhaps reach additional conclusions. Further consideration may lead us to decide whether note taking may have very different meanings for other analysts and analyst-patient pairs, and whether it may serve useful functions in addition to the one that I have described.

The spectral transform as a tool for solving nonlinear discrete evolution equations

International Nuclear Information System (INIS)

Levi, D.

1979-01-01

In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

Simple Parametric Model for Airfoil Shape Description

Science.gov (United States)

Ziemkiewicz, David

2017-12-01

We show a simple, analytic equation describing a class of two-dimensional shapes well suited for representation of aircraft airfoil profiles. Our goal was to create a description characterized by a small number of parameters with easily understandable meaning, providing a tool to alter the shape with optimization procedures as well as manual tweaks by the designer. The generated shapes are well suited for numerical analysis with 2D flow solving software such as XFOIL.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

Science.gov (United States)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

The kinematic algebras from the scattering equations

International Nuclear Information System (INIS)

Monteiro, Ricardo; O’Connell, Donal

2014-01-01

We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.

Implications of observing and writing field notes through different lenses

Directory of Open Access Journals (Sweden)

Hellesø R

2015-04-01

Full Text Available Ragnhild Hellesø,1 Line Melby,1 Solveig Hauge21Department of Nursing Science, Institute of Health and Society, Faculty of Medicine, University of Oslo, Oslo, Norway; 2Faculty of Health and Social Studies, Telemark University College, Porsgrunn, NorwayBackground: From a philosophy of science perspective, the literature has posited that different research approaches influence field studies. Studies addressing interdisciplinary research have focused on the challenges of organizing and running interdisciplinary teams, cultural differences between and within disciplines, and constraints in conducting interdisciplinary research. Studies exploring and discussing the process and outcome of transferring observations to notes from an interdisciplinary point of view are not identified. The aim of this paper is to explore the characteristics of field notes created by researchers representing different disciplines and experiences.Methods: A case study using a modified dynamic observation method was employed. The analyses were initiated by a researcher who had not been involved in the data collection. The field notes were analyzed using three main steps.Results: The structures of both researchers' field notes were characterized by similarities in their descriptions, but the notes' foci and analytical levels differed.Conclusion: The findings contribute new insights concerning the execution of interdisciplinary observational studies. Our findings demonstrate that entering the field with different lenses produced richer and more varied data, providing a broader platform from which to discuss and interpret a study's findings. From a theoretical point of view, the findings enable a more nuanced discussion and a conceptual elaboration regarding how observational approaches should be pursued in future studies. On a practical level, the findings show that even if the researchers agree on what the overall focus in the observations should be, differences can occur in

Nonaligned shocks for discrete velocity models of the Boltzmann equation

Directory of Open Access Journals (Sweden)

J. M. Greenberg

1991-05-01

Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

A note on the translation of conceptual data models into description logics: disjointness and covering assumptions

CSIR Research Space (South Africa)

Casini, G

2012-10-01

Full Text Available possibilities for conceptual data modeling. It also raises the question of how existing conceptual models using ER, UML or ORM could be translated into Description Logics (DLs), a family of logics that have proved to be particularly appropriate for formalizing...

Multi criteria evaluation for universal soil loss equation based on geographic information system

Science.gov (United States)

Purwaamijaya, I. M.

2018-05-01

The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.

Another comment on 'relativistic description of quark-antiquark bound states'

International Nuclear Information System (INIS)

Lucha, W.; Rupprecht, H.; Schoeberl, F.F.

1991-04-01

We point out some ambiguities in the treatment of fermion-antifermion bound states by solving the reduced Salpeter equation in coordinate space. Our observations allow to cast some doubt on the validity of the conclusion of Gara et al. that moving from a nonrelativistic to a relativistic description makes things worse. (authors)

Research Note: The sensitivity of surface seismic P-wave data in transversely isotropic media to reflector depth

KAUST Repository

Alkhalifah, Tariq Ali

2016-01-01

The leading component of the high-frequency asymptotic description of the wavefield, given by the travel time, is governed by the eikonal equation. In anisotropic media, traveltime measurements from seismic experiments conducted along one surface

Singular integral equations boundary problems of function theory and their application to mathematical physics

CERN Document Server

Muskhelishvili, N I

2011-01-01

Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem

TBA equations for excited states in the sine-Gordon model

International Nuclear Information System (INIS)

Balog, Janos; Hegedus, Arpad

2004-01-01

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found

On integration of the first order differential equations in a finite terms

International Nuclear Information System (INIS)

Malykh, M D

2017-01-01

There are several approaches to the description of the concept called briefly as integration of the first order differential equations in a finite terms or symbolical integration. In the report three of them are considered: 1.) finding of a rational integral (Beaune or Poincaré problem), 2.) integration by quadratures and 3.) integration when the general solution of given differential equation is an algebraical function of a constant (Painlevé problem). Their realizations in Sage are presented. (paper)

Constitutive equations for describing high-temperature inelastic behavior of structural alloys

International Nuclear Information System (INIS)

Robinson, D.N.; Pugh, C.E.; Corum, J.M.

1976-01-01

This paper addresses constitutive equations for the description of inelastic behavior of LMFBR structural alloys at elevated temperatures. Both elastic-plastic (time-independent) and creep (time-dependent) deformations are considered for types 304 and 316 stainless steel and 2 1 / 4 Cr--1 Mo steel. The constitutive equations identified for interim use in design analyses are described along with the assumptions and data on which they are based. Areas where improvements are needed are identified, and some alternate theories that are being pursued are outlined

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

Science.gov (United States)

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Towards a worldsheet description of N=8 supergravity

International Nuclear Information System (INIS)

Lipstein, Arthur; Schomerus, Volker

2015-10-01

In this note we address the worldsheet description of 4-dimensional N=8 supergravity using ambitwistors. After gauging an appropriate current algebra, we argue that the only physical vertex operators correspond to the N=8 supermultiplet. It has previously been shown that worldsheet correlators give rise to supergravity tree level scattering amplitudes. We extend this work by proposing a definition for genus-one amplitudes that passes several consistency checks such as exhibiting modular invariance and reproducing the expected infrared behavior of 1-loop supergravity amplitudes.

Equations of multiparticle dynamics

International Nuclear Information System (INIS)

Chao, A.W.

1987-01-01

The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions

Open Oncology Notes: A Qualitative Study of Oncology Patients' Experiences Reading Their Cancer Care Notes.

Science.gov (United States)

Kayastha, Neha; Pollak, Kathryn I; LeBlanc, Thomas W

2018-04-01

Electronic medical records increasingly allow patients access to clinician notes. Although most believe that open notes benefits patients, some suggest negative consequences. Little is known about the experiences of patients with cancer reading their medical notes; thus we aimed to describe this qualitatively. We interviewed 20 adults with metastatic or incurable cancer receiving cancer treatment. The semistructured qualitative interviews included four segments: assessing their overall experience reading notes, discussing how notes affected their cancer care experiences, reading a real note with the interviewer, and making suggestions for improvement. We used a constant comparison approach to analyze these qualitative data. We found four themes. Patients reported that notes resulted in the following: (1) increased comprehension; (2) ameliorated uncertainty, relieved anxiety, and facilitated control; (3) increased trust; and (4) for a subset of patients, increased anxiety. Patients described increased comprehension because notes refreshed their memory and clarified their understanding of visits. This helped mitigate the unfamiliarity of cancer, addressing uncertainty and relieving anxiety. Notes facilitated control, empowering patients to ask clinicians more questions. The transparency of notes also increased trust in clinicians. For a subset of patients, however, notes were emotionally difficult to read and raised concerns. Patients identified medical jargon and repetition in notes as areas for improvement. Most patients thought that reading notes improved their care experiences. A small subset of patients experienced increased distress. As reading notes becomes a routine part of the patient experience, physicians might want to elicit and address concerns that arise from notes, thereby further engaging patients in their care.

Thin-Layer Solutions of the Helmholtz and Related Equations

KAUST Repository

Ockendon, J. R.

2012-01-01

This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.

Poincare group and relativistic wave equations in 2+1 dimensions

Energy Technology Data Exchange (ETDEWEB)

Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)

1997-09-07

Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)

Fokker-Planck description for the queue dynamics of large tick stocks

Science.gov (United States)

Garèche, A.; Disdier, G.; Kockelkoren, J.; Bouchaud, J.-P.

2013-09-01

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. “Jump” events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

Intensity-interferometric test of nuclear collision geometries obtained from the Boltzmann-Uehling-Uhlenbeck equation

International Nuclear Information System (INIS)

Gong, W.G.; Bauer, W.; Gelbke, C.K.; Carlin, N.; de Souza, R.T.; Kim, Y.D.; Lynch, W.G.; Murakami, T.; Poggi, G.; Sanderson, D.P.; Tsang, M.B.; Xu, H.M.; Pratt, S.; Fields, D.E.; Kwiatkowski, K.; Planeta, R.; Viola, V.E. Jr.; Yennello, S.J.

1990-01-01

Two-proton correlation functions measured for the 14 N+ 27 Al reaction at E/A=75 MeV are compared to correlation functions predicted for collision geometries obtained from numerical solutions of the Boltzmann-Uehling-Uhlenbeck (BUU) equation. The calculations are in rather good agreement with the experimental correlation function, indicating that the BUU equation gives a reasonable description of the space-time evolution of the reaction

A systematic approach to sketch Bethe-Salpeter equation

Directory of Open Access Journals (Sweden)

Qin Si-xue

2016-01-01

Full Text Available To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark–anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD’s gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB. The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Numerical solution of the kinetic equation in reactor shielding

International Nuclear Information System (INIS)

Germogenova, T.A.

1975-01-01

A review is made of methods of solving marginal problems of multi-group systems of equations of neutron and γ radiation transfer. The first stage of the solution - the quantification of the basic task, is determined by the qualitative behaviour of the solution - is the nature of its performance and asymptotics. In the second stage - solution of the approximating system, various modifications of the iterative method are as a rule used. A description is given of the features of the major Soviet complexes of programmes (ROZ and RADUGA) for the solution of multi-group systems of transfer equations and some methodological research findings are presented. (author)

Refinement of the Korteweg–de Vries equation from the Fermi–Pasta–Ulam model

Energy Technology Data Exchange (ETDEWEB)

Kudryashov, Nikolay A., E-mail: nakudr@gmail.com

2015-10-23

We study a generalization of the Korteweg–de Vries equation obtained from the Fermi–Pasta–Ulam problem. We get the fifth-order nonlinear evolution equation for description of perturbations in the mass chain. Using the Painlevé test, we analyze this equation and show that it does not pass the Painlevé test in the general case. However, the necessary condition for existence of the meromorphic solution is carried out and some exact solutions can be found. We present a new approach to look for traveling wave solutions of the generalization of the Korteweg–de Vries equation. Solitary wave and elliptic solutions of the equation are found and discussed, compared to the Korteweg–de Vries soliton. - Highlights: • The Painlevé test for studying of the generalized Korteweg–de Vries equation is used. • It is shown the generalized Korteweg–de Vries of the fifth order equation does not pass the Painlevé test. • The approach for finding exact solution of nonlinear equations is presented. • Solitary wave and elliptic solutions of the equation are found.

Scaled equation of state parameters for gases in the critical region

Science.gov (United States)

Sengers, J. M. H. L.; Greer, W. L.; Sengers, J. V.

1976-01-01

In the light of recent theoretical developments, the paper presents an accurate characterization of anomalous thermodynamic behavior of xenon, helium 4, helium 3, carbon dioxide, steam and oxygen in the critical region. This behavior is associated with long range fluctuations in the system and the physical properties depend primarily on a single variable, namely, the correlation length. A description of the thermodynamic behavior of fluids in terms of scaling laws is formulated, and the two successfully used scaled equations of state (NBS equation and Linear Model parametric equation) are compared. Methods for fitting both equations to experimental equation of state data are developed and formulated, and the optimum fit for each of the two scaled equations of the above gases are presented and the results are compared. By extending the experimental data for the above one-component fluids to partially miscible binary liquids, superfluid liquid helium, ferromagnets and solids exhibiting order-disorder transitions, the principle of universality is concluded. Finally by using this principle, the critical regions for nine additional fluids are described.

Notes on Two Newly Naturalized Plants in Taiwan: Evolvulus nummularius (L. L. (Convolvulaceae and Acalypha aristata Kunth (Euphorbiaceae

Directory of Open Access Journals (Sweden)

Shih-Huei Chen

2009-09-01

Full Text Available Evolvulus nummularius (L. L. and Acalypha aristata Kunth, originally native to tropical America, were recently found naturalized in disturbed sites of Taiwan. The present study gives the taxonomic description and line drawings of the two species. In addition, their distributions and notes on ecology are provided.

A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Qiang Ru

2013-01-01

Full Text Available We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.

Description of the electrodynamics of a gas by molecular-electromagnetic correlation functions

International Nuclear Information System (INIS)

Coulter, C.A.; Howgate, D.W.

1985-01-01

Starting from basic principles, we develop a description of the electromagnetic interactions of a molecular gas in terms of a set of correlation functions which we call the molecular-electromagnetic correlation functions (MECF's). First we use the energy eigenfunctions for an isolated molecule of the species of interest to define a set of molecular creation and annihilation operators. We then derive a closed set of operator equations for these molecular creation and annihilation operators and the electromagnetic vector potential. Explicit definitions of the lowest-order MECF's are given in terms of these operators, and it is shown how the operator equations which have been obtained can be used to derive equations of motion for the MECF's. Finally, we illustrate the use of the MECF's in describing physical properties of the molecular gas and the electromagnetic field. Brief indications are given of the application of the MECF formulation to the semiclassical approximation and to the description of quantum emission of radiation, topics which are treated in greater detail in subsequent papers. The basic MECF formulation described here contains three rather mild approximations: (1) Atomic nuclei are treated as elementary particles; (2) nuclei and electrons are treated nonrelativistically; and (3) the effect of molecular collisions with the container walls on the internal molecular state is neglected. Consequently, the physical description contained in the formulation is rather complete; and the MECF results can be used both to provide a sound basis for some aspects of the usual heuristic models, and to ascertain the ways in which those models are incomplete

Iterative channel decoding of FEC-based multiple-description codes.

Science.gov (United States)

Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B

2012-03-01

Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.

A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

Directory of Open Access Journals (Sweden)

Gisle M. Mophou

2010-01-01

Full Text Available We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t+Ax(t=f(t,xt, t∈[0,T], x(t=ϕ(t, t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(tt≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.

Entropy and convexity for nonlinear partial differential equations.

Science.gov (United States)

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Calculus for cognitive scientists partial differential equation models

CERN Document Server

Peterson, James K

2016-01-01

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics.  A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

Non-Linear Transmission Line (NLTL) Microwave Source Lecture Notes the United States Particle Accelerator School

Energy Technology Data Exchange (ETDEWEB)

Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory

2012-06-26

We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.

Integral equations for composite-particle scattering taking the Pauli principle into account

International Nuclear Information System (INIS)

Kukulin, V.I.; Neudatchin, V.G.; Pomerantsev, V.N.

1978-01-01

An approximate description of a system of three composite particles in terms of the Saito (Prog. Theor. Phys.; 41:705 (1969)) orthogonality condition model is proposed. The orthogonalising pseudopotential technique is used to derive a modified set of Fadde'ev equations where the two- and three-body exchanges due to the Pauli principle are included by orthogonalising to two-and three-body forbidden states. The scope of applicability of and the method for solving the derived equations are discussed briefly. (author)

Simplified equations for transient heat transfer problems at low Fourier numbers

DEFF Research Database (Denmark)

Christensen, Martin Gram; Adler-Nissen, Jens

2015-01-01

and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...

Dynamics and local boundary properties of the dawn-side magnetopause under conditions observed by Equator-S

Directory of Open Access Journals (Sweden)

M. W. Dunlop

Full Text Available Magnetic field measurements, taken by the magnetometer experiment (MAM on board the German Equator-S spacecraft, have been used to identify and categorise 131 crossings of the dawn-side magnetopause at low latitude, providing unusual, long duration coverage of the adjacent magnetospheric regions and near magnetosheath. The crossings occurred on 31 orbits, providing unbiased coverage over the full range of local magnetic shear from 06:00 to 10:40 LT. Apogee extent places the spacecraft in conditions associated with intermediate, rather than low, solar wind dynamic pressure, as it processes into the flank region. The apogee of the spacecraft remains close to the magnetopause for mean solar wind pressure. The occurrence of the magnetopause encounters are summarised and are found to compare well with predicted boundary location, where solar wind conditions are known. Most scale with solar wind pressure. Magnetopause shape is also documented and we find that the magnetopause orientation is consistently sunward of a model boundary and is not accounted for by IMF or local magnetic shear conditions. A number of well-established crossings, particularly those at high magnetic shear, or exhibiting unusually high-pressure states, were observed and have been analysed for their boundary characteristics and some details of their boundary and near magnetosheath properties are discussed. Of particular note are the occurrence of mirror-like signatures in the adjacent magnetosheath during a significant fraction of the encounters and a high number of multiple crossings over a long time period. The latter is facilitated by the spacecraft orbit which is designed to remain in the near magnetosheath for average solar wind pressure. For most encounters, a well-ordered, tangential (draped magnetosheath field is observed and there is little evidence of large deviations in local boundary orientations. Two passes corresponding to close conjunctions of the Geotail spacecraft

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

Integral-equation formulation for drift eigenmodes in cylindrically symmetric systems

International Nuclear Information System (INIS)

Linsker, R.

1980-12-01

A method for solving the integral eigenmode equation for drift waves in cylindrical (or slab) geometry is presented. A leading-order kinematic effect that has been noted in the past, but incorrectly ignored in recent integral-equation calculations, is incorporated. The present method also allows electrons to be treated with a physical mass ratio (unlike earlier work that is restricted to artificially small m/sub i//m/sub e/ owing to resolution limitations). Results for the universal mode and for the ion-temperature-gradient driven mode are presented. The kinematic effect qualitatively changes the spectrum of the ion mode, and a new second region of instability for k/sub perpendicular to/rho/sub i/greater than or equal to 1 is found

Equation of state description of the dark energy transition between quintessence and phantom regimes

International Nuclear Information System (INIS)

Stefancic, Hrvoje

2006-01-01

The dark energy crossing of the cosmological constant boundary (the transition between the quintessence and phantom regimes) is described in terms of the implicitly defined dark energy equation of state. The generalizations of the models explicitly constructed to exhibit the crossing provide the insight into the cancellation mechanism which makes the transition possible

Averaged description of 3D MHD equilibrium

International Nuclear Information System (INIS)

Medvedev, S.Yu.; Drozdov, V.V.; Ivanov, A.A.; Martynov, A.A.; Pashekhonov, Yu.Yu.; Mikhailov, M.I.

2001-01-01

A general approach by S.A.Galkin et al. in 1991 to 2D description of MHD equilibrium and stability in 3D systems was proposed. The method requires a background 3D equilibrium with nested flux surfaces to generate the metric of a Riemannian space in which the background equilibrium is described by the 2D equation of Grad-Shafranov type. The equation can be solved then varying plasma profiles and shape to get approximate 3D equilibria. In the framework of the method both planar axis conventional stellarators and configurations with spatial magnetic axis can be studied. In the present report the formulation and numerical realization of the equilibrium problem for stellarators with planar axis is reviewed. The input background equilibria with nested flux surfaces are taken from vacuum magnetic field approximately described by analytic scalar potential

The Schroedinger and Dirac free particle equations without quantum mechanics

International Nuclear Information System (INIS)

Ord, G.N.

1996-01-01

Einstein close-quote s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schroedinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. copyright 1996 Academic Press, Inc

How neutron stars constrain the nuclear equation of state

Directory of Open Access Journals (Sweden)

Hell Thomas

2014-03-01

Full Text Available Recent neutron star observations set new constraints for the equation of state of baryonic matter. A chiral effective field theory approach is used for the description of neutron-dominated nuclear matter present in the outer core of neutron stars. Possible hybrid stars with quark matter in the inner core are discussed using a three-flavor Nambu–Jona-Lasinio model.

1. On note taking.

Science.gov (United States)

Plaut, Alfred B J

2005-02-01

In this paper the author explores the theoretical and technical issues relating to taking notes of analytic sessions, using an introspective approach. The paper discusses the lack of a consistent approach to note taking amongst analysts and sets out to demonstrate that systematic note taking can be helpful to the analyst. The author describes his discovery that an initial phase where as much data was recorded as possible did not prove to be reliably helpful in clinical work and initially actively interfered with recall in subsequent sessions. The impact of the nature of the analytic session itself and the focus of the analyst's interest on recall is discussed. The author then describes how he modified his note taking technique to classify information from sessions into four categories which enabled the analyst to select which information to record in notes. The characteristics of memory and its constructive nature are discussed in relation to the problems that arise in making accurate notes of analytic sessions.

What happens when patients can see their doctors' note? - the Open Notes movement

OpenAIRE

Mende, Susan

2017-01-01

Introduction:  The Open Notes movement represents a culture change, enabling patients’ access to their providers’ notes, thereby increasing transparency and patient engagement.Policy context, objective and highlights:  OpenNotes involves allowing patients on-line or hard copy access to their providers’ notes. The one-year initial pilot began in 2010 with twenty thousand patients and one hundred primary care physicians at three medical centers in the United States.  The pilot’s evaluation foun...

Mathematical description of tooth flank surface of globoidal worm gear with straight axial tooth profile

Science.gov (United States)

Połowniak, Piotr; Sobolak, Mariusz

2017-12-01

In this article, a mathematical description of tooth flank surface of the globoidal worm and worm wheel generated by the hourglass worm hob with straight tooth axial profile is presented. The kinematic system of globoidal worm gear is shown. The equation of globoid helix and tooth axial profile of worm is derived to determine worm tooth surface. Based on the equation of meshing the contact lines are obtained. The mathematical description of globoidal worm wheel tooth flank is performed on the basis of contact lines and generating the tooth side by the extreme cutting edge of worm hob. The presented mathematical model of tooth flank of TA worm and worm wheel can be used e.g. to analyse the contact pattern of the gear.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

Science.gov (United States)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Poisson's theorem and integrals of KdV equation

International Nuclear Information System (INIS)

Tasso, H.

1978-01-01

Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)

"E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

OpenAIRE

Gerbracht, Eberhard H. -A.

2008-01-01

In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differential equations which is used to model the analog circuit. For nonlinear circuits and their corresponding nonlinear differential equations, we show how to employ computer algebra tools implemented in Maple, which are based on diff...

A concise course on stochastic partial differential equations

CERN Document Server

Prévôt, Claudia

2007-01-01

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

Receptor binding kinetics equations: Derivation using the Laplace transform method.

Science.gov (United States)

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time

Maximal stochastic transport in the Lorenz equations

Energy Technology Data Exchange (ETDEWEB)

Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

2016-01-08

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

Note Taking and Recall

Science.gov (United States)

Fisher, Judith L.; Harris, Mary B.

1974-01-01

To study the effect of note taking and opportunity for review on subsequent recall, 88 college students were randomly assigned to five treatment groups utilizing different note taking and review combinations. No treatment effects were found, although quality of notes was positively correlated with free recall an multiple-choice measures.…

The Dirac equation

International Nuclear Information System (INIS)

Thaller, B.

1992-01-01

This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics

Sewall Wright's equation Deltaq=(q(1-q) partial differentialw/ partial differentialq)/2w.

Science.gov (United States)

Edwards, A W

2000-02-01

An equation of Sewall Wright's expresses the change in the frequency of an allele under selection at a multiallelic locus as a function of the gradient of the mean fitness "surface" in the direction in which the relative proportions of the other alleles do not change. An attempt to derive this equation using conventional vector calculus shows that this description leads to a different equation and that the purported gradient in Wright's equation is not a gradient of the mean fitness surface except in the diallelic case, where the two equations are the same. It is further shown that if Fisher's angular transformation is applied to the diallelic case the genic variance is exactly equal to one-eighth of the square of the gradient of the mean fitness with respect to the transformed gene frequency. Copyright 2000 Academic Press.

Towards a Unified Quark-Hadron-Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions

Directory of Open Access Journals (Sweden)

Niels-Uwe F. Bastian

2018-05-01

Full Text Available We outline an approach to a unified equation of state for quark-hadron matter on the basis of a Φ − derivable approach to the generalized Beth-Uhlenbeck equation of state for a cluster decomposition of thermodynamic quantities like the density. To this end we summarize the cluster virial expansion for nuclear matter and demonstrate the equivalence of the Green’s function approach and the Φ − derivable formulation. As an example, the formation and dissociation of deuterons in nuclear matter is discussed. We formulate the cluster Φ − derivable approach to quark-hadron matter which allows to take into account the specifics of chiral symmetry restoration and deconfinement in triggering the Mott-dissociation of hadrons. This approach unifies the description of a strongly coupled quark-gluon plasma with that of a medium-modified hadron resonance gas description which are contained as limiting cases. The developed formalism shall replace the common two-phase approach to the description of the deconfinement and chiral phase transition that requires a phase transition construction between separately developed equations of state for hadronic and quark matter phases. Applications to the phenomenology of heavy-ion collisions and astrophysics are outlined.

Modified Van der Waals equation and law of corresponding states

Science.gov (United States)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

Notes in Colombian Herpetology, II Notes in Colombian Herpetology, II

Directory of Open Access Journals (Sweden)

Dunn Emmett Reid

1944-03-01

Full Text Available The Lizard Genus Echinosaura (Teiidae in Colombia / Notes on the habits of the Tadpole-Carrying Frog Hyloxalus granuliventris / A New Marsupian Frog (Gastrotheca from Colombia The Lizard Genus Echinosaura (Teiidae in Colombia / Notes on the habits of the Tadpole-Carrying Frog Hyloxalus granuliventris / A New Marsupian Frog (Gastrotheca from Colombia.

A note on exponential convergence of neural networks with unbounded distributed delays

Energy Technology Data Exchange (ETDEWEB)

Chu Tianguang [Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)]. E-mail: chutg@pku.edu.cn; Yang Haifeng [Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)

2007-12-15

This note examines issues concerning global exponential convergence of neural networks with unbounded distributed delays. Sufficient conditions are derived by exploiting exponentially fading memory property of delay kernel functions. The method is based on comparison principle of delay differential equations and does not need the construction of any Lyapunov functionals. It is simple yet effective in deriving less conservative exponential convergence conditions and more detailed componentwise decay estimates. The results of this note and [Chu T. An exponential convergence estimate for analog neural networks with delay. Phys Lett A 2001;283:113-8] suggest a class of neural networks whose globally exponentially convergent dynamics is completely insensitive to a wide range of time delays from arbitrary bounded discrete type to certain unbounded distributed type. This is of practical interest in designing fast and reliable neural circuits. Finally, an open question is raised on the nature of delay kernels for attaining exponential convergence in an unbounded distributed delayed neural network.

A note on exponential convergence of neural networks with unbounded distributed delays

International Nuclear Information System (INIS)

Chu Tianguang; Yang Haifeng

2007-01-01

This note examines issues concerning global exponential convergence of neural networks with unbounded distributed delays. Sufficient conditions are derived by exploiting exponentially fading memory property of delay kernel functions. The method is based on comparison principle of delay differential equations and does not need the construction of any Lyapunov functionals. It is simple yet effective in deriving less conservative exponential convergence conditions and more detailed componentwise decay estimates. The results of this note and [Chu T. An exponential convergence estimate for analog neural networks with delay. Phys Lett A 2001;283:113-8] suggest a class of neural networks whose globally exponentially convergent dynamics is completely insensitive to a wide range of time delays from arbitrary bounded discrete type to certain unbounded distributed type. This is of practical interest in designing fast and reliable neural circuits. Finally, an open question is raised on the nature of delay kernels for attaining exponential convergence in an unbounded distributed delayed neural network

POSSOL, 2-D Poisson Equation Solver for Nonuniform Grid

International Nuclear Information System (INIS)

Orvis, W.J.

1988-01-01

1 - Description of program or function: POSSOL is a two-dimensional Poisson equation solver for problems with arbitrary non-uniform gridding in Cartesian coordinates. It is an adaptation of the uniform grid PWSCRT routine developed by Schwarztrauber and Sweet at the National Center for Atmospheric Research (NCAR). 2 - Method of solution: POSSOL will solve the Helmholtz equation on an arbitrary, non-uniform grid on a rectangular domain allowing only one type of boundary condition on any one side. It can also be used to handle more than one type of boundary condition on a side by means of a capacitance matrix technique. There are three types of boundary conditions that can be applied: fixed, derivative, or periodic

Note Taking for Geography Students.

Science.gov (United States)

Kneale, Pauline E.

1998-01-01

Addresses geography students' questions about why, when, and how to take notes. Outlines a step-by-step process for taking notes from written sources and from class lectures. Discusses what types of notes are appropriate for various types of sources. Suggests some ideas for making notes useful for individual learning styles. (DSK)

On that Note...

Science.gov (United States)

Stein, Harry

1988-01-01

Provides suggestions for note-taking from books, lectures, visual presentations, and laboratory experiments to enhance student knowledge, memory, and length of attention span during instruction. Describes topical and structural outlines, visual mapping, charting, three-column note-taking, and concept mapping. Benefits and application of…

Filtering of sound from the Navier-Stokes equations. [An approximation for describing thermal convection in a compressible fluid

Energy Technology Data Exchange (ETDEWEB)

Paolucci, S.

1982-12-01

An approximation leading to anelastic equations capable of describing thermal convection in a compressible fluid is given. These equations are more general than the Oberbeck-Boussinesq equations and different than the standard anelastic equations in that they can be used for the computation of convection in a fluid with large density gradients present. We show that the equations do not contain acoustic waves, while at the same time they can still describe the propagation of internal waves. Throughout we show that the filtering of acoustic waves, within the limits of the approximation, does not appreciably alter the description of the physics.

Some Notes and Critiques of Selected Lexicographic Texts in Bikol

Directory of Open Access Journals (Sweden)

Louward Allen Zubiri

2014-12-01

Full Text Available This study revolves around notes and critiques of Bikol lexicography. Based on a selection of six dictionaries, the structure and diachronic development of Bikol lexicography were analyzed. Half of the selected dictionaries were authored in full or part by Malcolm Mintz, a renowned Bikol expert. These enabled a linear analysis of changes in lexicography that have occurred within the span of four decades. The dictionaries studied include the earliest and most influential Bikol dictionary of Lisboa (1865. The study presents a preliminary description of lexicographic work done in Bikol and traces the shift in the paradigm of dictionary making from the Spanish era to the present.

Quantization of Equations of Motion

Directory of Open Access Journals (Sweden)

D. Kochan

2007-01-01

Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail. 

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

International Nuclear Information System (INIS)

EL Safadi, M.

2007-03-01

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT DOI: http://dx.doi.org/10.22342/jme.7.1.2814.19-30

An Efficient Hierarchical Multiscale Finite Element Method for Stokes Equations in Slowly Varying Media

KAUST Repository

Brown, Donald L.; Efendiev, Yalchin; Hoang, Viet Ha

2013-01-01

Direct numerical simulation (DNS) of fluid flow in porous media with many scales is often not feasible, and an effective or homogenized description is more desirable. To construct the homogenized equations, effective properties must be computed

Mathematical description of adsorption and transport of reactive solutes in soil: a review of selected literature

International Nuclear Information System (INIS)

Travis, C.C.

1978-10-01

This report reviews selected literature related to the mathematical description of the transport of reactive solutes through soil. The primary areas of the literature reviewed are (1) mathematical models in current use for description of the adsorption-desorption interaction between the soil solution and the soil matrix and (2) analytic solutions of the differential equations describing the convective-dispersive transport of reactive solutes through soil

Dynamical equations and transport coefficients for the metals at high pulse electromagnetic fields

International Nuclear Information System (INIS)

Volkov, N B; Chingina, E A; Yalovets, A P

2016-01-01

We offer a metal model suitable for the description of fast electrophysical processes in conductors under influence of powerful electronic and laser radiation of femto- and picosecond duration, and also high-voltage electromagnetic pulses with picosecond front and duration less than 1 ns. The obtained dynamic equations for metal in approximation of one quasineutral liquid are in agreement with the equations received by other authors formerly. New wide-range expressions for the electronic conduction in strong electromagnetic fields are obtained and analyzed. (paper)

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.

2014-12-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam

2014-01-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

Numerical integration of the Teukolsky equation in the time domain

International Nuclear Information System (INIS)

Pazos-Avalos, Enrique; Lousto, Carlos O.

2005-01-01

We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code

Analytic, Algebraic and Geometric Aspects of Differential Equations

CERN Document Server

Haraoka, Yoshishige; Michalik, Sławomir

2017-01-01

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of i...

Dark energy cosmology with generalized linear equation of state

International Nuclear Information System (INIS)

Babichev, E; Dokuchaev, V; Eroshenko, Yu

2005-01-01

Dark energy with the usually used equation of state p = wρ, where w const 0 ), where the constants α and ρ 0 are free parameters. This non-homogeneous linear equation of state provides the description of both hydrodynamically stable (α > 0) and unstable (α < 0) fluids. In particular, the considered cosmological model describes the hydrodynamically stable dark (and phantom) energy. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by using phase trajectories analysis. For the dark energy case, some distinctive types of cosmological scenarios are possible: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the big rip and with the anti-big rip. In the framework of a linear equation of state the universe filled with a phantom energy, w < -1, may have either the de Sitter attractor or the big rip

Dose concept of oncological hyperthermia: Heat-equation considering the cell destruction

Directory of Open Access Journals (Sweden)

Szasz A

2006-01-01

Full Text Available We shall assume, of course, that the objective of hyperthermia is to destroy the malignant cells. Destruction definitely needs energy. Description and quality assurance of hyperthermia use the Pennes heat equation to describe the processes. However the energy balance of the Pennes-equation does not contain the hyperthermic cell-destruction energy, which is a mandatory factor of the process. We propose a generalization of the Pennes-equation, inducing the entire energy balance. The new paradigm could be a theoretical basis of the till now empirical dose-construction for oncological hyperthermia. The cell destruction is a non-equilibrium thermodynamical process, described by the equations of chemical reactions. The dynamic behavior (time dependence has to be considered in this approach. We are going to define also a dose concept that can be objectively compared with other oncological methods. We show how such empirical dose as CEM43oC could be based theoretically as well.

Regularity theory for quasilinear elliptic systems and Monge—Ampère equations in two dimensions

CERN Document Server

Schulz, Friedmar

1990-01-01

These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère equations, a theory largely developed by H. Lewy and E. Heinz which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.

Monte Carlo method implementation on IPSC 860 for the resolution of the Boltzmann equation

International Nuclear Information System (INIS)

AloUGES, Francois

1993-01-01

This note deals with the implementation on a massively parallel machine (IPSC-860) of a Monte-Carlo method aiming at resolving the Boltzmann equation. The parallelism of the machine incites to consider a multi-domain approach and poses the problem of the automatic generation of local meshes from a non-structured 3-D global mesh [fr

Description of high-power laser radiation in the paraxial approximation

Energy Technology Data Exchange (ETDEWEB)

Milant' ev, V P; Karnilovich, S P; Shaar, Ya N [Peoples' Friendship University of Russia, Moscow (Russian Federation)

2015-11-30

We consider the feasibility of an adequate description of a laser pulse of arbitrary shape within the framework of the paraxial approximation. In this approximation, using a parabolic equation and an expansion in the small parameter, expressions are obtained for the field of a sufficiently intense laser radiation given in the form of axially symmetric Hermite – Gaussian beams of arbitrary mode and arbitrary polarisation. It is shown that in the case of sufficiently short pulses, corrections to the transverse components of the laser field are the first-order rather than the secondorder quantities in the expansion in the small parameter. The peculiarities of the description of higher-mode Hermite – Gaussian beams are outlined. (light wave transformation)

Properties of coupled-cluster equations originating in excitation sub-algebras

Science.gov (United States)

Kowalski, Karol

2018-03-01

In this paper, we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving the corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending active-space and seniority number concepts to provide an accurate description of electron correlation effects. Moreover, a new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for tough cases defined by the presence of strong static and dynamical correlation effects. We will also explore invariance properties associated with excitation sub-algebras to define a new class of CC approximations referred to in this paper as the sub-algebra-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Towards reproducible descriptions of neuronal network models.

Directory of Open Access Journals (Sweden)

Eilen Nordlie

2009-08-01

Full Text Available Progress in science depends on the effective exchange of ideas among scientists. New ideas can be assessed and criticized in a meaningful manner only if they are formulated precisely. This applies to simulation studies as well as to experiments and theories. But after more than 50 years of neuronal network simulations, we still lack a clear and common understanding of the role of computational models in neuroscience as well as established practices for describing network models in publications. This hinders the critical evaluation of network models as well as their re-use. We analyze here 14 research papers proposing neuronal network models of different complexity and find widely varying approaches to model descriptions, with regard to both the means of description and the ordering and placement of material. We further observe great variation in the graphical representation of networks and the notation used in equations. Based on our observations, we propose a good model description practice, composed of guidelines for the organization of publications, a checklist for model descriptions, templates for tables presenting model structure, and guidelines for diagrams of networks. The main purpose of this good practice is to trigger a debate about the communication of neuronal network models in a manner comprehensible to humans, as opposed to machine-readable model description languages. We believe that the good model description practice proposed here, together with a number of other recent initiatives on data-, model-, and software-sharing, may lead to a deeper and more fruitful exchange of ideas among computational neuroscientists in years to come. We further hope that work on standardized ways of describing--and thinking about--complex neuronal networks will lead the scientific community to a clearer understanding of high-level concepts in network dynamics, and will thus lead to deeper insights into the function of the brain.

Computer models for kinetic equations of magnetically confined plasmas

International Nuclear Information System (INIS)

Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.

1987-01-01

This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method

From BBGKY hierarchy to non-Markovian evolution equations

International Nuclear Information System (INIS)

Gerasimenko, V.I.; Shtyk, V.O.; Zagorodny, A.G.

2009-01-01

The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for the average value of the microscopic phase density is given, and the non-Markovian generalization of the Fokker-Planck collision integral is proposed

VA OpenNotes: exploring the experiences of early patient adopters with access to clinical notes.

Science.gov (United States)

Nazi, Kim M; Turvey, Carolyn L; Klein, Dawn M; Hogan, Timothy P; Woods, Susan S

2015-03-01

To explore the experience of early patient adopters who accessed their clinical notes online using the Blue Button feature of the My HealtheVet portal. A web-based survey of VA patient portal users from June 22 to September 15, 2013. 33.5% of respondents knew that clinical notes could be viewed, and nearly one in four (23.5%) said that they had viewed their notes at least once. The majority of VA Notes users agreed that accessing their notes will help them to do a better job of taking medications as prescribed (80.1%) and be better prepared for clinic visits (88.6%). Nine out of 10 users agreed that use of visit notes will help them understand their conditions better (91.8%), and better remember the plan for their care (91.9%). In contrast, 87% disagreed that VA Notes will make them worry more, and 88.4% disagreed that access to VA Notes will be more confusing than helpful. Users who had either contacted their provider or healthcare team (11.9%) or planned to (13.5%) primarily wanted to learn more about a health issue, medication, or test results (53.7%). Initial assessment of the patient experience within the first 9 months of availability provides evidence that patients both value and benefit from online access to clinical notes. These findings are congruent with OpenNotes study findings on a broader scale. Additional outreach and education is needed to enhance patient awareness. Healthcare professionals should author notes keeping in mind the opportunity patient access presents for enhanced communication. © The Author 2014. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Hamilton-Jacobi equations and brane associated Lagrangians

International Nuclear Information System (INIS)

Baker, L.M.; Fairlie, D.B.

2001-01-01

This article seeks to relate a recent proposal for the association of a covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi formalism for strings and branes. It turns out that since in this special case, the Hamiltonian depends only upon the momenta of the Jacobi fields and not the fields themselves, it is the same as a Lagrangian, subject to a constancy constraint. We find that the associated Lagrangians for strings or branes have a covariant description in terms of the square root of the same Lagrangian. If the Hamilton-Jacobi function is zero, rather than a constant, then it is in in one dimension lower, reminiscent of the 'holographic' idea. In the second part of the paper, we discuss properties of these Lagrangians, which lead to what we have called 'Universal Field Equations', characteristic of covariant equations of motion

Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

International Nuclear Information System (INIS)

Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

2001-01-01

The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

Semi-classical analysis for nonlinear Schrödinger equations

CERN Document Server

Carles, Remi

2008-01-01

These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger e

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

Science.gov (United States)

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Lagrangian formulation and symmetrical description of liquid dynamics.

Science.gov (United States)

Trachenko, K

2017-12-01

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Lagrangian fluid description with simple applications in compressible plasma and gas dynamics

International Nuclear Information System (INIS)

Schamel, Hans

2004-01-01

The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum--as seen in laboratory experiments--is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one

Lagrangian fluid description with simple applications in compressible plasma and gas dynamics

Science.gov (United States)

Schamel, Hans

2004-03-01

The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

Science.gov (United States)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

An alternative to the breeder's and Lande's equations.

Science.gov (United States)

Houchmandzadeh, Bahram

2014-01-10

The breeder's equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) - E(Z0) to the selection differential S = E(ZW) - E(Z0) through a simple proportionality relation R = h(2)S, where the heritability coefficient h(2) is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R' = j(2)S' can be derived, regardless of the parental genotype distribution. Here R' = E(Z1) - μ and S' = E(ZW) - μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j(2) is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande's equation Δ(z) = GP(-1)S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.

Grouping Notes Through NodesThe Functions of Post-It™ Notes in Design Team Cognition

DEFF Research Database (Denmark)

Dove, Graham; Abildgaard, Sille Julie; Biskjaer, Michael Mose

The Post-It™ note is a frequently used, and yet seldom studied, design material. We investigate the functions Post-It™ notes serve when providing cognitive support for creative design team practice. Our investigation considers the ways in which Post-It™ notes function as design externalisations......, both individually and when grouped, and their role in categorisation in semantic long-term memory. To do this, we adopt a multimodal analytical approach focusing on interaction between humans, and between humans and artefacts, alongside language. We discuss in detail examples of four different...... externalisation functions served by Post-It™ notes, and show how these functions are present in complex overlapping combinations rather than being discrete. We then show how the temporal development of Post-It™ note interactions supports categorisation qualities of semantic long-term memory....

A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Scholle, M., E-mail: markus.scholle@hs-heilbronn.de; Marner, F., E-mail: florian.marner@hs-heilbronn.de

2016-09-23

In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.

A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations

International Nuclear Information System (INIS)

Scholle, M.; Marner, F.

2016-01-01

In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

Energy Technology Data Exchange (ETDEWEB)

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

2016-01-15

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

International Nuclear Information System (INIS)

Kalayci, Ulku; Ozer, Umit

2016-01-01

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r"2 of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Essential equivalence of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and steepest-entropy-ascent models of dissipation for nonequilibrium thermodynamics.

Science.gov (United States)

Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo

2015-04-01

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.

Particle number fluctuations for the van der Waals equation of state

International Nuclear Information System (INIS)

Vovchenko, V; Anchishkin, D V; Gorenstein, M I

2015-01-01

The van der Waals (VDW) equation of state describes a thermal equilibrium in system of particles, where both repulsive and attractive interactions between them are included. This equation predicts the existence of the first order liquid–gas phase transition and the critical point. The standard form of the VDW equation is given by the pressure function in a canonical ensemble (CE) with a fixed number of particles. In this paper the VDW equation is derived within the grand canonical ensemble (GCE) formulation. We argue that this procedure can be useful for new physical applications, in particular, the fluctuations of the number of particles, which are absent in the CE, can be studied in the GCE. For the VDW equation of state in the GCE the particle number fluctuations are calculated for the whole phase diagram, both outside and inside the liquid–gas mixed phase region. It is shown that the scaled variance of these fluctuations remains finite within the mixed phase and goes to infinity at the critical point. The GCE formulation of the VDW equation of state can also be an important step for its application in the statistical description of hadronic systems, where numbers of different particle species are usually not conserved. (paper)

Nuclear structure information studied through Dirac equation with deformed mean fields

International Nuclear Information System (INIS)

Dudek, J.

2000-01-01

Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)

Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence

Science.gov (United States)

Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen

2018-04-01

The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.

The Dirichlet problem of a conformable advection-diffusion equation

Directory of Open Access Journals (Sweden)

Avci Derya

2017-01-01

Full Text Available The fractional advection-diffusion equations are obtained from a fractional power law for the matter flux. Diffusion processes in special types of porous media which has fractal geometry can be modelled accurately by using these equations. However, the existing nonlocal fractional derivatives seem complicated and also lose some basic properties satisfied by usual derivatives. For these reasons, local fractional calculus has recently been emerged to simplify the complexities of fractional models defined by nonlocal fractional operators. In this work, the conformable, a local, well-behaved and limit-based definition, is used to obtain a local generalized form of advection-diffusion equation. In addition, this study is devoted to give a local generalized description to the combination of diffusive flux governed by Fick’s law and the advection flux associated with the velocity field. As a result, the constitutive conformable advection-diffusion equation can be easily achieved. A Dirichlet problem for conformable advection-diffusion equation is derived by applying fractional Laplace transform with respect to time t and finite sin-Fourier transform with respect to spatial coordinate x. Two illustrative examples are presented to show the behaviours of this new local generalized model. The dependence of the solution on the fractional order of conformable derivative and the changing values of problem parameters are validated using graphics held by MATLcodes.

SAFETY NOTES

CERN Document Server

TIS Secretariat

2001-01-01

Please note that the revisions of safety notes no 3 (NS 3 Rev. 2) and no 24 (NS 24 REV.) entitled respectively 'FIRE PREVENTION FOR ENCLOSED SPACES IN LARGE HALLS' and 'REMOVING UNBURIED ELV AND LVA ELECTRIC CONDUITS' are available on the web at the following urls: http://edmsoraweb.cern.ch:8001/cedar/doc.download?document_id=322811&version=1&filename=version_francaise.pdf http://edmsoraweb.cern.ch:8001/cedar/doc.download?document_id=322861&version=2&filename=version_francaise.pdf Paper copies can also be obtained from the TIS Divisional Secretariat, email tis.secretariat@cern.ch

Single-order-parameter description of glass-forming liquids

DEFF Research Database (Denmark)

Ellegaard, Niels Langager; Christensen, Tage Emil; Christiansen, Peder Voetmann

2007-01-01

Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear...... dynamic Prigogine-Defay ratio" with the property that if this ratio is unity at one frequency, then it is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter which may be nonexponential...

Existence and Uniqueness of Solutions to the Stochastic Porous Media Equations of Saturated Flows

International Nuclear Information System (INIS)

Ciotir, Ioana

2010-01-01

This paper proves the existence and uniqueness of nonnegative solutions for the stochastic porous media equations with multiplicative noise, infinite jump and discontinuous diffusivity function relevant in description of saturation processes in underground water infiltration in a bounded domain of R 3 .

Multiple soliton production and the Korteweg-de Vries equation.

Science.gov (United States)

Hershkowitz, N.; Romesser, T.; Montgomery, D.

1972-01-01

Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

On the Lippmann--Schwinger equation for atom--diatom collisions: A rotating frame treatment

International Nuclear Information System (INIS)

Kouri, D.J.; Heil, T.G.; Shimoni, Y.

1976-01-01

The use of a rotating frame description of molecular collisions is reconsidered within the framework of the Lippmann--Schwinger equation for the transition or T operator. The present approach explicitly displays the proper boundary conditions which apply to descriptions of such collisions in the rotating frame whose Z axis follows the scattering vector. The resulting body frame equations are shown to lead naturally to the introduction of ''body frame Bessel and Hankel functions,'' J/subJ//subj//sup lambda//sup lambda//sup prime/ and H/subJ//subj//sup lambda//sup lambda//sup prime/ (BFBF), which are solutions of the unperturbed Hamiltonian for the collision transformed to the rotating frame. It is found that the BFBF can be defined in several ways differing by phase factors that affect their asymptotic form. Two particular choices are examined, one of which leads to a simple asymptotic form of the wavefunction, and the other leads to a somewhat more complicated form. Both are shown to yield the j/subz/-conserving coupled states equations of McGuire and Kouri but slightly different approximations are required in the two cases. The implication of these results as to the accuracy of the j/subz/CCS method are discussed

Exact analytic solutions for a global equation of plant cell growth.

Science.gov (United States)

Pietruszka, Mariusz

2010-05-21

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Quantum theory as the most robust description of reproducible experiments

International Nuclear Information System (INIS)

De Raedt, Hans; Katsnelson, Mikhail I.; Michielsen, Kristel

2014-01-01

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out. - Highlights: • It is shown that logical inference, that is, inductive reasoning, provides a rational explanation for the success of quantum theory. • The Schrödinger equation is obtained through logical inference applied to robust experiments. • The singlet and triplet states follow from logical inference applied to the Einstein-Podolsky-Rosen-Bohm experiment. • Robustness also leads to the quantum theoretical description of the Stern-Gerlach experiment

Quantum theory as the most robust description of reproducible experiments

Energy Technology Data Exchange (ETDEWEB)

De Raedt, Hans, E-mail: h.a.de.raedt@rug.nl [Department of Applied Physics, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747AG Groningen (Netherlands); Katsnelson, Mikhail I., E-mail: M.Katsnelson@science.ru.nl [Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525AJ Nijmegen (Netherlands); Michielsen, Kristel, E-mail: k.michielsen@fz-juelich.de [Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich (Germany); RWTH Aachen University, D-52056 Aachen (Germany)

2014-08-15

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out. - Highlights: • It is shown that logical inference, that is, inductive reasoning, provides a rational explanation for the success of quantum theory. • The Schrödinger equation is obtained through logical inference applied to robust experiments. • The singlet and triplet states follow from logical inference applied to the Einstein-Podolsky-Rosen-Bohm experiment. • Robustness also leads to the quantum theoretical description of the Stern-Gerlach experiment.

Semiconductor color-center structure and excitation spectra: Equation-of-motion coupled-cluster description of vacancy and transition-metal defect photoluminescence

Science.gov (United States)

Lutz, Jesse J.; Duan, Xiaofeng F.; Burggraf, Larry W.

2018-03-01

Valence excitation spectra are computed for deep-center silicon-vacancy defects in 3C, 4H, and 6H silicon carbide (SiC), and comparisons are made with literature photoluminescence measurements. Optimizations of nuclear geometries surrounding the defect centers are performed within a Gaussian basis-set framework using many-body perturbation theory or density functional theory (DFT) methods, with computational expenses minimized by a QM/MM technique called SIMOMM. Vertical excitation energies are subsequently obtained by applying excitation-energy, electron-attached, and ionized equation-of-motion coupled-cluster (EOMCC) methods, where appropriate, as well as time-dependent (TD) DFT, to small models including only a few atoms adjacent to the defect center. We consider the relative quality of various EOMCC and TD-DFT methods for (i) energy-ordering potential ground states differing incrementally in charge and multiplicity, (ii) accurately reproducing experimentally measured photoluminescence peaks, and (iii) energy-ordering defects of different types occurring within a given polytype. The extensibility of this approach to transition-metal defects is also tested by applying it to silicon-substituted chromium defects in SiC and comparing with measurements. It is demonstrated that, when used in conjunction with SIMOMM-optimized geometries, EOMCC-based methods can provide a reliable prediction of the ground-state charge and multiplicity, while also giving a quantitative description of the photoluminescence spectra, accurate to within 0.1 eV of measurement for all cases considered.

Approaches to the mathematical description of NPP operational safety management and oversight

International Nuclear Information System (INIS)

Bilej, D.V.; Berzhanskij, S.V.

2014-01-01

The paper presents analysis of features related to NPP operational safety management and oversight. According to analysis results, approaches are proposed to perform mathematical description of specific processes and to develop a scale for management to the current safety level as regards NPP power generation. Proposed approaches are making experimental equations and process approach of ISO-9001 quality system

Shock formation in small-data solutions to 3D quasilinear wave equations

CERN Document Server

Speck, Jared

2016-01-01

In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he prov...

Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

International Nuclear Information System (INIS)

Eliezer, S.; Falquina, R.; Minguez, E.

1994-01-01

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

Microscopical description of isovector collective Osup(+) states in atomic nuclei

International Nuclear Information System (INIS)

Chekanov, N.A.

1983-01-01

A microscopical consistent description of isobar-analogue states and isovector monopole giant resonances is given in framework of the random-phase theory. The necessary one-particle basis, including the continuous spectrum, is determined by solution of the Hartree-Fock equations with the effective Skyrme-type interaction. An important feature of such a description is an automatical fulfilment of the consistency conditions relating the shell potential, nuclear density and the residual interaction. Effects due to Coulomb interaction in nuclei are investigated, such as the Coulomb shift energies, isospin admixtures to the ground state of the parent nucleus. Transition densities for the analogue states are obtained. Numerical calculations have been performed in the coordinate space for a number of neutron-rich nuclei

Employers' views on the fit note.

Science.gov (United States)

Kotze, E

2014-12-01

The fit note replaced the sick note in 2010. The statement of fitness for work (fit note) is expected to benefit the British economy by helping more people stay in work and prevent long-term sickness absence. Understanding and responding to employers' views on the fit note is key, in order for this goal to be achieved. To explore employers' views on the fit note. A qualitative study was undertaken and face-to-face interviews were conducted with participants representing employers from a variety of industries. There were 21 participants who were mainly human resources officers and line managers. Employers welcomed the introduction of the fit note and felt that it was an improvement on the sick note. The majority of employers felt the fit note had the potential to promote an earlier return to work, if used properly. The main problems reported were the completion of the fit notes and quality of advice received from general practitioners. Employers felt that the most helpful advice came from fit notes with information on the functional effects of the medical condition. Some employers found return to work decisions problematic. The fit note has the potential to promote an earlier return to work. In order for the fit note to achieve its aim, further understanding of the difficulties employers are having when making return to work decisions is important, in order to develop guidance to enable them to provide the practical support employees need to return to work sooner. © The Author 2014. Published by Oxford University Press on behalf of the Society of Occupational Medicine. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

Science.gov (United States)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

Finite element and discontinuous Galerkin methods for transient wave equations

CERN Document Server

Cohen, Gary

2017-01-01

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

International Nuclear Information System (INIS)

Donker, H.C.; Katsnelson, M.I.; De Raedt, H.; Michielsen, K.

2016-01-01

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.

Development of a set of benchmark problems to verify numerical methods for solving burnup equations

International Nuclear Information System (INIS)

Lago, Daniel; Rahnema, Farzad

2017-01-01

Highlights: • Description transmutation chain benchmark problems. • Problems for validating numerical methods for solving burnup equations. • Analytical solutions for the burnup equations. • Numerical solutions for the burnup equations. - Abstract: A comprehensive set of transmutation chain benchmark problems for numerically validating methods for solving burnup equations was created. These benchmark problems were designed to challenge both traditional and modern numerical methods used to solve the complex set of ordinary differential equations used for tracking the change in nuclide concentrations over time due to nuclear phenomena. Given the development of most burnup solvers is done for the purpose of coupling with an established transport solution method, these problems provide a useful resource in testing and validating the burnup equation solver before coupling for use in a lattice or core depletion code. All the relevant parameters for each benchmark problem are described. Results are also provided in the form of reference solutions generated by the Mathematica tool, as well as additional numerical results from MATLAB.

EndNote 7.0

Directory of Open Access Journals (Sweden)

Eapen Bell

2006-01-01

Full Text Available EndNote is a useful software for online literature search and efficient bibliography management. It helps to format the bibliography according to the citation style of each journal. EndNote stores references in a library file, which can be shared with others. It can connect to online resources like PubMed and retrieve search results as per the search criteria. It can also effortlessly integrate with popular word processors like MS Word. The Indian Journal of Dermatology, Venereology and Leprology website has a provision to import references to EndNote.

The impact of note taking style and note availability at retrieval on mock jurors' recall and recognition of trial information.

Science.gov (United States)

Thorley, Craig; Baxter, Rebecca E; Lorek, Joanna

2016-01-01

Jurors forget critical trial information and what they do recall can be inaccurate. Jurors' recall of trial information can be enhanced by permitting them to take notes during a trial onto blank sheets of paper (henceforth called freestyle note taking). A recent innovation is the trial-ordered-notebook (TON) for jurors, which is a notebook containing headings outlining the trial proceedings and which has space beneath each heading for notes. In a direct comparison, TON note takers recalled more trial information than freestyle note takers. This study investigated whether or not note taking improves recall as a result of enhanced encoding or as a result of note access at retrieval. To assess this, mock jurors watched and freely recalled a trial video with one-fifth taking no notes, two-fifths taking freestyle notes and two-fifths using TONs. During retrieval, half of the freestyle and TON note takers could access their notes. Note taking enhanced recall, with the freestyle note takers and TON note takers without note access performing equally as well. Note taking therefore enhances encoding. Recall was greatest for the TON note takers with note access, suggesting a retrieval enhancement unique to this condition. The theoretical and applied implications of these findings are discussed.

Magnetoresistance in organic semiconductors: Including pair correlations in the kinetic equations for hopping transport

Science.gov (United States)

Shumilin, A. V.; Kabanov, V. V.; Dediu, V. I.

2018-03-01

We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.

Mathematical description and program documentation for CLASSY, an adaptive maximum likelihood clustering method

Science.gov (United States)

Lennington, R. K.; Rassbach, M. E.

1979-01-01

Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.

A general thermodynamical description of the event horizon in the FRW universe

International Nuclear Information System (INIS)

Tu, Fei-Quan; Chen, Yi-Xin

2016-01-01

The Friedmann equation in the Friedmann-Robertson-Walker (FRW) universe with any spatial curvature is derived from the first law of thermodynamics on the event horizon. The key idea is to redefine a Hawking temperature on the event horizon. Furthermore, we obtain the evolution equations of the universe including the quantum correction and explore the evolution of the universe in f(R) gravity. In addition, we also investigate the generalized second law of thermodynamics in Einstein gravity and f(R) gravity. This perspective also implies that the first law of thermodynamics on the event horizon has a general description in respect of the evolution of the FRW universe. (orig.)

Breather management in the derivative nonlinear Schrödinger equation with variable coefficients

Energy Technology Data Exchange (ETDEWEB)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Huang, Tingwen [Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar)

2015-04-15

We investigate breather solutions of the generalized derivative nonlinear Schrödinger (DNLS) equation with variable coefficients, which is used in the description of femtosecond optical pulses in inhomogeneous media. The solutions are constructed by means of the similarity transformation, which reduces a particular form of the generalized DNLS equation into the standard one, with constant coefficients. Examples of bright and dark breathers of different orders, that ride on finite backgrounds and may be related to rogue waves, are presented. - Highlights: • Exact solutions of a generalized derivative NLS equation are obtained. • The solutions are produced by means of a transformation to the usual integrable equation. • The validity of the solutions is verified by comparing them to numerical counterparts. • Stability of the solutions is checked by means of direct simulations. • The model applies to the propagation of ultrashort pulses in optical media.

Equations of State: From the Ideas of van der Waals to Association Theories

DEFF Research Database (Denmark)

Kontogeorgis, Georgios; Economou, Ioannis G.

2010-01-01

equations of state are sensitive to the mixing and combining rules used. Moreover, it is shown that previously reported deficiencies for size-asymmetric systems are more related to the van der Waals one fluid mixing rules used rather than the functionality of the cubic equation of state itself. Improved...... models for polar systems have been developed using the so-called EoS/GE mixing rules and we illustrate with the same methodology how these mixing rules should best be used for size-asymmetric systems. Despite the significant capabilities of cubic equations of state, their limitations lie especially...... in the description of complex phase behavior, e.g. liquid–liquid equilibria for highly polar and/or hydrogen bonding containing molecules. In these cases, advanced equations of state based on statistical mechanics that incorporate ideas from perturbation (e.g. SAFT and CPA), chemical (e.g. APACT) and lattice (e...

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

An Information Foraging Analysis of Note Taking and Note Sharing While Browsing Campaign Information

DEFF Research Database (Denmark)

Vatrapu, Ravi; Robertson, Scott

2010-01-01

In this paper, we present an experimental study of political information foraging in the context of e-voting. Participants were observed while searching and browsing the internet for campaign information in a mock-voting situation in three online note-taking conditions: No Notes, Private Notes...... with lack of scent, low value perception, and value depletion of information. Implications for the voter centered design of e-voting portals are discussed....

About the statistical description of gas-liquid flows

Energy Technology Data Exchange (ETDEWEB)

Sanz, D.; Guido-Lavalle, G.; Carrica, P. [Centro Atomico Bariloche and Instituto Balseiro (Argentina)] [and others

1995-09-01

Elements of the probabilistic geometry are used to derive the bubble coalescence term of the statistical description of gas liquid flows. It is shown that the Boltzmann`s hypothesis, that leads to the kinetic theory of dilute gases, is not appropriate for this kind of flows. The resulting integro-differential transport equation is numerically integrated to study the flow development in slender bubble columns. The solution remarkably predicts the transition from bubbly to slug flow pattern. Moreover, a bubbly bimodal size distribution is predicted, which has already been observed experimentally.

MHD description of plasma: handbook of plasma physics

International Nuclear Information System (INIS)

Kulsrud, R.M.

1980-10-01

The basic sets of MHD equations for the description of a plasma in various limits are derived and their usefulness and limits of validity are discussed. These limits are: the one fluid collisional plasma, the two fluid collisional plasma, the Chew-Goldberger Low formulation of the guiding center limit of a collisionless plasma and the double-adiabatic limit. Conservation relations are derived from these sets and the mathematics of the concept of flux freezing is given. An example is given illustrating the differences between guiding center theory and double adiabatic theory

Studies of P-matrix formalism on the basis of the potential description of two-particle interaction

International Nuclear Information System (INIS)

Babenko, V.A.; Petrov, N.M.

1991-01-01

A study is made of mathematical and physical aspects of the P-matrix approach within the framework of the potential description of two particle interaction when the dynamics is based on the nonrelativistic Schroedinger equation. A dispersion formula for the P-matrix is derived correctly, different ways of its expansion by means of which it is possible to develop different methods of an approximate description of the quantities characterizing the two-particle interaction are suggested. 15 refs. (author)

New Numerical Solution of von Karman Equation of Lengthwise Rolling

Directory of Open Access Journals (Sweden)

Rudolf Pernis

2015-01-01

Full Text Available The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a by polygonal curve and (b by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.

On the problem of a consistent description of kinetic and hydrodynamic processes in dense gases and liquids

Directory of Open Access Journals (Sweden)

B.B. Markiv

2010-01-01

Full Text Available For a consistent description of kinetic and hydrodynamic processes in dense gases and liquids the generalized non-Markovian equations for the nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density are obtained. The inner structure of the generalized transport kernels for these equations is established. It is shown that the collision integral of the kinetic equation has the Fokker-Planck form with the generalized friction coefficient in momentum space. It also contains contributions from the generalized diffusion coefficient and dissipative processes connected with the potential part of the enthalpy density.

Application of the descriptive function on non-linear electromagnetic phenomena

International Nuclear Information System (INIS)

Silva, H.T.

1982-01-01

This paper presents the solution of the nonlinear plan wave equation in non-equilibrium dielectric medium. The descriptive function appears as a useful tool to describe the medium response when it is possible to consider intensive electromagnetic response. Despite it has been considered an ideal situation of a limitless nonlinear medium, the results constitute a solid basis to mold more complex processes, such as those which take place in the plasma physics

An implementation of Kovacic's algorithm for solving ordinary differential equations in FORMAC

International Nuclear Information System (INIS)

Zharkov, A.Yu.

1987-01-01

An implementation of Kovacic's algorithm for finding Liouvillian solutions of the differential equations y'' + a(x)y' + b(x)y = 0 with rational coefficients a(x) and b(x) in the Computer Algebra System FORMAC is described. The algorithm description is presented in such a way that one can easily implement it in a suitable Computer Algebra System

Integral equations of hadronic correlation functions a functional- bootstrap approach

CERN Document Server

Manesis, E K

1974-01-01

A reasonable 'microscopic' foundation of the Feynman hadron-liquid analogy is offered, based on a class of models for hadron production. In an external field formalism, the equivalence (complementarity) of the exclusive and inclusive descriptions of hadronic reactions is specifically expressed in a functional-bootstrap form, and integral equations between inclusive and exclusive correlation functions are derived. Using the latest CERN-ISR data on the two-pion inclusive correlation function, and assuming rapidity translational invariance for the exclusive one, the simplest integral equation is solved in the 'central region' and an exclusive correlation length in rapidity predicted. An explanation is also offered for the unexpected similarity observed between pi /sup +/ pi /sup -/ and pi /sup -/ pi /sup -/ inclusive correlations. (31 refs).

A systematic iterative approach to the equations of low type

International Nuclear Information System (INIS)

Znojil, M.

1987-01-01

Nonlinear singular integral equations of the Low type appear in the description of π-N scattering amplitude at relativistic energies. The standard iteration solution differs and does not give sufficiently exact results even using the Pade approximation. A new approach is proposed. Its essence lies in a repeated formal simplification of the equation accompanied by a representation of the simplified amplitude in a generalized continued-fractional form. A simple example demonstrate that the new method improves the convergence of previous approach and essentially expands the region of its convergence. From the other side, its nonequivalence to a more complicate Newton-Kantorovich method is shown. In the future more realistic applications of the method one can expect increasing of result reliability

Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation

Directory of Open Access Journals (Sweden)

Sergey V. Ershkov

2017-05-01

Full Text Available The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we revisit the results of J. Wisdom et al. (1984, in which, by the elegant change of variables (considering the true anomaly f as the independent variable, the governing equation of satellite rotation takes the form of an Abel ordinary differential equation (ODE of the second kind, a sort of generalization of the Riccati ODE. We note that due to the special character of solutions of a Riccati-type ODE, there exists the possibility of sudden jumping in the magnitude of the solution at some moment of time. In the physical sense, this jumping of the Riccati-type solutions of the governing ODE could be associated with the effect of sudden acceleration/deceleration in the satellite rotation around the chosen principle axis at a definite moment of parametric time. This means that there exists not only a chaotic satellite rotation regime (as per the results of J. Wisdom et al. (1984, but a kind of gradient catastrophe (Arnold, 1992 could occur during the satellite rotation process. We especially note that if a gradient catastrophe could occur, this does not mean that it must occur: such a possibility depends on the initial conditions. In addition, we obtained asymptotical solutions that manifest a quasi-periodic character even with the strong simplifying assumptions e→0, p=1, which reduce the governing equation of J. Wisdom et al. (1984 to a kind of Beletskii’s equation.

Graph theory and the Virasoro master equation

International Nuclear Information System (INIS)

Obers, N.A.J.

1991-01-01

A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) metric in the Pauli-like basis of SU(n). Finally, he defines the 'sine-area graphs' of SU(n), which label the conformal field theories of SU(n) metric , and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g metric

Effects of Note-Taking Instruction and Note-Taking Languages on College EFL Students' Listening Comprehension

Science.gov (United States)

Tsai-Fu, Tsai; Wu, Yongan

2010-01-01

Background: The effect of note-taking has been well-recognized by EFL educators. However, little empirical research has been done to investigate combined effects of note-taking instruction and note-taking language (whether in L1 or L2) in an acquisition-poor environment, where English is used as an instructional language yet the audience is…

Technical note: Evaluation of the simultaneous measurements of mesospheric OH, HO2, and O3 under a photochemical equilibrium assumption - a statistical approach

Science.gov (United States)

Kulikov, Mikhail Y.; Nechaev, Anton A.; Belikovich, Mikhail V.; Ermakova, Tatiana S.; Feigin, Alexander M.

2018-05-01

This Technical Note presents a statistical approach to evaluating simultaneous measurements of several atmospheric components under the assumption of photochemical equilibrium. We consider simultaneous measurements of OH, HO2, and O3 at the altitudes of the mesosphere as a specific example and their daytime photochemical equilibrium as an evaluating relationship. A simplified algebraic equation relating local concentrations of these components in the 50-100 km altitude range has been derived. The parameters of the equation are temperature, neutral density, local zenith angle, and the rates of eight reactions. We have performed a one-year simulation of the mesosphere and lower thermosphere using a 3-D chemical-transport model. The simulation shows that the discrepancy between the calculated evolution of the components and the equilibrium value given by the equation does not exceed 3-4 % in the full range of altitudes independent of season or latitude. We have developed a statistical Bayesian evaluation technique for simultaneous measurements of OH, HO2, and O3 based on the equilibrium equation taking into account the measurement error. The first results of the application of the technique to MLS/Aura data (Microwave Limb Sounder) are presented in this Technical Note. It has been found that the satellite data of the HO2 distribution regularly demonstrate lower altitudes of this component's mesospheric maximum. This has also been confirmed by model HO2 distributions and comparison with offline retrieval of HO2 from the daily zonal means MLS radiance.

NOTES: issues and technical details with introduction of NOTES into a small general surgery residency program.

Science.gov (United States)

Kavic, Michael S; Mirza, Brian; Horne, Walter; Moskowitz, Jesse B

2008-01-01

Natural orifice translumenal endoscopic surgery (NOTES) is a development of recent origin. In 2004, Kalloo et al first described NOTES investigation in an animal model. Since then, several investigators have pursued NOTES study in animal survival and nonsurvival models. Our objectives for this project included studying NOTES intervention in a laboratory environment using large animal (swine) models and learning to do so in a safe, controlled manner. Ultimately, we intend to introduce NOTES methodology into our surgical residency training program. The expertise of an experienced laparoscopic surgeon, fellowship-trained laparoendoscopic surgeon, and veterinarian along with a senior surgical resident was utilized to bring the input of several disciplines to this study. The Institutional Animal Care and Use Committee (IACUC) of Northeastern Ohio Universities College of Medicine and Pharmacy (NEOUCOM/COP) approved this study. A series of 5 laboratory sessions using mixed breed farm swine varying in weight from 37 kg to 43.1 kg was planned for the initial phase of NOTES introduction into our residency program. Animals were not kept alive in this investigation. All animals were anesthetized using a standard swine protocol and euthanized following guidelines issued by the American Veterinary Medical Association Panel on Euthanasia. Equipment included a Fujinon EVE endoscope 0.8 cm in diameter with a suction/irrigation channel and one working channel. Initially, a US Endoscopy gastric overtube, 19.5 mm OD and 50 cm in length, was used to facilitate passage of the endoscope. However, this device was found to have insufficient length. Subsequently, commercially available 5/8" diameter clear plastic tubing, 70 cm to 80 cm in length, was adapted for use as an overtube. Standard endoscopic instruments included Boston Scientific biopsy forceps, needle-knife, papillotome, endoscopic clip applier, and Valley Lab electrosurgical unit. A Karl Storz laparoscope and tower were used for

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

Notes on the genus Conchapelopia Fittkau (Diptera: Chironomidae: Tanypodinae) from southern China, with description of a new species.

Science.gov (United States)

Niitsuma, Hiromi; Tang, Hongqu

2017-02-22

Two interesting species, Conchapelopia togamaculosa Sasa & Okazawa and a new species, Conchapelopia brachiata sp. n., were collected from southern China. The male, pupa and larva of the new species are described, and new distributions of the former species are noted. Although the male of the new species is very distinct from that of the former in the hypopygial median volsella, the pupa and larva stunningly resemble those of the former.

Physicians’ Progress Notes

DEFF Research Database (Denmark)

Bansler, Jørgen; Havn, Erling C.; Mønsted, Troels

2013-01-01

in patient care, they have not dealt specifically with the role, structure, and content of the progress notes. As a consequence, CSCW research has not yet taken fully into account the fact that progress notes are coordinative artifacts of a rather special kind, an open-ended chain of prose texts, written...... sequentially by cooperating physicians for their own use as well as for that of their colleagues. We argue that progress notes are the core of the medical record, in that they marshal and summarize the overwhelming amount of data that is available in the modern hospital environment, and that their narrative...... format is uniquely adequate for the pivotal epistemic aspect of cooperative clinical work: the narrative format enables physicians to not only record ‘facts’ but also—by filtering, interpreting, organizing, and qualifying information—to make sense and act concertedly under conditions of uncertainty...

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

Science.gov (United States)

Faye, Grégory; Rankin, James; Chossat, Pascal

2013-05-01

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

Science.gov (United States)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

Understanding Digital Note-Taking Practice for Visualization.

Science.gov (United States)

Willett, Wesley; Goffin, Pascal; Isenberg, Petra

2015-05-13

We present results and design implications from a study of digital note-taking practice to examine how visualization can support revisitation, reflection, and collaboration around notes. As digital notebooks become common forms of external memory, keeping track of volumes of content is increasingly difficult. Information visualization tools can help give note-takers an overview of their content and allow them to explore diverse sets of notes, find and organize related content, and compare their notes with their collaborators. To ground the design of such tools, we conducted a detailed mixed-methods study of digital note-taking practice. We identify a variety of different editing, organization, and sharing methods used by digital note-takers, many of which result in notes becoming "lost in the pile''. These findings form the basis for our design considerations that examine how visualization can support the revisitation, organization, and sharing of digital notes.

Drift-Alfven eigenmodes in inhomogeneous electron-positron-ion plasmas

Energy Technology Data Exchange (ETDEWEB)

Haque, Q; Ahmad, Ali [Theoretical Plasma Physics Division, PINSTECH, PO Nilore, Islamabad (Pakistan); Yamin, S, E-mail: qamar@pinstech.org.pk [Physics Division, PO Nilore, Islamabad (Pakistan)

2011-03-15

An analytical description of drift-Alfven modes in nonuniform bounded magnetized electron-positron-ion plasmas is presented here. In the linear domain, linearized equations are solved by considering the Gaussian density profile in the radial direction. For this bounded plasma, the condition for the quantization of the modes is found. We note that the condition depends upon the density ratios of different plasma species. The full set of nonlinear equations is also solved, yielding stationary rotating solutions in terms of Bessel functions. We also note that the behavior of the nonlinear structures can be affected by the concentration of the positrons in the system. The importance of the present results with respect to astrophysical plasmas is pointed out.

On the solution of the equations for nonlinear interaction of three damped waves

International Nuclear Information System (INIS)

1976-01-01

Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr

Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian

Directory of Open Access Journals (Sweden)

A. Zabrodin

2018-02-01

Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.

Nonlinear evolution equations for waves in random media

International Nuclear Information System (INIS)

Pelinovsky, E.; Talipova, T.

1994-01-01

The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs

Problems which are well posed in a generalized sense with applications to the Einstein equations

International Nuclear Information System (INIS)

Kreiss, H-O; Winicour, J

2006-01-01

In the harmonic description of general relativity, the principal part of the Einstein equations reduces to a constrained system of ten curved space wave equations for the components of the spacetime metric. We use the pseudo- differential theory of systems which are strongly well posed in the generalized sense to establish the well posedness of constraint-preserving boundary conditions for this system when treated in a second-order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation

Macroscopic and microscopic description of HE-HI collisions; classical equations of motion calculations. [Rapidity, cross sections, central and noncentral collisions

Energy Technology Data Exchange (ETDEWEB)

Bodmer, A. R.

1978-01-01

The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references. (JFP)

Noted

Science.gov (United States)

Nunberg, Geoffrey

2013-01-01

Considering how much attention people lavish on the technologies of writing--scroll, codex, print, screen--it's striking how little they pay to the technologies for digesting and regurgitating it. One way or another, there's no sector of the modern world that is not saturated with note-taking--the bureaucracy, the liberal professions, the…

Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill-string

Energy Technology Data Exchange (ETDEWEB)

Balanov, A.G.; Janson, N.B. E-mail: n.janson@lancaster.ac.uk; McClintock, P.V.E.; Tucker, R.W.; Wang, C.H.T

2003-01-01

Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string.

Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill-string

International Nuclear Information System (INIS)

Balanov, A.G.; Janson, N.B.; McClintock, P.V.E.; Tucker, R.W.; Wang, C.H.T.

2003-01-01

Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string

Description of the female of Navicordulia aemulatrix Pinto & Lamas and additional notes on the male (Odonata: Corduliidae).

Science.gov (United States)

Pinto, A P; Lamas, C J E

2011-01-01

The female of Navicordulia aemulatrix Pinto & Lamas is described and illustrated for the first time based on a single specimen from the same locality of the type series (state of Santa Catarina, [municipality of São Bento do Sul, 26°14'58"S, 49°22'59"W, railroad station] Rio Vermelho, 29.I.1952, in MZSP). In addition, further morphological notes for the male are provided based on three specimens collected at the type locality and at a new locality in the state of Santa Catarina (Timbó municipality). The pronotal process present in N. aemulatrix is re-evaluated and considered non-homologous to that found in Neocordulia setifera (Hagen in Selys) as previously suggested.

Making Notes, Making Meaning.

Science.gov (United States)

Burke, Jim

2002-01-01

Introduces notetaking tools used successfully with English-as-a-second-language students and low-achieving high school freshmen. Provides an overview of each tool and explains how students use them to take notes when reading textbooks and articles. Notes these tools and academic habits have helped students succeed in their mainstream academic…

PREFACE: Symmetries and Integrability of Difference Equations

Science.gov (United States)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches

Some results on the neutron transport and the coupling of equations; Quelques resultats sur le transport neutronique et le couplage d`equations

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.

Dissipation and fluctuations within a timedependent microscopic description of deep inelastic collisions

International Nuclear Information System (INIS)

Hofmann, H.

1978-01-01

In this talk I want to give a brief description of the linear response approach to deep inelastic collisions. In this model the relative motion of the two fragments as well as all slow 'shape-degrees' of the composite system are treated within the same physical picture. Among these 'shape-degrees' the most important ones will be those which represent: mass asymmetry, collective vibrations, and, possibly, rotations. The goal of the approach is an equation of motion which accounts for dissipative effects as well as for statistical fluctuations of all these macroscopic degrees and their conjugate momenta. It will be a Fokker Planck equation for the probability distribution in the classical phase space. (orig.) [de

Exact coherent structures in an asymptotically reduced description of parallel shear flows

Science.gov (United States)

Beaume, Cédric; Knobloch, Edgar; Chini, Gregory P.; Julien, Keith

2015-02-01

A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.

Exact coherent structures in an asymptotically reduced description of parallel shear flows

International Nuclear Information System (INIS)