Measure-valued solutions to the complete Euler system revisited

Czech Academy of Sciences Publication Activity Database

Březina, J.; Feireisl, Eduard

2018-01-01

Roč. 69, č. 3 (2018), č. článku 57. ISSN 0044-2275 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * measure-valued solution * vanishing dissipation limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.687, year: 2016 https://link.springer.com/article/10.1007/s00033-018-0951-8

Uniqueness of rarefaction waves in multidimensional compressible Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Kreml, Ondřej

2015-01-01

Roč. 12, č. 3 (2015), s. 489-499 ISSN 0219-8916 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler system * uniqueness * rarefaction wave * Riemann problem Subject RIV: BA - General Mathematics Impact factor: 0.556, year: 2015 http://www.worldscientific.com/doi/abs/10.1142/S0219891615500149

Maximal dissipation and well-posedness for the compressible Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2014-01-01

Roč. 16, č. 3 (2014), s. 447-461 ISSN 1422-6928 EU Projects: European Commission(XE) 320078 - MATHEF Keywords : maximal dissipation * compressible Euler system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007/s00021-014-0163-8

Nonconformally flat initial data for binary compact objects

International Nuclear Information System (INIS)

Uryu, Koji; Limousin, Francois; Gourgoulhon, Eric; Friedman, John L.; Shibata, Masaru

2009-01-01

A new method is described for constructing initial data for a binary neutron-star system in quasiequilibrium circular orbit. Two formulations for nonconformally flat data, waveless and near-zone helically symmetric, are introduced; in each formulation, the Einstein-Euler system, written in 3+1 form on an asymptotically flat spacelike hypersurface, is exactly solved for all metric components, including the spatially nonconformally flat potentials, and for irrotational flow. A numerical method applicable to both formulations is explained with an emphasis on the imposition of a spatial gauge condition. Results are shown for solution sequences of irrotational binary neutron-stars with matter approximated by parametrized equations of state that use a few segments of polytropic equations of state. The binding energy and total angular momentum of solution sequences computed within the conformally flat--Isenberg-Wilson-Mathews--formulation are closer to those of the third post-Newtonian (3PN) two point particles up to the closest orbits, for the more compact stars, whereas sequences resulting from the waveless/near-zone helically symmetric formulations deviate from the 3PN curve even more for the sequences with larger compactness. We think it likely that this correction reflects an overestimation in the Isenberg-Wilson-Mathews formulation as well as in the 3PN formula, by ∼1 cycle in the gravitational-wave phase during the last several orbits. The work suggests that imposing spatial conformal flatness results in an underestimate of the quadrupole deformation of the components of binary neutron-star systems in the last few orbits prior to merger.

A counterexample of the Euler condition: the Appell–Hamel dynamical system on a horizontally moving plate

International Nuclear Information System (INIS)

Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar

2009-01-01

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell–Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces. (general)

Stability of periodic steady-state solutions to a non-isentropic Euler-Poisson system

Science.gov (United States)

Liu, Cunming; Peng, Yue-Jun

2017-06-01

We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler-Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.

Generation of static solutions of self-consistent system of Einstein-Maxwell equations

International Nuclear Information System (INIS)

Anchikov, A.M.; Daishev, R.A.

1988-01-01

The theorem, according to which the static solution of the self-consistent system of the Einstein-Maxwell equations is assigned to energy static solution of the Einstein equations with the arbitrary energy-momentum tensor in the right part, is proved. As a consequence of this theorem, the way of the generation of the static solutions of the self-consistent system of the Einstein-Maxwell equations with charged dust as a source of the vacuum solutions of the Einstein equations is shown

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.

Generation of static solutions of the self-consistent system of Einstein-Maxwell equations

International Nuclear Information System (INIS)

Anchikov, A.M.; Daishev, R.A.

1988-01-01

A theorem is proved, according to which to each solution of the Einstein equations with an arbitrary momentum-energy tensor in the right hand side there corresponds a static solution of the self-consistent system of Einstein-Maxwell equations. As a consequence of this theorem, a method is established of generating static solutions of the self-consistent system of Einstein-Maxwell equations with a charged grain as a source of vacuum solutions of the Einstein equations

The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.

Science.gov (United States)

Kalinina, Elizabeth A

2013-08-01

The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Numerical Tribute to Achievement of Euler

Science.gov (United States)

Figueroa-Navarro, Carlos; Molinar-Tabares, Martín Eduardo; Castro-Arce, Lamberto; Campos-García, Julio Cesar

2014-03-01

This work aims to make a tribute to one of the world's brightest personalities as it was the mathematical physicist Leonhard Euler (1707-1783). Some results where the influence of Euler persists with the novelty of applying numerical analysis using Matlab are here exposed. A first analysis was done with the series that defines Euler numbers and polynomials of Frobenius-Euler; another result is the characterization of the functions that carry to Euler-Macheroni constant. In hydrodynamics is also feasible to evaluate graphically the relationship between dimensions in diameter and the exit angle of the height of Euler for turbomachines. In differential equations of Cauchy-Euler solutions for the cases of distinct real roots and complex roots are generated. Furthermore we report the generation of the Fourier series and the Fourier transform calculated by using Direct Commands of Matlab. In variational calculus it is possible to obtain plots from a problem of the Euler Lagrange equations. Finally, the Euler function is analyzed. Our purpose is to present a tribute to this giant of science also it could be an excuse to study his legacy by utilizing modern computational techniques.

Well/ill posedness for the Euler-Korteweg-Poisson system and related problems

Czech Academy of Sciences Publication Activity Database

Donatelli, D.; Feireisl, Eduard; Marcati, P.

2015-01-01

Roč. 40, č. 7 (2015), s. 1314-1335 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : convex integration * Euler-Korteweg system * quantum hydrodynamics Subject RIV: BA - General Mathematics Impact factor: 1.444, year: 2015 http://www.tandfonline.com/doi/abs/10.1080/03605302.2014.972517

Euler-Poincare Reduction of a Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2005-01-01

|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems......-known Euler-Poincare reduction to a rigid body motion with forcing....

Derivation of the Euler equations in Thomas-Fermi theories of a hot nuclear system

International Nuclear Information System (INIS)

Wang, C.

1992-01-01

The variational extreme condition with respect to statistical distribution of nucleons in momentum space is applied to derive the Euler equation of the nuclear density profile. The resultant Euler equation of the nuclear density profile is proven to be identical with that obtained in the usual Thomas-Fermi theories of a hot nuclear system where the variation is made with respect to the nuclear density profile. A Fermi-Dirac-type distribution appears as a result of variation in the present approach, while it is used as a given expression in obtaining the variation of the nuclear density profile in the usual Thomas-Fermi theories

PID position regulation in one-degree-of-freedom Euler-Lagrange systems actuated by a PMSM

Science.gov (United States)

Verastegui-Galván, J.; Hernández-Guzmán, V. M.; Orrante-Sakanassi, J.

2018-02-01

This paper is concerned with position regulation in one-degree-of-freedom Euler-Lagrange Systems. We consider that the mechanical subsystem is actuated by a permanent magnet synchronous motor (PMSM). Our proposal consists of a Proportional-Integral-Derivative (PID) controller for the mechanical subsystem and a slight variation of field oriented control for the PMSM. We take into account the motor electric dynamics during the stability analysis. We present, for the first time, a global asymptotic stability proof for such a control scheme without requiring the mechanical subsystem to naturally possess viscous friction. Finally, as a corollary of our main result we prove global asymptotic stability for output feedback PID regulation of one-degree-of-freedom Euler-Lagrange systems when generated torque is considered as the system input, i.e. when the electric dynamics of PMSM's is not taken into account.

Leonhard Euler and the mechanics of rigid bodies

Science.gov (United States)

Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.

2017-01-01

In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).

Stability of the isentropic Riemann solutions of the full multidimensional Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Kreml, Ondřej; Vasseur, A.

2015-01-01

Roč. 47, č. 3 (2015), s. 2416-2425 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * isentropic solutions * Riemann problem * rarefaction wave Subject RIV: BA - General Mathematics Impact factor: 1.486, year: 2015 http://epubs.siam.org/doi/abs/10.1137/140999827

Nuclear power history calculation for subcritical systems using Euler-MacLaurin formula

International Nuclear Information System (INIS)

Henrice Junior, Edson; Goncalves, Alessandro da Cruz

2013-01-01

This paper presents an efficient method for calculating the reactivity using inverse point kinetic equation for subcritical systems by applying the Euler-MacLaurin summation formula to calculate the nuclear power history. In accordance with the accuracy of the numerical results, this method does not require a large number of points for calculation, providing accurate results with low computational cost. (author)

Einstein solvmanifolds and the pre-Einstein derivation

OpenAIRE

Nikolayevsky, Y.

2008-01-01

An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable extension. For every nilpotent Lie algebra, we construct an (essentially unique) derivation, the pre...

Euler-Poincare Reduction of Externall Forced Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

Euler-Poincaré Reduction of a Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

Euler polynomials and identities for non-commutative operators

Science.gov (United States)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

Bose–Einstein condensation temperature of finite systems

Science.gov (United States)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

International Nuclear Information System (INIS)

Bogdanos, C.; Charmousis, C.; Gouteraux, B.; Zegers, R.

2009-01-01

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.

Euler-Poincaré Reduction of Externally Forced Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

Three dimensional steady subsonic Euler flows in bounded nozzles

Science.gov (United States)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Determination of regional Euler pole parameters for Eastern Austria

Science.gov (United States)

Umnig, Elke; Weber, Robert; Schartner, Matthias; Brueckl, Ewald

2017-04-01

The horizontal motion of lithospheric plates can be described as rotations around a rotation axes through the Earth's center. The two possible points where this axes intersects the surface of the Earth are called Euler poles. The rotation is expressed by the Euler parameters in terms of angular velocities together with the latitude and longitude of the Euler pole. Euler parameters were calculated from GPS data for a study area in Eastern Austria. The observation network is located along the Mur-Mürz Valley and the Vienna Basin. This zone is part of the Vienna Transfer Fault, which is the major fault system between the Eastern Alps and the Carpathians. The project ALPAACT (seismological and geodetic monitoring of ALpine-PAnnonian ACtive Tectonics) investigated intra plate tectonic movements within the Austrian part in order to estimate the seismic hazard. Precise site coordinate time series established from processing 5 years of GPS observations are available for the regional network spanning the years from 2010.0 to 2015.0. Station velocities with respect to the global reference frame ITRF2008 have been computed for 23 sites. The common Euler vector was estimated on base of a subset of reliable site velocities, for stations directly located within the area of interest. In a further step a geokinematic interpretation shall be carried out. Therefore site motions with respect to the Eurasian Plate are requested. To obtain this motion field different variants are conceivable. In a simple approach the mean ITRF2008 velocity of IGS site GRAZ can be adopted as Eurasian rotational velocity. An improved alternative is to calculate site-specific velocity differences between the Euler rotation and the individual site velocities. In this poster presentation the Euler parameters, the residual motion field as well as first geokinematic interpretation results are presented.

Thermodynamics in Einstein's thought

International Nuclear Information System (INIS)

Klein, M.J.

1983-01-01

The role of the thermodynamical approach in the Einstein's scientific work is analyzed. The Einstein's development of a notion about statistical fluctuations of thermodynamical systems that leads him to discovery of corpuscular-wave dualism is retraced

Einstein-Podolsky-Rosen paradox and measurement of quantum system

OpenAIRE

Kladko, Konstantin

1999-01-01

Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.

On Euler's problem

International Nuclear Information System (INIS)

Egorov, Yurii V

2013-01-01

We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.

A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

International Nuclear Information System (INIS)

Chandrasekhar, Subrahmanyan

1989-01-01

A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-centre problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons. (author)

3D GIS spatial operation based on extended Euler operators

Science.gov (United States)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

Einstein today; Einstein aujourd'hui

Energy Technology Data Exchange (ETDEWEB)

Aspect, A.; Grangier, Ph. [Centre National de la Recherche Scientifique (CNRS), Lab. Charles Fabry de l' Institut d' Optique a Orsay, 91 - Orsay (France); Bouchet, F.R. [Institut d' Astrophysique de Paris, CNRS, 75 - Paris (France); Brunet, E.; Derrida, B. [Universite Pierre et Marie Curie, Ecole Normale Superieure, 75 - Paris (France); Cohen-Tannoudji, C. [Academie des Sciences, 75 - Paris (France); Dalibard, J.; Laloe, F. [Laboratoire Kastler Brossel. UMR 8552 (ENS, UPMC, CNRS), 75 - Paris (France); Damour, Th. [Institut des Hautes Etudes Scientifiques, 91 - Bures sur Yvette (France); Darrigol, O. [Centre National de la Recherche Scientifique (CNRS), Groupe Histoire des Sciences Rehseis, 75 - Paris (France); Pocholle, J.P. [Thales Research et Technology France, 91 - Palaiseau (France)

2005-07-01

The most important contributions of Einstein involve 5 fields of physics : the existence of quanta (light quanta, stimulated radiation emission and Bose-Einstein condensation), relativity, fluctuations (Brownian motion and thermodynamical fluctuations), the basis of quantum physics and cosmology (cosmological constant and the expansion of the universe). Diverse and renowned physicists have appreciated the development of modern physics from Einstein's ideas to the knowledge of today. This book is a collective book that gathers their work under 7 chapters: 1) 1905, a new beginning; 2) from the Einstein, Podolsky and Rosen's article to quantum information (cryptography and quantum computers); 3) the Bose-Einstein condensation in gases; 4) from stimulated emission to the today's lasers; 5) Brownian motion and the fluctuation-dissipation theory; 6) general relativity; and 7) cosmology. (A.C.)

Teaching possibilities of some elements of Albert Einstein's Gravitation theory in frame of physics courses taught at technical universities

International Nuclear Information System (INIS)

Iordache, Dan-Alexandru

2005-01-01

As in the period of creation of the 'monumental' works of A. Einstein (1905-1920, mainly), when many outstanding physicists [theoreticians, inclusively, as Albert Einstein (alumni of the Polytechnics from Geneva), as Paul Adrian Maurice Dirac, Alexandru Proca (alumni of Bucharest Polytechnics), et al., finished their academic studies to different Polytechnics Universities, presently many students of technical Universities obtained (as high-school students) some outstanding results in the Physics field. Particularly, the leadership of the Faculty of Control Systems and Computers of the Bucharest University has found that 'the best students in their divisions are winners at the Physics Olympics Contests'. These students and many of their colleagues (those with special scientific aptitudes) want to know more details about the most difficult scientific creation of Albert Einstein: the Gravitation Theory. Taking into account that the Einstein's Gravitation Theory is particularly difficult (from mathematical point of view, especially), and the duration of the Physics study in our technical universities is so restricted (totally 42 to 98 teaching hours, depending on the technical division profile), we have to answer to the question: what elements of the Einstein's gravity theory could be presented in frame of Physics courses taught in our technical universities? After accomplishing our analysis, we concluded as possible and useful - for the scientific training of the best students 'engineers' - the assimilation of the following elements of the Einstein's gravity theory: - The time and space concepts in the Einstein's gravitation theory, in connection with the equation of electromagnetic waves in ideal media and - eventually - in relation with the Larmor's theory of the electrical dipole radiation [which needs the expressions in curvilinear coordinates of the gradient and divergence (the main elements of the mathematical theory of fields)]; - The applications of the

Equivariant analogues of the Euler characteristic and Macdonald type equations

Science.gov (United States)

Gusein-Zade, S. M.

2017-02-01

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representations of the group or as an element of the Burnside ring of the group. From physics came the notion of the orbifold Euler characteristic, and this was generalized to orbifold Euler characteristics of higher orders. The main property of the Euler characteristic (defined in terms of the cohomology with compact support) is its additivity. On some classes of spaces there are additive invariants other than the Euler characteristic, and they can be regarded as generalized Euler characteristics. For example, the class of a variety in the Grothendieck ring of complex quasi-projective varieties is a universal additive invariant on the class of complex quasi-projective varieties. Generalized analogues of the Euler characteristic can also be defined in the equivariant setting. There is a simple formula — the Macdonald equation — for the generating series of the Euler characteristics of the symmetric powers of a space: it is equal to the series (1-t)-1=1+t+t^2+\\cdots independent of the space, raised to a power equal to the Euler characteristic of the space itself. Equations of a similar kind for other invariants (`equivariant and generalized Euler characteristics') are called Macdonald type equations. This survey discusses different versions of the Euler characteristic in the equivariant setting and describes some of their properties and Macdonald type equations. Bibliography: 59 titles.

Einstein and Austria

International Nuclear Information System (INIS)

Broda, E.

1979-01-01

This text was written by Engelbert Broda in 1979 and is about Albert Einstein and his relation to Austria. This text is split in different sections which are amongst others: Einstein und Mach; Einstein und Boltzmann; Positivism, Atoms and Relativity; Einstein as an Austrian professor; Einstein’s visits to Austria; Einstein and Viennese friends; Einstein and Friedrich Adler; Einstein and the Austrian mentality; (nowak)

Discrete Bose-Einstein systems in a box with low adiabatic invariant

International Nuclear Information System (INIS)

Vlad, V.I.; Ionescu-Pallas, N.

2002-03-01

The Bose-Einstein energy spectrum of a quantum gas, confined in a (cubic) box, is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, A at and the adiabatic invariant, TV 2/3 , i.e. on γ=A at TV 2/3 . Even within the approximation of noninteracting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. It is solved in the textbooks and most papers by approximating the sums by integrals. The present study compares the total number of particles and the total energy obtained by summing up the exact contributions of the eigenvalues and their weights, for defined values of γ, to the results of the approximate integrals. Then, the passage from sums to integrals is done in a more rigorous manner and better analytical approximations are found. The corrected thermodynamic functions depend on γ. The critical temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems and their onset of the phase transition. (author)

Drawing Euler Diagrams with Circles

OpenAIRE

Stapleton, Gem; Zhang, Leishi; Howse, John; Rodgers, Peter

2010-01-01

Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis. As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of manual data analysis and the subsequent task of drawing an appropriate diagram. Various methods have emerged that automatically dra...

Euler and His Contribution Number Theory

Science.gov (United States)

Len, Amy; Scott, Paul

2004-01-01

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Directory of Open Access Journals (Sweden)

Pengcheng HAN

2017-12-01

Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.

IMPROVED ENTROPY-ULTRA-BEE SCHEME FOR THE EULER SYSTEM OF GAS DYNAMICS

Institute of Scientific and Technical Information of China (English)

Rongsan Chen; Dekang Mao

2017-01-01

The Entropy-Ultra-Bee scheme was developed for the linear advection equation and extended to the Euler system of gas dynamics in [13].It was expected that the technology be applied only to the second characteristic field of the system and the computation in the other two nonlinear fields be implemented by the Godunov scheme.However,the numerical experiments in [13] showed that the scheme,though having improved the wave resolution in the second field,produced numerical oscillations in the other two nonlinear fields.Sophisticated entropy increaser was designed to suppress the spurious oscillations by increasing the entropy when there are waves in the two nonlinear fields presented.However,the scheme is then not efficient neither robust with problem-related parameters.The purpose of this paper is to fix this problem.To this end,we first study a 3 × 3 linear system and apply the technology precisely to its second characteristic field while maintaining the computation in the other two fields be implemented by the Godunov scheme.We then follow the discussion for the linear system to apply the Entropy-Ultra-Bee technology to the second characteristic field of the Euler system in a linearlized field-byfield fashion to develop a modified Entropy-Ultra-Bee scheme for the system.Meanwhile a remark is given to explain the problem of the previous Entropy-Ultra-Bee scheme in [13].A reference solution is constructed for computing the numerical entropy,which maintains the feature of the density and flats the velocity and pressure to constants.The numerical entropy is then computed as the entropy cell-average of the reference solution.Several limitations are adopted in the construction of the reference solution to further stabilize the scheme.Designed in such a way,the modified Entropy-Ultra-Bee scheme has a unified form with no problem-related parameters.Numerical experiments show that all the spurious oscillations in smooth regions are gone and the results are better than that

EULER - A Real Virtual Library for Mathematics

CERN Document Server

Jost, Michael

2004-01-01

The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...

Refinement of RAIM via Implementation of Implicit Euler Method

Energy Technology Data Exchange (ETDEWEB)

Lee, Yoonhee; Kim, Han-Chul [Korea Institute of Nuclear and Safety, Daejeon (Korea, Republic of)

2016-10-15

The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed

Refinement of RAIM via Implementation of Implicit Euler Method

International Nuclear Information System (INIS)

Lee, Yoonhee; Kim, Han-Chul

2016-01-01

The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed

Improving Euler computations at low Mach numbers

NARCIS (Netherlands)

Koren, B.; Leer, van B.; Deconinck, H.; Koren, B.

1997-01-01

The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of

Improving Euler computations at low Mach numbers

NARCIS (Netherlands)

Koren, B.

1996-01-01

This paper consists of two parts, both dealing with conditioning techniques for low-Mach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized linearized 1-D Euler equations, the smoothing behavior of

Analogues of Euler and Poisson Summation Formulae

Indian Academy of Sciences (India)

... f ( n ) have been obtained in a unified manner, where (()) is a periodic complex sequence; () is the divisor function and () is a sufficiently smooth function on [, ]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.

Einstein's Tea Leaves and Pressure Systems in the Atmosphere

Science.gov (United States)

Tandon, Amit; Marshall, John

2010-01-01

Tea leaves gather in the center of the cup when the tea is stirred. In 1926 Einstein explained the phenomenon in terms of a secondary, rim-to-center circulation caused by the fluid rubbing against the bottom of the cup. This explanation can be connected to air movement in atmospheric pressure systems to explore, for example, why low-pressure…

Weberized Mumford-Shah Model with Bose-Einstein Photon Noise

International Nuclear Information System (INIS)

Shen Jianhong; Jung, Yoon-Mo

2006-01-01

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in detail are issues concerning why the classical Mumford-Shah model lacks light adaptivity, and why its 'weberized' version can more faithfully reflect human vision's superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein's distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford-Shah model with Bose-Einstein noise. In particular, Ambrosio-Tortorelli's Γ-convergence approximation theory is adapted (Boll. Un. Mat. Ital. B, vol. 6, pp. 105-123, 1992), and stable numerical algorithms are developed for the associated pair ofnonlinear Euler-Lagrange PDEs

Variational problems with fractional derivatives: Euler-Lagrange equations

International Nuclear Information System (INIS)

Atanackovic, T M; Konjik, S; Pilipovic, S

2008-01-01

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense

Unique Stellar System Gives Einstein a Thumbs-Up

Science.gov (United States)

2008-07-01

Taking advantage of a unique cosmic coincidence, astronomers have measured an effect predicted by Albert Einstein's theory of General Relativity in the extremely strong gravity of a pair of superdense neutron stars. The new data indicate that the famed physicist's 93-year-old theory has passed yet another test. Double Pulsar Graphic Artist's Conception of Double Pulsar System PSR J0737-3039A/B CREDIT: Daniel Cantin, DarwinDimensions, McGill University Click on image for more graphics. The scientists used the National Science Foundation's Robert C. Byrd Green Bank Telescope (GBT) to make a four-year study of a double-star system unlike any other known in the Universe. The system is a pair of neutron stars, both of which are seen as pulsars that emit lighthouse-like beams of radio waves. "Of about 1700 known pulsars, this is the only case where two pulsars are in orbit around each other," said Rene Breton, a graduate student at McGill University in Montreal, Canada. In addition, the stars' orbital plane is aligned nearly perfectly with their line of sight to the Earth, so that one passes behind a doughnut-shaped region of ionized gas surrounding the other, eclipsing the signal from the pulsar in back. "Those eclipses are the key to making a measurement that could never be done before," Breton said. Einstein's 1915 theory predicted that, in a close system of two very massive objects, such as neutron stars, one object's gravitational tug, along with an effect of its spinning around its axis, should cause the spin axis of the other to wobble, or precess. Studies of other pulsars in binary systems had indicated that such wobbling occurred, but could not produce precise measurements of the amount of wobbling. "Measuring the amount of wobbling is what tests the details of Einstein's theory and gives a benchmark that any alternative gravitational theories must meet," said Scott Ransom of the National Radio Astronomy Observatory. The eclipses allowed the astronomers to pin

Development of Euler's ideas at the Moscow State Regional University

Science.gov (United States)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

Combinatorial Aspects of the Generalized Euler's Totient

Directory of Open Access Journals (Sweden)

Nittiya Pabhapote

2010-01-01

Full Text Available A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.

Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

International Nuclear Information System (INIS)

De Gandt, Francois

2006-01-01

In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?

The Einstein dossiers science and politics - Einstein's Berlin period with an appendix on Einstein's FBI file

CERN Document Server

Grundmann, Siegfried

2004-01-01

In 1919 the Prussian Ministry of Science, Arts and Culture opened a dossier on "Einstein's Theory of Relativity." It was rediscovered by the author in 1961 and is used in conjunction with numerous other subsequently identified 'Einstein' files as the basis of this fascinating book. In particular, the author carefully scrutinizes Einstein's FBI file from 1950-55 against mostly unpublished material from European including Soviet sources and presents hitherto unknown documentation on Einstein's alleged contacts with the German Communist Party and the Comintern. Siegfried Grundmann's thorough study of Einstein's participation on a committee of the League of Nations, based on archival research in Geneva, is also new. This book outlines Einstein's image in politics and German science policy. It covers the period from his appointment as a researcher in Berlin to his fight abroad against the "boycott of German science" after World War I and his struggle at home against attacks on "Jewish physics" of which he was made...

Einstein today

International Nuclear Information System (INIS)

Aspect, A.; Grangier, Ph.; Bouchet, F.R.; Brunet, E.; Derrida, B.; Cohen-Tannoudji, C.; Dalibard, J.; Laloe, F.; Damour, Th.; Darrigol, O.; Pocholle, J.P.

2005-01-01

The most important contributions of Einstein involve 5 fields of physics : the existence of quanta (light quanta, stimulated radiation emission and Bose-Einstein condensation), relativity, fluctuations (Brownian motion and thermodynamical fluctuations), the basis of quantum physics and cosmology (cosmological constant and the expansion of the universe). Diverse and renowned physicists have appreciated the development of modern physics from Einstein's ideas to the knowledge of today. This book is a collective book that gathers their work under 7 chapters: 1) 1905, a new beginning; 2) from the Einstein, Podolsky and Rosen's article to quantum information (cryptography and quantum computers); 3) the Bose-Einstein condensation in gases; 4) from stimulated emission to the today's lasers; 5) Brownian motion and the fluctuation-dissipation theory; 6) general relativity; and 7) cosmology. (A.C.)

Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system

Science.gov (United States)

Chen, Shuxing; Li, Dening

2014-09-01

We study the Cauchy problems for the isentropic 2-d Euler system with discontinuous initial data along a smooth curve. All three singularities are present in the solution: shock wave, rarefaction wave and contact discontinuity. We show that the usual restrictive high order compatibility conditions for the initial data are automatically satisfied. The local existence of piecewise smooth solution containing all three waves is established.

Euler European Libraries and Electronic Resources in Mathematical Sciences

CERN Document Server

The Euler Project. Karlsruhe

The European Libraries and Electronic Resources (EULER) Project in Mathematical Sciences provides the EulerService site for searching out "mathematical resources such as books, pre-prints, web-pages, abstracts, proceedings, serials, technical reports preprints) and NetLab (for Internet resources), this outstanding engine is capable of simple, full, and refined searches. It also offers a browse option, which responds to entries in the author, keyword, and title fields. Further information about the Project is provided at the EULER homepage.

Euler deconvolution and spectral analysis of regional aeromagnetic ...

African Journals Online (AJOL)

Existing regional aeromagnetic data from the south-central Zimbabwe craton has been analysed using 3D Euler deconvolution and spectral analysis to obtain quantitative information on the geological units and structures for depth constraints on the geotectonic interpretation of the region. The Euler solution maps confirm ...

On Euler's problem

Energy Technology Data Exchange (ETDEWEB)

Egorov, Yurii V [Institute de Mathematique de Toulouse, Toulouse (France)

2013-04-30

We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.

A-free rigidity and applications to the compressible Euler system

Czech Academy of Sciences Publication Activity Database

Chiodaroli, E.; Feireisl, Eduard; Kreml, Ondřej; Wiedemann, E.

2017-01-01

Roč. 196, č. 4 (2017), s. 1557-1572 ISSN 0373-3114 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : A-free condition * compressible Euler equations * measure-valued solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.864, year: 2016 https://link.springer.com/article/10.1007%2Fs10231-016-0629-9

Einstein was right!

CERN Document Server

Hess, Karl

2014-01-01

All modern books on Einstein emphasize the genius of his relativity theory and the corresponding corrections and extensions of the ancient space-time concept. However, Einstein's opposition to the use of probability in the laws of nature and particularly in the laws of quantum mechanics is criticized and often portrayed as outdated. The author of Einstein Was Right! takes a unique view and shows that Einstein created a ""Trojan horse"" ready to unleash forces against the use of probability as a basis for the laws of nature. Einstein warned that the use of probability would, in the final analys

Intra- and interobserver reliability of glenoid fracture classifications by Ideberg, Euler and AO.

Science.gov (United States)

Gilbert, F; Eden, L; Meffert, R; Konietschke, F; Lotz, J; Bauer, L; Staab, W

2018-03-27

Representing 3%-5% of shoulder girdle injuries scapula fractures are rare. Furthermore, approximately 1% of scapula fractures are intraarticularfractures of the glenoid fossa. Because of uncertain fracture morphology and limited experience, the treatment of glenoid fossa fractures is difficult. The glenoid fracture classification by Ideberg (1984) and Euler (1996) is still commonly used in literature. In 2013 a new glenoid fracture classification was introduced by the AO. The purpose of this study was to examine the new AO classification in clinical practice in comparison with the classifications by Ideberg and Euler. In total CT images of 84 patients with glenoid fossa fractures from 2005 to 2018 were included. Parasagittal, paracoronary and axial reconstructions were examined according to the classifications of Ideberg, Euler and the AO by 3 investigators (orthopedic surgeon, radiologist, student of medicine) at three individual time settings. Inter- and intraobserver reliability of the three classification systems were ascertained by computing Inter- and Intraclass (ICCs) correlation coefficients using Spearman's rank correlation coefficient, 95%-confidence intervals as well as F-tests for correlation coefficients. Inter- and intraobserver reliability for the AO classification showed a perspicuous coherence (R = 0.74 and R = 0.79). Low to moderate intraobserver reliability for Ideberg (R = 0.46) and Euler classification (R = 0.41) was found. Furthermore, data show a low Interobserver reliability for both Ideberg and Euler classification (R reliability using AO is significantly higher than those using Ideberg and Euler (p reliable grading of glenoid fossa fractures with high inter- and intraobserver reliability in 84 patients using CT images. It should possibly be applied in order to enable a valid, reliable and consistent academic description of glenoid fossa fractures. The established classifications by Euler and Ideberg are not capable of

Maja Winteler-Einstein

Indian Academy of Sciences (India)

Einstein. Articles written in Resonance – Journal of Science Education. Volume 5 Issue 4 April 2000 pp 111-120 Reflections. Albert Einstein: A Biographical Sketch · Maja Winteler-Einstein · More Details Fulltext PDF ...

Remarks on Heisenberg-Euler-type electrodynamics

Science.gov (United States)

Kruglov, S. I.

2017-05-01

We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at r →∞ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at r →∞. Corrections to the Reissner-Nordström solution are obtained.

Classical mechanics on the GL(n, R) group and Euler-Calogero-Sutherland model

International Nuclear Information System (INIS)

Khvedelidze, A.M.; Mladenov, D.M.

2002-01-01

Relations between free motion on the GL + (n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with a pairwise 1/sinh 2 x 'potential' (Euler-Calogero-Sutherland model) are discussed within a Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: that which is due to continuous invariance and that which is due to discrete symmetry. It is shown that, upon projecting onto the corresponding invariant manifolds, the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases

Dr. Euler's fabulous formula Cures many mathematical ills

CERN Document Server

Nahin, Paul J

2006-01-01

I used to think math was no fun'Cause I couldn't see how it was doneNow Euler's my heroFor I now see why zeroEquals e[pi] i+1--Paul Nahin, electrical engineer In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the seque

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Universal Themes of Bose-Einstein Condensation

Science.gov (United States)

Proukakis, Nick P.; Snoke, David W.; Littlewood, Peter B.

2017-04-01

Foreword; List of contributors; Preface; Part I. Introduction: 1. Universality and Bose-Einstein condensation: perspectives on recent work D. W. Snoke, N. P. Proukakis, T. Giamarchi and P. B. Littlewood; 2. A history of Bose-Einstein condensation of atomic hydrogen T. Greytak and D. Kleppner; 3. Twenty years of atomic quantum gases: 1995-2015 W. Ketterle; 4. Introduction to polariton condensation P. B. Littlewood and A. Edelman; Part II. General Topics: Editorial notes; 5. The question of spontaneous symmetry breaking in condensates D. W. Snoke and A. J. Daley; 6. Effects of interactions on Bose-Einstein condensation R. P. Smith; 7. Formation of Bose-Einstein condensates M. J. Davis, T. M. Wright, T. Gasenzer, S. A. Gardiner and N. P. Proukakis; 8. Quenches, relaxation and pre-thermalization in an isolated quantum system T. Langen and J. Schmiedmayer; 9. Ultracold gases with intrinsic scale invariance C. Chin; 10. Berezinskii-Kosterlitz-Thouless phase of a driven-dissipative condensate N. Y. Kim, W. H. Nitsche and Y. Yamamoto; 11. Superfluidity and phase correlations of driven dissipative condensates J. Keeling, L. M. Sieberer, E. Altman, L. Chen, S. Diehl and J. Toner; 12. BEC to BCS crossover from superconductors to polaritons A. Edelman and P. B. Littlewood; Part III. Condensates in Atomic Physics: Editorial notes; 13. Probing and controlling strongly correlated quantum many-body systems using ultracold quantum gases I. Bloch; 14. Preparing and probing chern bands with cold atoms N. Goldman, N. R. Cooper and J. Dalibard; 15. Bose-Einstein condensates in artificial gauge fields L. J. LeBlanc and I. B. Spielman; 16. Second sound in ultracold atomic gases L. Pitaevskii and S. Stringari; 17. Quantum turbulence in atomic Bose-Einstein condensates N. G. Parker, A. J. Allen, C. F. Barenghi and N. P. Proukakis; 18. Spinor-dipolar aspects of Bose-Einstein condensation M. Ueda; Part IV. Condensates in Condensed Matter Physics: Editorial notes; 19. Bose-Einstein

Structure of the space of solutions of Einstein's equations II: Several killing fields and the Einstein-Yang-Mills equations

International Nuclear Information System (INIS)

Arms, J.M.; Marsden, J.E.; Moncrief, V.

1982-01-01

The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members. Contents: Introduction 1. The Kuranishi map and its properties. 2. The momentum constraints. 3. The Hamiltonian constraints. 4. The Einstein-Yang-Mills system. 5. Discussion and examples

Einstein and Prague

International Nuclear Information System (INIS)

Bicak, J.

1979-01-01

A commemorative publication is submitted issued on the occasion of Albert Einstein's centenary remembering Einstein's sojourn and work in Prague. In addition to the article Ueber den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes the publications contains the author's preface to the Czech edition of his Theory, the list of studies written by Einstein while in Prague, an assay on the great physicist's life and work, and extracts from the memoires of Philipp Frank published under the title Einstein, His Life and Times. (L.O.)

Leonhard Euler's Wave Theory of Light

DEFF Research Database (Denmark)

Pedersen, Kurt Møller

2008-01-01

is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction......Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...

Entropy viscosity method applied to Euler equations

International Nuclear Information System (INIS)

Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

2013-01-01

The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

International Nuclear Information System (INIS)

Brechet, S D; Hobson, M P; Lasenby, A N

2008-01-01

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1 + 3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the spacetime metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalized scale factor R(t) in spatially curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data

Generalized force in classical field theory. [Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-02-01

The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.

Einstein and Planck

Science.gov (United States)

Heilbron, John

2005-03-01

As an editor of the Annalen der Physik, Max Planck published Einstein's early papers on thermodynamics and on special relativity, which Planck probably was the first major physicist to appreciate. They respected one another not only as physicists but also, for their inspired creation of world pictures, as artists. Planck helped to establish Einstein in a sinecure at the center of German physics, Berlin. Despite their differences in scientific style, social life, politics, and religion, they became fast friends. Their mutual admiration survived World War I, during which Einstein advocated pacifism and Planck signed the infamous Manifesto of the 93 Intellectuals supporting the German invasion of Belgium. It also survived the Weimar Republic, which Einstein favored and Planck disliked. Physics drew them together, as both opposed the Copenhagen Interpretation; so did common decency, as Planck helped to protect Einstein from anti-semitic attacks. Their friendship did not survive the Nazis. As a standing secretary of the Berlin Academy, Planck had to advise Einstein to resign from it before his colleagues, outraged at his criticism of the new Germany from the safety of California, expelled him. Einstein never forgave his old friend and former fellow artist for not protesting publicly against his expulsion and denigration, and other enormities of National Socialism. .

Some preliminary results on the dynamics of Einstein-Yang-Mills-Higgs systems

Energy Technology Data Exchange (ETDEWEB)

Csizmadia, Peter; Racz, Istvan [RMKI, Budapest, Konkoly Thege Miklos ut 29-33, H-1121 (Hungary); Kovacs, Gergely, E-mail: gkovacs@rmki.kfki.h, E-mail: iracz@rmki.kfki.h [Eoetvoes University, Department of Astronomy, Budapest, POB. 32, H-1518 (Hungary)

2010-03-01

A mathematical and numerical framework for the study of dynamical properties of spherically symmetric Einstein-Yang-Mills-Higgs systems is introduced. The quantitative investigations of the time evolution of some simple magnetic monopole type configurations are presented. Long living breather type states are found to develop.

Einsteins dream

International Nuclear Information System (INIS)

Parker, B.

1986-01-01

This book discusses the following topics: the search for meaning; Einstein's dream; curved space; Einstein and warped space-time and extreme wraping; early unified field theories; star death; beyond the white dwarf; the early universe; the hadron, Lepton, and Radiation eras; the redshift controversy; other universes; the final fate of the universe; the missing mass; bounce; fate of the open universe; the world of particles and fields; Dirac's equation; Yukawa; gauge theory; quantum chromodynamics; supergravity and superstrings; twistors and heaven; and the new Einstein

Drawing Euler Diagrams with Circles: The Theory of Piercings.

Science.gov (United States)

Stapleton, Gem; Leishi Zhang; Howse, John; Rodgers, Peter

2011-07-01

Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less comprehensible. In this paper, we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints, then it can be drawn with circles, which are more esthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.

Analogies between dark solitons in atomic Bose-Einstein condensates and optical systems

International Nuclear Information System (INIS)

Proukakis, N P; Parker, N G; Frantzeskakis, D J; Adams, C S

2004-01-01

Dark solitons have been observed in optical systems (optical fibres, dielectric guides and bulk media), and, more recently, in harmonically confined atomic Bose-Einstein condensates. This paper presents an overview of some of the common features and analogies experienced by these two intrinsically nonlinear systems, with emphasis on the stability of dark solitons in such systems and their decay via emission of radiation. The closely related issue of vortex dynamics in such systems is also briefly discussed

Covariant Conformal Decomposition of Einstein Equations

Science.gov (United States)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Euler numbers of four-dimensional rotating black holes with the Euclidean signature

International Nuclear Information System (INIS)

Ma Zhengze

2003-01-01

For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology

Classes of general axisymmetric solutions of Einstein-Maxwell equations

International Nuclear Information System (INIS)

Krori, K.D.; Choudhury, T.

1981-01-01

An exact solution of the Einstein equations for a stationary axially symmetric distribution of mass composed of all types of multipoles is obtained. Following Ernst (1968), from this vacuum solution the corresponding solution of the coupled Einstein-Maxwell equations is derived. A solution of Einstein-Maxwell fields for a static axially symmetric system composed of all types of multipoles is also obtained. (author)

A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

Science.gov (United States)

Komathiraj, K.; Sharma, Ranjan

2018-05-01

In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

Science.gov (United States)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Resonances for coupled Bose-Einstein condensates

International Nuclear Information System (INIS)

Haroutyunyan, H.L.; Nienhuis, G.

2004-01-01

The properties of a Bose-Einstein condensate in a two-well potential can be manipulated by periodic modulation of the potential parameters. We study the effects arising from modulating the barrier height and the difference in well depth. At certain modulation frequencies the system exhibits resonances, which may show up in an enhancement of the tunneling rate between the wells. Resonances can be used to control the particle distribution over the wells. Some of the effects occurring in the two-well system also arise for a Bose-Einstein condensate in an optical lattice

Additivity for parametrized topological Euler characteristic and Reidemeister torsion

OpenAIRE

Badzioch, Bernard; Dorabiala, Wojciech

2005-01-01

Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.

The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces

International Nuclear Information System (INIS)

Bergqvist, Goeran; Eriksson, Ingemar

2007-01-01

In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces

Structure of the space of solutions of Einstein's equations II: Several killing fields and the Einstein-Yang-Mills equations

Energy Technology Data Exchange (ETDEWEB)

Arms, J.M.; Marsden, J.E.; Moncrief, V.

1982-11-01

The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members. Contents: Introduction 1. The Kuranishi map and its properties. 2. The momentum constraints. 3. The Hamiltonian constraints. 4. The Einstein-Yang-Mills system. 5. Discussion and examples.

Einstein's meanders

Science.gov (United States)

Lomnitz, C.

2007-05-01

What does Einstein have to do with subduction? Good question. Peaceful Lake Budi, lying at the heart of an Indian reservation in the Deep South of Chile, had subsided by two meters in the 1960 mega-thrust earthquake. This unique South American salt lake was hiding an awful secret: it was actually an oxbow, not a lake. But Einstein had realized in 1926 that meanders are natural freaks. Rivers will not flow uphill, yet - he claimed - they don't flow down the path of steepest descent either. This anomaly was put at the doorstep of a weak Coriolis Force. Thus Einstein problematized the dilemma of the earth sciences. How can a non-force produce margin-parallel compression in a convergent margin where extension is expected? In fact, where does the energy for meander formation come from? Good question . . . Even Wikipedia knows that Coriolis is not a “force” but an “effect”. So is the obliquity of plate convergence in subduction. Where did Einstein err, and where was he a pioneer? Coastal ablation plus alternating subsidence and emergence in giant earthquakes may yield an answer. Einstein, A. (1926). Die Ursache der Maeanderbildung der Flusslaeufe und das sogenannte Baersche Gesetz, Naturwissenschaften, 14, fascicle II.

Canonical form of Euler-Lagrange equations and gauge symmetries

Energy Technology Data Exchange (ETDEWEB)

Geyer, B [Naturwissenschaftlich-Theoretisches Zentrum und Institut fuer Theoretische Physik, Universitaet Leipzig, Leipzig (Germany); Gitman, D M [Institute of Physics, University of Sao Paulo, Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

2003-06-13

The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter the right-hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proved that for local theories all the gauge generators are local in time operators.

Celebrating Einstein

Science.gov (United States)

Shapiro Key, Joey; Yunes, Nicolas

2013-04-01

The Gravity Group at Montana State University (MSU) hosted Celebrating Einstein, a free public arts and multimedia event celebrating Einstein and his ideas in Bozeman, Montana April 2-6, 2013. The products of our efforts are now available to any party interested in hosting a similar event. Celebrating Einstein is a truly interdisciplinary effort including art, film, dance, music, physics, history, and education. Events included a black hole immersive art installation, a series of public talks by physicists, and Einstein lessons in the public schools leading up to a live free public multimedia performance including a professional dance company, a live interview with a renowned physicist, and an original score composed for the MSU student symphony to be performed with an original film produced by the Science and Natural History film program at MSU. This project is funded by the Montana Space Grant Consortium, Montana State University, and the National Science Foundation.

The Einstein almanac

CERN Document Server

Calaprice, Alice

2005-01-01

Albert Einstein was an exceptional human being. Perhaps nothing reflects the breadth and scope of his brilliance, his interests, and his influence better than his publications -- more than six hundred scientific papers, books, essays, reviews, and opinion pieces. Einstein began publishing in March 1901 with a scientific work that appeared in the German journal Annalen der Physik when he was twenty-two; the last publication was an editorial in the journal Common Cause which appeared a few months before his death in 1955. In the fifty-four-year interval, his published work ranged widely over relativity theory and quantum physics, nationalism, Judaism, war, peace, and education. Indeed, Einstein's literary output was so abundant that even many of his most informed admirers are not familiar with all of it. The Einstein Almanac takes a look at Einstein's year-by-year output, explaining his three-hundred most important publications and setting them into the context of his life, science, and world history. Concentr...

Euler-Lagrange Equations of Networks with Higher-Order Elements

Directory of Open Access Journals (Sweden)

Z. Biolek

2017-06-01

Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

Einstein and relativity

International Nuclear Information System (INIS)

Cullwick, E.G.

1979-01-01

Einstein published his Special Theory of Relativity in 1905 and in 1915 his General Theory which predicted the bending of light rays passing near the sun. This prediction was apparently confirmed experimentally in 1919 bringing Einstein popular acclaim. Einstein's work is reviewed and the question of whether he was in fact first in the field is examined with especial reference to the work of Maxwell, Lorentz and Poincare. (U.K.)

Distributed Fault-Tolerant Control of Networked Uncertain Euler-Lagrange Systems Under Actuator Faults.

Science.gov (United States)

Chen, Gang; Song, Yongduan; Lewis, Frank L

2016-05-03

This paper investigates the distributed fault-tolerant control problem of networked Euler-Lagrange systems with actuator and communication link faults. An adaptive fault-tolerant cooperative control scheme is proposed to achieve the coordinated tracking control of networked uncertain Lagrange systems on a general directed communication topology, which contains a spanning tree with the root node being the active target system. The proposed algorithm is capable of compensating for the actuator bias fault, the partial loss of effectiveness actuation fault, the communication link fault, the model uncertainty, and the external disturbance simultaneously. The control scheme does not use any fault detection and isolation mechanism to detect, separate, and identify the actuator faults online, which largely reduces the online computation and expedites the responsiveness of the controller. To validate the effectiveness of the proposed method, a test-bed of multiple robot-arm cooperative control system is developed for real-time verification. Experiments on the networked robot-arms are conduced and the results confirm the benefits and the effectiveness of the proposed distributed fault-tolerant control algorithms.

Einstein the searcher his work explained from dialogues with Einstein

CERN Document Server

Moszkowski, Alexander

2014-01-01

This volume, first published in 1921, presents a series of portraits of Einstein, thus offering glimpses in the character and private reflections of the man who changed the course of modern science. Intended neither as a biography, nor as a résumé of Einsteinian physics, Einstein: The Searcher instead focusses on Einstein's relationship with the scientific project as he himself conceived it, and so is still of contemporary significance for those puzzled by the spirit of scientific enquiry.

From Einstein to AXAF

International Nuclear Information System (INIS)

Tananbaum, H.

1990-01-01

The presentations at the 10th Anniversary Einstein Symposium and the articles in this book cover a wide variety of scientific topics describing some of the important advances and discoveries made with the Einstein Observatory. The breadth and depth of science carried out with Einstein has made it essentially impossible to cover fully individual subdisciplines in single review talks and papers. Some of the major Einstein highlights are summarized and the scientific prospects for AXAF are assessed. (author)

Einstein. A centenary volume

International Nuclear Information System (INIS)

French, A.P.

1979-01-01

The subject is divided as follows: part 1, reminiscences (of Einstein and his life, by various authors); part 2, Einstein and his work (includes accounts of special and general relativity, gravitation, the development of quantum physics and concepts of space and time); part 3, Einstein's letters; part 4, Einstein's writings (including accounts of electrodynamics of moving bodies, general relativity, method of theoretical physics and an elementary derivation of the equivalence of mass and energy). (U.K.)

An experiment for determining the Euler load by direct computation

Science.gov (United States)

Thurston, Gaylen A.; Stein, Peter A.

1986-01-01

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

International Nuclear Information System (INIS)

Kaneko, Yuta; Yoshida, Zensho

2014-01-01

Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term −ΔQ, just representing the current density (Q is a Clebsch variable, and Δ is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated

Euler Polynomials and Identities for Non-Commutative Operators

OpenAIRE

De Angelis, V.; Vignat, C.

2015-01-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

Classes of exact Einstein Maxwell solutions

Science.gov (United States)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes

Directory of Open Access Journals (Sweden)

Qinghui Du

2014-01-01

Full Text Available We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.

Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

Science.gov (United States)

Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

2018-04-01

The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

Methodology Einstein for energy audit and design of solar heat systems in industrial processes; Metodologia Einstein para auditoria energetica y diseno de sistemas de calor solar en procesos industriales

Energy Technology Data Exchange (ETDEWEB)

Schweiger, H.; Vannoni, C.; Danov, S.; Facci, E.

2008-07-01

Estimates show that 57% of the total industrial heat demand in EU countries is required at low (up to 100 degree centigrade) and medium temperature (up to 400 degree centigrade). An important part of this thermal energy demand can be covered by solar thermal energy. In the framework of the European project EINSTEIN (Expert-system for an Intelligent Supply of Thermal Energy in Industry), an expert system is being developed, where process optimisation, heat recovery, intelligent cold supply and renewable energy are integrated into a holistic energy audit methodology with the objective of reducing energy consumption in the industrial sector. EINSTEIN is being developed as a free and open source software project. (Author)

The ultimate quotable Einstein

CERN Document Server

2011-01-01

Here is the definitive new edition of the hugely popular collection of Einstein quotations that has sold tens of thousands of copies worldwide and been translated into twenty-five languages. The Ultimate Quotable Einstein features 400 additional quotes, bringing the total to roughly 1,600 in all. This ultimate edition includes new sections--"On and to Children," "On Race and Prejudice," and "Einstein's Verses: A Small Selection"--as well as a chronology of Einstein's life and accomplishments, Freeman Dyson's authoritative foreword, and new commentary by Alice Calaprice.

Ferroelectricity by Bose-Einstein condensation in a quantum magnet.

Science.gov (United States)

Kimura, S; Kakihata, K; Sawada, Y; Watanabe, K; Matsumoto, M; Hagiwara, M; Tanaka, H

2016-09-26

The Bose-Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose-Einstein condensates. Realization of Bose-Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose-Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose-Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl 3 , leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose-Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets.

Einstein from 'B' to 'Z'

CERN Document Server

Stachel, John

2002-01-01

John Stachel, the author of this collection of 37 published and unpublished articles on Albert Einstein, has written about Einstein and his work for over 40 years. Trained as a theoretical physicist specializing in the theory of relativity, he was chosen as the founding editor of The Collected papers of Albert Einstein 25 years ago, and is currently Director of the Boston University Center for Einstein Studies. Based on a detailed study of documentary evidence, much of which was newly discovered in the course of his work, Stachel debunks many of the old (and some new) myths about Einstein and offers novel insight into his life and work. Throughout the volume, a new, more human picture of Einstein is offered to replace the plaster saint of popular legend. In particular, a youthful Einstein emerges from the obscurity that previously shrouded his early years, and much new light is shed on the origins of the special and general theories of relativity. Also discussed in some detail are Einstein's troubled relatio...

Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates

Science.gov (United States)

Wasak, Tomasz; Chwedeńczuk, Jan

2018-04-01

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F =1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure—the local operations, the measurements, and the inequality—necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.

Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates.

Science.gov (United States)

Wasak, Tomasz; Chwedeńczuk, Jan

2018-04-06

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F=1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure-the local operations, the measurements, and the inequality-necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.

Einstein

CERN Document Server

Smith, Peter D

2003-01-01

Albert Einstein re-wrote the textbooks of science in 1905: physics since has been little more than a series of footnotes to the theories of a 26-year-old patent-office clerk. Einstein's science and emotional life come together in this vivid portrait of a rebellious and contradictory figure, a pacifist whose legendary equation E=mc2 opened scientists' eyes to the terrible power within every atom. 'To punish me for my contempt for authority,' he lamented, 'Fate has made me an authority myself.'

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system

Euler's pioneering equation the most beautiful theorem in mathematics

CERN Document Server

Wilson, Robin

2018-01-01

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Einstein-Friedmann equation, nonlinear dynamics and chaotic behaviours

International Nuclear Information System (INIS)

Tanaka, Yosuke; Nakano, Shingo; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

2009-01-01

We have studied the Einstein-Friedmann equation [Case 1] on the basis of the bifurcation theory and shown that the chaotic behaviours in the Einstein-Friedmann equation [Case 1] are reduced to the pitchfork bifurcation and the homoclinic bifurcation. We have obtained the following results: (i) 'The chaos region diagram' (the p-λ plane) in the Einstein-Friedmann equation [Case 1]. (ii) 'The chaos inducing chart' of the homoclinic orbital systems in the unforced differential equations. We have discussed the non-integrable conditions in the Einstein-Friedmann equation and proposed the chaotic model: p=p 0 ρ n (n≥0). In case n≠0,1, the Einstein-Friedmann equation is not integrable and there may occur chaotic behaviours. The cosmological constant (λ) turns out to play important roles for the non-integrable condition in the Einstein-Friedmann equation and also for the pitchfork bifurcation and the homoclinic bifurcation in the relativistic field equation. With the use of the E-infinity theory, we have also discussed the physical quantities in the gravitational field equations, and obtained the formula logκ=-10(1/φ) 2 [1+(φ) 8 ]=-26.737, which is in nice agreement with the experiment (-26.730).

Nilakantha, Euler and 1t

Indian Academy of Sciences (India)

It is not hard to show that the series converges, for by com- bining pairs of terms it can be ..... not escape Euler's attention-but then few things did!) We consider the function ... the proof. In particular there is no such thing as an unrig- orous proof.

An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

Euler's fluid equations: Optimal control vs optimization

International Nuclear Information System (INIS)

Holm, Darryl D.

2009-01-01

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

CERN Document Server

Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu

2015-01-01

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...

Albert Einstein a biography

CERN Document Server

Fölsing, Albrecht

1997-01-01

Albert Einstein's achievements are not just milestones in the history of science; decades ago they became an integral part of the twentieth-century world in which we live. Like no other modern physicist he altered and expanded our understanding of nature. Like few other scholars, he stood fully in the public eye. In a world changing with dramatic rapidity, he embodied the role of the scientist by personal example. Albrecht Folsing, relying on previously unknown sources and letters, brings Einstein's "genius" into focus. Whereas former biographies, written in the tradition of the history of science, seem to describe a heroic Einstein who fell to earth from heaven, Folsing attempts to reconstruct Einstein's thought in the context of the state of research at the turn of the century. Thus, perhaps for the first time, Einstein's surroundings come to light.

Optical absorption in a degenerate Bose-Einstein gas

International Nuclear Information System (INIS)

Yip, S.K.

2002-01-01

We develop a theory on optical absorption in a dilute Bose-Einstein gas at low temperatures. This theory is motivated by the Bogoliubov theory of elementary excitations for this system, and takes into account explicitly the modification of the nature and dispersion of elementary excitations due to Bose-Einstein condensation. Our results show important differences from existing theories

Einstein's statistical mechanics

Energy Technology Data Exchange (ETDEWEB)

Baracca, A; Rechtman S, R

1985-08-01

The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject.

Einstein's statistical mechanics

International Nuclear Information System (INIS)

Baracca, A.; Rechtman S, R.

1985-01-01

The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject. (author)

Einstein algebras and general relativity

International Nuclear Information System (INIS)

Heller, M.

1992-01-01

A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs

Albert Einsteins Wonderjaar

NARCIS (Netherlands)

Dieks, D.G.B.J.

In het jaar 1905 publiceerde Albert Einstein een reeks artikelen die een omwenteling voor de wetenschap betekende. En toch bleef Einstein een kind van zijn tijd, van een eeuw die in het teken stond van dynamo’s, raderen en stoommachines.

ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.

On the Euler Function of the Catalan Numbers

Science.gov (United States)

2012-02-26

ON THE EULER FUNCTION OF THE CATALAN NUMBERS FLORIAN LUCA AND PANTELIMON STĂNICĂ Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r...where r is a fixed rational number , Ck is the kth Catalan number and φ is the Euler function. We note that the number r = 4 is special for this...observation concerning φ(Cn+1)/φ(Cn) For a positive integer n, let (1) Cn = 1 n+ 1 ( 2n n ) be the n-th Catalan number . For a positive integer m we put φ(m) for

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

The Maxwell-Einstein system, Ward identities and the Vilkovisky construction

DEFF Research Database (Denmark)

Nielsen, N. K.

2012-01-01

The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell-Einstein theory. The construction of Vilkovisky and DeWitt for removal of this depende......The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell-Einstein theory. The construction of Vilkovisky and DeWitt for removal...

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

Science.gov (United States)

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

Local existence of solutions to the Euler-Poisson system, including densities without compact support

Science.gov (United States)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Rediscovering Einstein's legacy: How Einstein anticipates Kuhn and Feyerabend on the nature of science.

Science.gov (United States)

Oberheim, Eric

2016-06-01

Thomas Kuhn and Paul Feyerabend promote incommensurability as a central component of their conflicting accounts of the nature of science. This paper argues that in so doing, they both develop Albert Einstein's views, albeit in different directions. Einstein describes scientific revolutions as conceptual replacements, not mere revisions, endorsing 'Kant-on-wheels' metaphysics in light of 'world change'. Einstein emphasizes underdetermination of theory by evidence, rational disagreement in theory choice, and the non-neutrality of empirical evidence. Einstein even uses the term 'incommensurable' specifically to apply to challenges posed to comparatively evaluating scientific theories in 1949, more than a decade before Kuhn and Feyerabend. This analysis shows how Einstein anticipates substantial components of Kuhn and Feyerabend's views, and suggests that there are strong reasons to suspect that Kuhn and Feyerabend were directly inspired by Einstein's use of the term 'incommensurable', as well as his more general methodological and philosophical reflections. Copyright © 2015 Elsevier Ltd. All rights reserved.

Einstein and cosmology

International Nuclear Information System (INIS)

Gekman, O.

1982-01-01

The brief essay of the development of the main ideas of relativistic cosmology is presented. The Einstein's cosmological work about the Universe - ''Cosmological considerations in connection with the general relativity theory'' - gave the basis to all further treatments in this field. In 1922 A. Friedman's work appeared, in which the first expanding Universe model was proposed as a solution of the Einstein field equations. The model was spherically closed, but its curvature radius was a function of time. About 1955 the searches for anisotropic homogeneous solutions to Einstein field equation began. It turned out that isotropic cosmological models are unstable in general. The predominant part of them transform to anisotropic at insignificant breaking of isotropy. The discovery of isotropic background cosmic radiation in 1965, along with the Hubble low of the Universe expansion, served as the direct confirmation of cosmology based on the Einstein theory

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates

Science.gov (United States)

Fadel, Matteo; Zibold, Tilman; Décamps, Boris; Treutlein, Philipp

2018-04-01

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.

Einstein's error

International Nuclear Information System (INIS)

Winterflood, A.H.

1980-01-01

In discussing Einstein's Special Relativity theory it is claimed that it violates the principle of relativity itself and that an anomalous sign in the mathematics is found in the factor which transforms one inertial observer's measurements into those of another inertial observer. The apparent source of this error is discussed. Having corrected the error a new theory, called Observational Kinematics, is introduced to replace Einstein's Special Relativity. (U.K.)

De Sitter en Einstein. ‘Het lijkt mij dat Einstein hier een vergissing begaan heeft’

Directory of Open Access Journals (Sweden)

Jan Guichelaar

2016-10-01

Full Text Available De Sitter and EinsteinWillem de Sitter’s interest in gravity was based on his work on celestial mechanics, in particular on the four big moons of Jupiter. His work on cosmology was based on the general theory of relativity of Albert Einstein. De Sitter published in 1917, on request of Arthur Eddington to inform the English astronomers, a series of four articles in The Observatory and the Monthly Notices of the Royal Astronomical Society. Einstein developed his own cosmological models, containing mass. De Sitter found a different solution and described a universe without mass. Einstein could not accept De Sitter’s model and they ‘fought out’ two controversies in their correspondence. In theend Einstein had to confess De Sitter was mainly right in his criticisms. In 1932 Einstein and De Sitter published an article on a new model, the so-called Einstein-De Sitter Model of the universe. So, De Sitter was able to do fundamental work in classical celestial mechanics as well as in the new cosmological theories.

Einstein-Rosen gravitational waves

International Nuclear Information System (INIS)

Astefanoaei, Iordana; Maftei, Gh.

2001-01-01

In this paper we analyse the behaviour of the gravitational waves in the approximation of the far matter fields, considering the indirect interaction between the matter sources and the gravitational field, in a cosmological model based on the Einstein-Rosen solution, Because the properties of the gravitational waves obtained as the solutions of Einstein fields equations (the gravitational field equations) are most obvious in the weak gravitational fields we consider here, the gravitational field in the linear approximation. Using the Newman-Penrose formalism, we calculate in the null-tetradic base (e a ), the spin coefficients, the directional derivates and the tetradic components of Ricci and Weyl tensors. From the Einstein field equations we obtained the solution for b(z, t) what described the behaviour of gravitational wave in Einstein-Rosen Universe and in the particular case, when t → ∞, p(z, t) leads us to the primordial gravitational waves in the Einstein-Rosen Universe. (authors)

Bernoulli and Euler Numbers

Directory of Open Access Journals (Sweden)

Dae San Kim

2012-01-01

Full Text Available We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x∈ℚ[x]∣deg p(x≤n} be the (n+1-dimensional vector space over ℚ. Then we show that {H0(x,H1(x,…,Hn(x} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications.

Extrapolating an Euler class

NARCIS (Netherlands)

Van der Kallen, Wilberd|info:eu-repo/dai/nl/117156108

2015-01-01

Let R be a noetherian ring of dimension d and let n be an integer so that n≤d≤2n-3. Let (a1,..., an+1) be a unimodular row so that the ideal J=(a1,..., an) has height n. Jean Fasel has associated to this row an element [(J, ωJ)] in the Euler

Holonomy of Einstein Lorentzian manifolds

International Nuclear Information System (INIS)

Galaev, Anton S

2010-01-01

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.

Einstein (1879-1955)

International Nuclear Information System (INIS)

Anon.

1980-01-01

In the first part of this book a historical review of Einstein life and works are presented. In the second part papers about different aspects of quantum mechanics are given. The third part is devoted to a round table on Einstein, Podolski and Rosen paradox [fr

New Einstein-Sasaki and Einstein spaces from Kerr-de Sitter

International Nuclear Information System (INIS)

Cvetic, M.; Lue, H.; Pope, C.N.; Page, Don N.

2009-01-01

In this paper, which is an elaboration of our results in Phys. Rev. Lett. 95:071101, 2005 (hep-th/0504225), we construct new Einstein-Sasaki spaces L p,q,r 1 ,...,r n-1 in all odd dimensions D = 2n+1 ≥ 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1) n+1 principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r 1 ,...,r n-1 ), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds L p,q,r 1 ,...,r n-1 . We also construct new complete and non-singular compact Einstein spaces Λ p,q,r 1 ,...,r n in D = 2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken.

Once upon Einstein

CERN Document Server

Damour, Thibault

2006-01-01

It is well known that Einstein founded twentieth-century physics with his work on relativity and quanta, but what do we really know about these ground breaking ideas? How were they discovered? What should we retain today from the conceptual upheavals he initiated? Through a selection of concrete scenes taken from Einstein's life, the author offers a view into the formation of his theories, as well as reminders of the day-to-day applications of his ideas. Simultaneously the reader is lead through a reflection on their philosophical impact: How should we think of time according to the theory of relativity, which removes any meaningful "now" and shows that twins can have different ages? How should we think of reality when quantum theory predicts that spatially separated objects nevertheless remain connected through Einstein's notion of "entanglement," which has recently been verified through scientific observation? This book puts readers in Einstein's place, allowing them to share some of those particular moment...

Albert Einstein Centenary

CERN Document Server

Weisskopf, Victor Frederick; CERN. Geneva

1979-01-01

A socially engaged scientist by V. F. WEISSKOPF. On the origin of the Einstein-Russell statement on nuclear weapon by H. S. BURHOP. This week, we pay homage to Albert Einstein, the giant of twentieth-century physics born exactly 100 years ago on 14 March 1879 in Ulm, Germany. At the height of his career, Einstein made a whole series of monumental contributions to physics, including the elaborate theories of special and general relativity which revolutionized human thought and marked a major breakthrough in our understanding to the Universe. Along with quantum mechanics, relativity is one of the twin pillars of understanding which allow us here at CERN to study the behaviour of the tiniest components of matter. The development of quantum mechanics took the combined efforts of some of the greatest scientists the world has known, while relativity was developed almost single-handed by Einstein. The centenary of his birth is being commemorated all over the world. Exhibitions and symposia are being organized, books...

An Einstein encyclopedia

CERN Document Server

Calaprice, Alice; Schulmann, Robert

2015-01-01

This is the single most complete guide to Albert Einstein’s life and work for students, researchers, and browsers alike. Written by three leading Einstein scholars who draw on their combined wealth of expertise gained during their work on the Collected Papers of Albert Einstein, this authoritative and accessible reference features more than one hundred entries and is divided into three parts covering the personal, scientific, and public spheres of Einstein’s life. An Einstein Encyclopedia contains entries on Einstein’s birth and death, family and romantic relationships, honors and awards, educational institutions where he studied and worked, citizenships and immigration to America, hobbies and travels, plus the people he befriended and the history of his archives and the Einstein Papers Project. Entries on Einstein’s scientific theories provide useful background and context, along with details about his assistants, collaborators, and rivals, as well as physics concepts related to his work. Coverage o...

Thermodynamic fluctuations within the Gibbs and Einstein approaches

International Nuclear Information System (INIS)

Rudoi, Yurii G; Sukhanov, Alexander D

2000-01-01

A comparative analysis of the descriptions of fluctuations in statistical mechanics (the Gibbs approach) and in statistical thermodynamics (the Einstein approach) is given. On this basis solutions are obtained for the Gibbs and Einstein problems that arise in pressure fluctuation calculations for a spatially limited equilibrium (or slightly nonequilibrium) macroscopic system. A modern formulation of the Gibbs approach which allows one to calculate equilibrium pressure fluctuations without making any additional assumptions is presented; to this end the generalized Bogolyubov - Zubarev and Hellmann - Feynman theorems are proved for the classical and quantum descriptions of a macrosystem. A statistical version of the Einstein approach is developed which shows a fundamental difference in pressure fluctuation results obtained within the context of two approaches. Both the 'genetic' relation between the Gibbs and Einstein approaches and the conceptual distinction between their physical grounds are demonstrated. To illustrate the results, which are valid for any thermodynamic system, an ideal nondegenerate gas of microparticles is considered, both classically and quantum mechanically. Based on the results obtained, the correspondence between the micro- and macroscopic descriptions is considered and the prospects of statistical thermodynamics are discussed. (reviews of topical problems)

Strong field effects on binary systems in Einstein-aether theory

International Nuclear Information System (INIS)

Foster, Brendan Z.

2007-01-01

'Einstein-aether' theory is a generally covariant theory of gravity containing a dynamical preferred frame. This article continues an examination of effects on the motion of binary pulsar systems in this theory, by incorporating effects due to strong fields in the vicinity of neutron star pulsars. These effects are included through an effective approach, by treating the compact bodies as point particles with nonstandard, velocity dependent interactions parametrized by dimensionless sensitivities. Effective post-Newtonian equations of motion for the bodies and the radiation damping rate are determined. More work is needed to calculate values of the sensitivities for a given fluid source; therefore, precise constraints on the theory's coupling constants cannot yet be stated. It is shown, however, that strong field effects will be negligible given current observational uncertainties if the dimensionless couplings are less than roughly 0.1 and two conditions that match the PPN parameters to those of pure general relativity are imposed. In this case, weak field results suffice. There then exists a one-parameter family of Einstein-aether theories with 'small-enough' couplings that passes all current observational tests. No conclusion can be reached for larger couplings until the sensitivities for a given source can be calculated

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations

International Nuclear Information System (INIS)

Yuen, Manwai

2011-01-01

In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.

A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

Czech Academy of Sciences Publication Activity Database

Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.

2016-01-01

Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963

Fractional Euler Limits and Their Applications

OpenAIRE

MacNamara, Shev; Henry, Bruce I; McLean, William

2016-01-01

Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.

Neuromythology of Einstein's brain.

Science.gov (United States)

Hines, Terence

2014-07-01

The idea that the brain of the great physicist Albert Einstein is different from "average" brains in both cellular structure and external shape is widespread. This belief is based on several studies examining Einstein's brain both histologically and morphologically. This paper reviews these studies and finds them wanting. Their results do not, in fact, provide support for the claim that the structure of Einstein's brain reflects his intellectual abilities. Copyright © 2014 Elsevier Inc. All rights reserved.

On some types of exact solutions of the Einstein equation. 2

International Nuclear Information System (INIS)

Obukhov, V.V.

1978-01-01

Several types of the Einstein spaces which can describe gravitational waves are investigated. When the solutions of the Einstein equations are found, additional conditions are imposed on the metrics under consideration. It is required: 1) that the spaces should admit the two-parametric Abelian group of motion; 2) that the wave coordinate system would be privileged; 3) that bicharacteristics of the Einstein equation would satisfy the harmonicity condition. The superposition of the enumerated conditions has made it possible to perform a complete integration of the Einstein equations. The solutions obtained are interpreted as the wave ones

How Einstein changed the world

International Nuclear Information System (INIS)

Boudenot, J.C.

2005-01-01

This book allows the reader to understand in a simple but detailed way the importance of the work of Einstein and its implications in the physics of today. The author first draws a biography of Einstein, then outlines the knowledge of physics at the beginning of the twentieth century, then describes the major contributions of Einstein to the brownian motion, the mass-energy equivalence, relativity and the notion of quantum, and ends by showing that the life-long Einstein's quest for a unitarian theory is still a present-day issue. (A.C.)

Properties of general relativistic irrotational binary neutron stars at the innermost orbit

International Nuclear Information System (INIS)

Uryu, K.; Shibata, M.

2001-01-01

We investigate properties of binary neutron stars around innermost orbits, assuming that the binary is equal mass and in quasiequilibrium. The quasiequilibrium configurations are numerically computed assuming the existence of a helicoidal Killing vector, conformal flatness for spatial components of the metric, and irrotational velocity field for the neutron stars. The computation is performed for the polytropic equation of state with a wide range of the polytropic index n (= 0.5, 0.66667, 0.8, 1, 1.25), and compactness of neutron stars (M/R) ∞ (= 0.03-0.3). Quasiequilibrium sequences of constant rest mass are appropriate models for the final evolution phase of binary neutron stars. It is found that these sequences are always terminated at the innermost orbit where a cusp (inner Lagrange point) appears at the inner edges of the stellar surface. We apply a turning point method to determine the stability of the innermost orbits and found that the innermost stable circular orbit (ISCO) exists for stiff equations of state (n = 0.5 with any (M/R) ∞ and n = 0.66667 with (M/R) ∞ > or ∼ 0.17). The ISCO for n = 0.5 is carefully analyzed. It is clarified that the ISCO are mainly determined by a hydrodynamic instability for realistic compactness of the neutron stars as 0.14 ∞ < or ∼ 0.2. These configurations at the innermost orbits can be used as initial conditions for fully general relativistic simulation for the binary neutron star merger. (author)

Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions

International Nuclear Information System (INIS)

Cordier, S.

1995-05-01

In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs

Once Upon Einstein

International Nuclear Information System (INIS)

Giannetto, E

2007-01-01

Thibault Damour is a theoretical physicist, and a member of the French Academy of Sciences. This book is the translation, by Eric Novak, of the original French Si Einstein m'etait conte (Le Cherche Midi, 2005). It is neither a book of theoretical physics nor a biography of Einstein. It is not a book of history nor philosophy of science. In Damour's words it was written to encourage the reader to share with Einstein 'those times when he understood some part of the hidden order of the universe'. It is a relatively short book, written in a very fluent style, but it deals with all the major problems and achievements of Einstein's works. Starting from special relativity, it continues with general relativity, quantum theories, unified field theory and a brief overview of the actual research related to Einstein's legacy. It is essentially a popular science book with some related exploration in history and philosophy to interpret physical theories. The most important problem discussed by Damour is the nature of time. On this subject, there is a very interesting short paragraph (pp 33--35) dedicated to the reception of the relativity idea by the great writer Marcel Proust and its counterpart within A la Recherche du Temps Perdu. A correct discussion of the implications of a relativistic time should imply the distinction of the different possible interpretations of this concept. Damour seems to conclude that only one interpretation is possible: 'time does not exist', flowing of time is an illusion. One has to know that Einstein's ideas on time were related to Spinoza's perspective of a knowledge sub specie aeternitatis. However, other interpretations are possible and are related to the idea of time as an actuality. Damour speaks about the controversy between Einstein and Bergson, but Bergson is considered as a philosopher who did not understand relativity. This philosophical problem of relativistic time is indeed related to a historical problem briefly discussed by Damour

More accurate theory for Bose-Einstein condensation fraction

International Nuclear Information System (INIS)

Biswas, Shyamal

2008-01-01

Bose-Einstein statistics is derived in the thermodynamic limit when the ratio of system size to thermal de Broglie wavelength goes to infinity. However, according to the experimental setup of Bose-Einstein condensation of harmonically trapped Bose gas of alkali atoms, the ratio near the condensation temperature (T o ) is 30-50. And, at ultralow temperatures well below T o , this ratio becomes comparable to 1. We argue that finite size as well as the ultralow temperature induces corrections to Bose-Einstein statistics. From the corrected statistics we plot condensation fraction versus temperature graph. This theoretical plot satisfies well with the experimental plot [A. Griesmaier et al., Phys. Rev. Lett. 94 (2005) 160401

Einstein-Rosen 'bridge' needs lightlike brane source

International Nuclear Information System (INIS)

Guendelman, Eduardo; Kaganovich, Alexander; Nissimov, Emil; Pacheva, Svetlana

2009-01-01

The Einstein-Rosen 'bridge' wormhole solution proposed in the classic paper (Einstein and Rosen (1935) ) does not satisfy the vacuum Einstein equations at the wormhole throat. We show that the fully consistent formulation of the original Einstein-Rosen 'bridge' requires solving Einstein equations of bulk D=4 gravity coupled to a lightlike brane with a well-defined world-volume action. The non-vanishing contribution of Einstein-Rosen 'bridge' solution to the right-hand side of Einstein equations at the throat matches precisely the surface stress-energy tensor of the lightlike brane which automatically occupies the throat ('horizon straddling') - a feature triggered by the world-volume lightlike brane dynamics.

Einstein's daughter the search for Lieserl

CERN Document Server

Zackheim, Michele

1999-01-01

A thoroughly gripping and groundbreaking investigation into the mysterious fate of Albert Einstein's illegitimate daughter. Albert Einstein fell in love with Mileva Maric, the woman who would become his first wife, when they were students at the Zurich Polytechnic Institute. When Maric conceived a child out of wedlock, she went home to her family in Serbia to have the child. Lieserl Maric Einstein was born in 1902. Though Einstein and Maric married the following year, Lieserl was left in the care of her grandparents and never became a part of the Einstein family. In fact, her very existence was unknown until the recent discovery of a cache of letters between Einstein and Maric. The final reference to Lieserl comes in a September 1903 letter, when, at the age of approximately eighteen months, she simply disappears. What happened to Einstein's daughter is the most potent mystery to emerge from the mythology that surrounds one of the century's legendary figures, owing in large part to the careful and apparent...

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper

2015-01-07

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.

The Einstein@Home search for gravitational waves and neutron stars

CERN Multimedia

CERN. Geneva

2012-01-01

Einstein@Home is a volunteer distributed computing project with more than 300,000 participants. Like other volunteer computing projects, Einstein@Home harvests idle computer cycles from the the laptop and desktop computers of the general public. This provides enormous computing power, on the scale of some of the world's fastest supercomputers, but at very low cost. I describe the current status of the Einstein@Home search for new neutron stars, using data from the Laser Interferometer Gravitational-wave Observatory (LIGO), from the Arecibo and Parkes radio telescopes, and from the Fermi gamma-ray satellite. The sensitivity of these searches is limited by computing power, so the Einstein@Home approach allows the detection of weaker signals than more conventional approaches. In the past 18 months, Einstein@Home has discovered more than 20 new radio and gamma-ray pulsars, including a number of particularly interesting and exotic systems.

Bose-Einstein correlations

International Nuclear Information System (INIS)

Zalewski, Kacper

2000-01-01

The effect of Bose-Einstein correlations on multiplicity distributions of identical pions is discussed. It is found that these correlations affect significantly the observed multiplicity distributions, but Einstein's condensation is unlikely to be achieved, unless 'cold spots', i.e. regions, where groups of pions with very small relative momenta are produced, occur in high energy heavy-ion collisions

Einstein's philosophy of physics

International Nuclear Information System (INIS)

Seeger, R.J.

1979-01-01

Sources of Einstein's philosophical ideas are discussed. Einstein was indebted to Mach and Poincare, and espoused more or less a logical empiricism. He looked upon Nature as real, rational, and understandable, at least to an extent

Leonhard Euler's Wave Theory of Light

DEFF Research Database (Denmark)

Pedersen, Kurt Møller

2008-01-01

Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...... of achromatic lenses, the explanation of colors of thin plates and of the opaque bodies as proof of his theory. When it came to the fundamental issues, the correctness of his dispersion law and the prediction of frequencies of light he was not at all successful. His wave theory degenerated, and it was not until...... is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction...

Superenergy tensors in the Einstein-Cartan theory of gravitation

International Nuclear Information System (INIS)

Garecki, J.

1981-01-01

In this paper we study systematically a generalization of the notion of ''superenergy tensors'' which has been introduced previously in the framework of the General Theory of Relativity on the Einstein-Cartan Theory of Gravitation. It is shown, by means of expansion in the normal coordinate system that the generalization is analytically simple only for the Einstein formulation of conservation laws. (author)

Bose-Einstein condensation and chiral phase transition in linear sigma model

International Nuclear Information System (INIS)

Shu Song; Li Jiarong

2005-01-01

With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A μ-T phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can occur either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area where there is no Bose-Einstein condensation

Correspondence passed between Einstein and Schroedinger; La correspondance entre Einstein et Schroedinger

Energy Technology Data Exchange (ETDEWEB)

Balibar, F. [Paris-7 Univ., 75 (France)

1992-12-31

The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories.

Einstein boundary conditions for the 3+1 Einstein equations

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2003-01-01

In the 3+1 framework of the Einstein equations for the case of a vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space derivatives of the three-metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations up to linear combinations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields

Euler-Vector Clustering of GPS Velocities Defines Microplate Geometry in Southwest Japan

Science.gov (United States)

Savage, J. C.

2018-02-01

I have used Euler-vector clustering to assign 469 GEONET stations in southwest Japan to k clusters (k = 2, 3,..., 9) so that, for any k, the velocities of stations within each cluster are most consistent with rigid-block motion on a sphere. That is, I attempt to explain the raw (i.e., uncorrected for strain accumulation), 1996-2006 velocities of those 469 Global Positioning System stations by rigid motion of k clusters on the surface of a spherical Earth. Because block geometry is maintained as strain accumulates, Euler-vector clustering may better approximate the block geometry than the values of the associated Euler vectors. The microplate solution for each k is constructed by merging contiguous clusters that have closely similar Euler vectors. The best solution consists of three microplates arranged along the Nankaido Trough-Ryukyu Trench between the Amurian and Philippine Sea Plates. One of these microplates, the South Kyushu Microplate (an extension of the Ryukyu forearc into the southeast corner of Kyushu), had previously been identified from paleomagnetic rotations. Relative to ITRF2000 the three microplates rotate at different rates about neighboring poles located close to the northwest corner of Shikoku. The microplate model is identical to that proposed in the block model of Wallace et al. (2009, https://doi.org/10.1130/G2522A.1) except in southernmost Kyushu. On Shikoku and Honshu, but not Kyushu, the microplate model is consistent with that proposed in the block models of Nishimura and Hashimoto (2006, https://doi.org/10.1016/j.tecto.2006.04.017) and Loveless and Meade (2010, https://doi.org/10.1029/2008JB006248) without the low-slip-rate boundaries proposed in the latter.

Perturbational blowup solutions to the compressible Euler equations with damping.

Science.gov (United States)

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Test of Einstein locality

International Nuclear Information System (INIS)

Roos, Matts

1980-11-01

Einstein locality imples that spacelike separated coherent quantum systems do not interfere, and that all interferences must propagate with at most the speed of light. It then follows that the reaction e + e - →K 0 antiK 0 must yield some Ksub(s)Ksuu(s) decays in apparent violation of P and C conservation. (author)

Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid

Directory of Open Access Journals (Sweden)

Kanok Hournkumnuard

2014-01-01

Full Text Available The process of high gradient magnetic separation (HGMS using a microferromagnetic wire for capturing weakly magnetic nanoparticles in the irrotational flow of inviscid fluid is simulated by using parallel algorithm developed based on openMP. The two-dimensional problem of particle transport under the influences of magnetic force and fluid flow is considered in an annular domain surrounding the wire with inner radius equal to that of the wire and outer radius equal to various multiples of wire radius. The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. Concentration distribution of the particles around the wire is investigated and compared with some previously reported results and shows the good agreement between them. The results show the feasibility of accumulating weakly magnetic nanoparticles in specific regions on the wire surface which is useful for applications in biomedical and environmental works. The speedup of parallel simulation ranges from 1.8 to 21 depending on the number of threads and the domain problem size as well as the number of iterations. With the nature of computing in the application and current multicore technology, it is observed that 4–8 threads are sufficient to obtain the optimized speedup.

On some classes of super quasi-Einstein manifolds

International Nuclear Information System (INIS)

Ozguer, Cihan

2009-01-01

Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition C ∼ .S=0 on a super quasi-Einstein manifold, where C ∼ and S denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.

Null strings and complex Einstein-Maxwell fields with cosmological constant

International Nuclear Information System (INIS)

Garcia, A.; Plebanski, J.F.; Robinson, I.

1977-01-01

Previous results of Plebanski and Robinson (Phys. Rev. Lett.; 37:493 (1976)) concerning left-degenerate Einstein-flat complex space-times and preliminary results concerning the electromagnetic field, are here generalized and worked out in some detail for the system of Einstein-Maxwell equations with a cosmological constant. On the assumption that there exists a congruence of totally null surfaces, the system is reduced to a pair of equations for the two unknown functions. (author)

Bose-Einstein condensation of excitons in Cu2O

International Nuclear Information System (INIS)

Snoke, D.W.

1990-01-01

Free excitons provide the only experimental system other than helium in which the behavior of particles with mass is known to follow Bose-Einstein statistics. Experimental observations are presented of the kinetic energy distribution of excitons in the direct-gap semiconductor Cu 2 O, both the triplet orthoexciton state and the singlet paraexciton state. The density and temperature of the exciton gas closely follow the phase boundary for Bose-Einstein condensation. At the highest densities, the lower-lying paraexcitons take on an anomalous energy distribution with a sharp, high-energy edge. This odd distribution of particle energies may be associated with Bose-Einstein condensation into a state with nonzero momentum. Indeed, the excitons leave the region of their creation at supersonic velocities. In addition to the experimental observations, theoretical models are presented for several aspects of this nonequilibrium system. The equilibration of a nearly-ideal boson gas is modeled, finding that a significant time is required for the approach to condensation. The temperature and density of the excitons in steady state are modeled based on known classical kinetic effects in semiconductors, and the effects of Bose-Einstein statistics on these processes estimated

Once Upon Einstein

Energy Technology Data Exchange (ETDEWEB)

Giannetto, E [Dipartimento di Fisica ' A Volta' , via A Bassi 6, I-27100 Pavia (Italy)

2007-07-20

Thibault Damour is a theoretical physicist, and a member of the French Academy of Sciences. This book is the translation, by Eric Novak, of the original French Si Einstein m'etait conte (Le Cherche Midi, 2005). It is neither a book of theoretical physics nor a biography of Einstein. It is not a book of history nor philosophy of science. In Damour's words it was written to encourage the reader to share with Einstein 'those times when he understood some part of the hidden order of the universe'. It is a relatively short book, written in a very fluent style, but it deals with all the major problems and achievements of Einstein's works. Starting from special relativity, it continues with general relativity, quantum theories, unified field theory and a brief overview of the actual research related to Einstein's legacy. It is essentially a popular science book with some related exploration in history and philosophy to interpret physical theories. The most important problem discussed by Damour is the nature of time. On this subject, there is a very interesting short paragraph (pp 33--35) dedicated to the reception of the relativity idea by the great writer Marcel Proust and its counterpart within A la Recherche du Temps Perdu. A correct discussion of the implications of a relativistic time should imply the distinction of the different possible interpretations of this concept. Damour seems to conclude that only one interpretation is possible: 'time does not exist', flowing of time is an illusion. One has to know that Einstein's ideas on time were related to Spinoza's perspective of a knowledge sub specie aeternitatis. However, other interpretations are possible and are related to the idea of time as an actuality. Damour speaks about the controversy between Einstein and Bergson, but Bergson is considered as a philosopher who did not understand relativity. This philosophical problem of relativistic time is indeed related to a

The matrix Euler-Fermat theorem

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2004-01-01

We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

Einstein-Podolsky-Rosen entanglement and steering in two-well Bose-Einstein-condensate ground states

Science.gov (United States)

He, Q. Y.; Drummond, P. D.; Olsen, M. K.; Reid, M. D.

2012-08-01

We consider how to generate and detect Einstein-Podolsky-Rosen (EPR) entanglement and the steering paradox between groups of atoms in two separated potential wells in a Bose-Einstein condensate. We present experimental criteria for this form of entanglement and propose experimental strategies for detecting entanglement using two- or four-mode ground states. These approaches use spatial and/or internal modes. We also present higher-order criteria that act as signatures to detect the multiparticle entanglement present in this system. We point out the difference between spatial entanglement using separated detectors and other types of entanglement that do not require spatial separation. The four-mode approach with two spatial and two internal modes results in an entanglement signature with spatially separated detectors, conceptually similar to the original EPR paradox.

Chaotic dynamics of flexible Euler-Bernoulli beams

Energy Technology Data Exchange (ETDEWEB)

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

Conformal Einstein spaces

International Nuclear Information System (INIS)

Kozameh, C.N.; Newman, E.T.; Tod, K.P.

1985-01-01

Conformal transformations in four-dimensional. In particular, a new set of two necessary and sufficient conditions for a space to be conformal to an Einstein space is presented. The first condition defines the class of spaces conformal to C spaces, whereas the last one (the vanishing of the Bach tensor) gives the particular subclass of C spaces which are conformally related to Einstein spaces. (author)

Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

International Nuclear Information System (INIS)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu

2015-01-01

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.

A New Euler's Formula for DNA Polyhedra

Science.gov (United States)

Hu, Guang; Qiu, Wen-Yuan; Ceulemans, Arnout

2011-01-01

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components , of crossings , and of Seifert circles are related by a simple and elegant formula: . This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus. PMID:22022596

Albert Einstein 1879-1955.

Science.gov (United States)

Physics Today, 1979

1979-01-01

Celebrates the centennial of Einstein's birth with an eight-page pictorial biography and two special articles: (1) Einstein the catalyst; and (2) Unitary field theories. His special and general theories of relativity and his contributions to quantum physics and other topics are also presented. (HM)

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates.

Science.gov (United States)

Fadel, Matteo; Zibold, Tilman; Décamps, Boris; Treutlein, Philipp

2018-04-27

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Einstein: A Historical Perspective

Science.gov (United States)

Kormos-Buchwald, Diana

2015-04-01

In late 1915, Albert Einstein (1879-1955) completed as series of papers on a generalized theory of gravitation that were to constitute a major conceptual change in the history of modern physics and the crowning achievement of his scientific career. But this accomplishment came after a decade of intense intellectual struggle and was received with muted enthusiasm. Einstein's previously unpublished writings and massive correspondence, edited by the Einstein Papers Project, provide vivid insights into the historical, personal, and scientific context of the formulation, completion, and reception of GR during the first decades of the 20th century.

An Einstein-Goedel universe

International Nuclear Information System (INIS)

Vaidya, P.C.

1978-01-01

The metric for the standard static Einstein model of the universe can be expressed in coordinates for which a congruence of spacelike world lines of the model will be twisting. A method of 'shifting the twist' has been devised by which the twist on spacelike world lines is shifted onto the timelike world lines. The model universe then becomes Goedel's model. A combined Einstein-Goedel model containing a parameter epsilon is obtained. Switching epsilon from +1 to -1 will effect the shift of twist in the world lines and lead from the Einstein model to the Goedel model. (author)

Beyond Einstein

Science.gov (United States)

Hertz, P.

2003-03-01

The Structure and Evolution of the Universe (SEU) theme within NASA's Office of Space Science seeks to explore and understand the dynamic transformations of energy in the Universe - the entire web of biological and physical interactions that determine the evolution of our cosmic habitat. This search for understanding will enrich the human spirit and inspire a new generation of explorers, scientists, and engineers. To that end, NASA's strategic planning process has generated a new Roadmap to enable those goals. Called "Beyond Einstein", this Roadmap identifies three science objectives for the SEU theme: (1) Find out what powered the Big Bang; (2) Observe how black holes manipulate space, time, and matter; and (3) Identify the mysterious dark energy pullingthe Universe apart. These objectives can be realized through a combination of large observatories (Constellation-X, LISA), moderate sized, PI-led missions (the Einstein Probes), and a contuinuing program of technology development, research and analysis, and education/public outreach. In this presentation, NASA's proposed Beyond Einstein Program will be described. The full Roadmap is available at http://universe.nasa.gov/.

The practical Einstein experiments, patents, inventions

CERN Document Server

Illy, József

2012-01-01

Albert Einstein may be best known as the wire-haired whacky physicist who gave us the theory of relativity, but that's just one facet of this genius' contribution to human knowledge and modern science. As Jozsef Illy expertly shows in this book, Einstein had an eminently practical side as well. As a youth, Einstein was an inveterate tinkerer in the electrical supply factory his father and uncle owned and operated. His first paid job was as a patent examiner. Later in life, Einstein contributed to many inventions, including refrigerators, microphones, and instruments for aviation. In published papers, Einstein often provided ways to test his theories and fundamental problems of the scientific community of his times. He delved deeply into a variety of technological innovations, most notably the gyrocompass, and consulted for industry in patent cases and on other legal matters. Einstein also provided explanations for common and mundane phenomena, such as the meandering of rivers. In these and other hands-on exam...

Exploitation of ISAR Imagery in Euler Parameter Space

National Research Council Canada - National Science Library

Baird, Christopher; Kersey, W. T; Giles, R; Nixon, W. E

2005-01-01

.... The Euler parameters have potential value in target classification but have historically met with limited success due to ambiguities that arise in decomposition as well as the parameters' sensitivity...

A new representation of rotational flow fields satisfying Euler's equation of an ideal compressible fluid

International Nuclear Information System (INIS)

Kambe, Tsutomu

2013-01-01

A new representation of the solution to Euler's equation of motion is presented by using a system of expressions for compressible rotational flows of an ideal fluid. This is regarded as a generalization of Bernoulli's theorem to compressible rotational flows. The present expressions are derived from the variational principle. The action functional for the principle consists of the main terms of the total kinetic, potential and internal energies, together with three additional terms yielding the equations of continuity, entropy and a third term that provides the rotational component of velocity field. The last term has the form of scalar product satisfying gauge symmetry with respect to both translation and rotation. This is a generalization of the Clebsch transformation from a physical point of view. It is verified that the system of new expressions, in fact, satisfies Euler's equation of motion. (paper)

Exact Solution of the Two-Level System and the Einstein Solid in the Microcanonical Formalism

Science.gov (United States)

Bertoldi, Dalia S.; Bringa, Eduardo M.; Miranda, E. N.

2011-01-01

The two-level system and the Einstein model of a crystalline solid are taught in every course of statistical mechanics and they are solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In…

Difference Discrete Variational Principle,EULER-Lagrange Cohomology and Symplectic, Multisymplectic Structures

OpenAIRE

Guo, H. Y.; Li, Y. Q.; Wu, K.; Wang, S. K.

2001-01-01

We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory. We also explore the difference discrete versions for the Euler...

Recent developments in Bose-Einstein condensation

International Nuclear Information System (INIS)

Kalman, G.

1997-01-01

This paper contains viewgraphs on developments on Bose-Einstein condensation. Some topics covered are: strongly coupled coulomb systems; standard response functions of the first and second kind; dynamical mean field theory; quasi localized charge approximation; and the main equations

Recent developments in Bose-Einstein condensation

Energy Technology Data Exchange (ETDEWEB)

Kalman, G.

1997-09-22

This paper contains viewgraphs on developments on Bose-Einstein condensation. Some topics covered are: strongly coupled coulomb systems; standard response functions of the first and second kind; dynamical mean field theory; quasi localized charge approximation; and the main equations.

Einstein's Revolutionary Light-Quantum Hypothesis

Science.gov (United States)

Stuewer, Roger H.

2005-05-01

The paper in which Albert Einstein proposed his light-quantum hypothesis was the only one of his great papers of 1905 that he himself termed ``revolutionary.'' Contrary to widespread belief, Einstein did not propose his light-quantum hypothesis ``to explain the photoelectric effect.'' Instead, he based his argument for light quanta on the statistical interpretation of the second law of thermodynamics, with the photoelectric effect being only one of three phenomena that he offered as possible experimental support for it. I will discuss Einstein's light-quantum hypothesis of 1905 and his introduction of the wave-particle duality in 1909 and then turn to the reception of his work on light quanta by his contemporaries. We will examine the reasons that prominent physicists advanced to reject Einstein's light-quantum hypothesis in succeeding years. Those physicists included Robert A. Millikan, even though he provided convincing experimental proof of the validity of Einstein's equation of the photoelectric effect in 1915. The turning point came after Arthur Holly Compton discovered the Compton effect in late 1922, but even then Compton's discovery was contested both on experimental and on theoretical grounds. Niels Bohr, in particular, had never accepted the reality of light quanta and now, in 1924, proposed a theory, the Bohr-Kramers-Slater theory, which assumed that energy and momentum were conserved only statistically in microscopic interactions. Only after that theory was disproved experimentally in 1925 was Einstein's revolutionary light-quantum hypothesis generally accepted by physicists---a full two decades after Einstein had proposed it.

Stability of trapped Bose—Einstein condensates in one-dimensional tilted optical lattice potential

International Nuclear Information System (INIS)

Fang Jian-Shu; Liao Xiang-Ping

2011-01-01

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose—Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose—Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable. (general)

Einstein Up in Smoke

Science.gov (United States)

Lisle, John

2016-01-01

Albert Einstein's biographers have not explained why he developed the abdominal aortic aneurysm that led to his death. Early conjectures proposed that it was caused by syphilis, without accurate evidence. The present article gives evidence to the contrary, and argues that the principal cause of Einstein's death was smoking.

Einstein and a century of time

Science.gov (United States)

Raine, D. J.

2005-09-01

suggests that Mach's principle may yet have a surprising role in expressing the fact that the Universe contains sufficient matter to exist as a classical system: that is, that it contains sufficient material degrees of freedom to allow quantum decoherence to occur. It would at least be a nice irony if Mach's principle turned out to be a necessary quantum condition for the existence of a classical universe! Coming now to the papers in this special feature, these include several that treat historical aspects of relativity. Brown offers us a novel insight into Einstein's ambivalence about the status of special relativity in providing a mechanism for the contraction hypothesis. Trainer looks at the way in which Einstein presented a brief account of relativity in a lecture that he gave in Glasgow in 1933. Galvangno and Giribet look at Einstein's approach to the representation of particles within general relativity, or variants thereof, while Battimelli provides an account of attempts at unification of electromagnetism and relativity from the point of view of the origin of mass. In their contribution, Guerra and de Abreu look again at the relationship between the constancy of the speed of light and the nature of time that was central to Einstein's thinking. Next we come to a group of papers that look at educational issues. Einstein's equation E = mc2 is now iconic even if general knowledge quizzes that ask what the c stands for miss the entire point of the equation! Thomas starts from the way in which perceptions of relativity still focus on this equation as the essential ingredient of nuclear power and the need to disabuse even students of physics of this notion. He also looks at how we can in fact demonstrate the significance of the equation to a lay audience. I have added a short note on friction, another topic that confuses teachers and students alike, that throws up problems to which the solutions are contained in Einstein's Brownian motion paper. The Open University in the

The Routledge guidebook to Einstein's relativity

CERN Document Server

Trefil, James

2015-01-01

Albert Einstein, one of the most prolific scientists of the twentieth century, developed the theory of relativity which was crucial for the advancement of modern physics. Young Einstein identified a paradox between Newtonian Mechanics and Maxwell's equations which pointed to a flawed understanding of space and time by the scientists of the day. In Relativity, Einstein presents his findings using a minimal amount of mathematical language, but the text can still be challenging for readers who lack an extensive scientific background.The Routledge Guidebook to Einstein's Relativity expands on and

Einstein's cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos

Science.gov (United States)

O'Raifeartaigh, Cormac; O'Keeffe, Michael; Nahm, Werner; Mitton, Simon

2015-09-01

We present a first English translation and analysis of a little-known review of relativistic cosmology written by Albert Einstein in late 1932. The article, which was published in 1933 in a book of Einstein papers translated into French, contains a substantial review of static and dynamic relativistic models of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The article offers a valuable contemporaneous insight into Einstein's cosmology in the early 1930s and confirms that his interest lay in the development of the simplest model of the cosmos that could account for observation. The article also confirms that Einstein did not believe that simplified relativistic models could give an accurate description of the early universe.

Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models

OpenAIRE

Berselli, Luigi C.; Bisconti, Luca

2010-01-01

We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.

Actuality of the Einstein theory of gravitation

International Nuclear Information System (INIS)

Ivanenko, D.D.

1982-01-01

Problems of actuality of the Einstein theory of gravitation are lightened. The great Einstein theory of gravitation is shown to remain a reliable base of understanding of modern physical world pattern and its inevitable further inexhaustible precising. The main GRT difficulties are enumirated: determination of reference systems, presence of singularities in the theory, absence of consistent determination of the gravity energy, impossibility of accounting the relations between atomic, gravitational and cosmological characteristics. The attention is paid to gauge, twistor problems and to unified interaction theory. The great contribution of the soviet science in the theory of gravitation is stressed

Stochastic Optimal Prediction with Application to Averaged Euler Equations

Energy Technology Data Exchange (ETDEWEB)

Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2017-04-24

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

The Einstein tensor characterizing some Riemann spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1993-07-01

A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

Einstein A to Z

CERN Document Server

Fox, Karen C

2004-01-01

Einstein was the twentieth century's most celebrated scientist - a man who developed the theory of relativity, revolutionised physics and became an iconic genius in the popular imagination. Essays range from the reasonably scientific including the theory of relativity, to the odd and engaging, such as Einstein's brain, his favourite jokes and films.

Physics before and after Einstein

CERN Document Server

Capria, M Mamone

2005-01-01

It is now a century ago that one of the icons of modern physics published some of the most influential scientific papers of all times. With his work on relativity and quantum theory, Albert Einstein has altered the field of physics forever. It should not come as a surprise that looking back at Einstein''s work, one needs to rethink the whole scope of physics, before and after his time. This books aims to provide a perspective on the history of modern physics, spanning from the late 19th century up to today. It is not an encyclopaedic work, but it presents the groundbreaking and sometimes provocative main contributions by Einstein as marking the line between ''old'' and ''new'' physics, and expands on some of the developments and open issues to which they gave rise.

Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2004-01-01

We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the Arnowitt-Deser-Misner formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as nontrivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced 'constraint-preserving' boundary conditions becomes apparent

Unified Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in five dimensions

International Nuclear Information System (INIS)

Guenaydin, Murat; Zagermann, Marco

2003-01-01

Unified N = 2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N = 2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets. (author)

Fluid-structure coupling in Lagrange-Lagrange and Euler-Lagrange descriptions

International Nuclear Information System (INIS)

Jones, A.V.

1981-01-01

Fluid-structure interaction problems are very common in the reactor safety field, examples being containment loading in LMFBR systems and the downcomer problem in LWRs. This article reviews the principal finite difference methodes employed for their solution. After a survey of the chief representations of the equations of motion of the fluid and structure and of their coupling, the Lagrange-Lagrange and Euler-Lagrange representations are examined in detail. The practical necessity of treating the structure in Lagrangian coordinates and the respective merits of the Lagrangian and Eulerian representations for the fluid are explained, both for coupling between continua and for coupling between a fluid and a thin shell. Detailed analyses of the stability and numerical dissipation of the Lagrange-Lagrange and Euler-Lagrange coupling techniques in a very simple one-dimensional problem are provided to supply indicators as to stability and dissipation in more complex multidimensional situations and to bring out the theoretical complexity of seemingly simple coupling algorithms. The article then presents some practical examples of coupled problems in which calculations can be compared with experiment, and concludes with a section on future trends in the field of fluid-structure coupling

Einstein's cosmos how Albert Einstein's vision transformed our understanding of space and time

CERN Document Server

Kaku, Michio

2004-01-01

Few figures loom as large as Albert Einstein in our contemporary culture. It is truly remarkable that a man from such humble beginnings, an unemployed dreamer without a future or a job, who was written off by his professors as a hopeless loser, could to dare to scale the heights he reached. In this enlightening book Michio Kaku reasseses Einstein's work by centering on his three great theories - special relativity, general relativity and the Unified Field Theory. The first yielded the equation E =mc which is now such a fixture in our culture that it is practically a ubiquitous slogan. But the subsequent theories led to the Big Bang theory and have changed irrevocably the way we perceive time and space. Michio Kaku gives a new, refreshing look at the pioneering work of Einstein, giving a more accurate portrayal of his enduring legacy than previous biographies. As today's advanced physicists continue their intense search to fulfill Einstein's most cherished dream, a 'theory of everything', he is recognised as a...

The NASA Beyond Einstein Program

Science.gov (United States)

White, Nicholas E.

2006-01-01

Einstein's legacy is incomplete, his theory of General relativity raises -- but cannot answer --three profound questions: What powered the big bang? What happens to space, time, and matter at the edge of a black hole? and What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's Office of Space Science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches towards shared science goals. The Beyond Einstein program has three linked elements which advance science and technology towards two visions; to detect directly gravitational wave signals from the earliest possible moments of the BIg Bang, and to image the event horizon of a black hole. The central element is a pair of Einstein Great Observatories, Constellation-X and LISA. Constellation-X is a powerful new X-ray observatory dedicated to X-Ray Spectroscopy. LISA is the first spaced based gravitational wave detector. These powerful facilities will blaze new paths to the questions about black holes, the Big Bang and dark energy. The second element is a series of competitively selected Einstein Probes, each focused on one of the science questions and includes a mission dedicated resolving the Dark Energy mystery. The third element is a program of technology development, theoretical studies and education. The Beyond Einstein program is a new element in the proposed NASA budget for 2004. This talk will give an overview of the program and the missions contained within it.

Einstein a hundred years of relativity

CERN Document Server

Robinson, Andrew

2015-01-01

"The eternal mystery of the world is its comprehensibility … The fact that it is comprehensible is a miracle." --Albert Einstein, 1936 Albert Einstein's universal appeal is only partially explained by his brilliant work in physics, as Andrew Robinson demonstrates in this authoritative, accessible, and richly illustrated biography. The main narrative is enriched by twelve essays by well-known scientists, scholars, and artists, including three Nobel Laureates. The book presents clearly the beautiful simplicity at the heart of Einstein's greatest discoveries, and explains how his ideas have continued to influence scientific developments such as lasers, the theory of the big bang, and "theories of everything." Einstein's life and activities outside of science are also considered, including his encounters with famous contemporaries such as Chaplin, Roosevelt, and Tagore, his love of music, and his troubled family life. The book recognizes that Einstein's striking originality was expressed in many ways, from hi...

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Science.gov (United States)

Micallef, Luana; Rodgers, Peter

2014-01-01

Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Directory of Open Access Journals (Sweden)

Luana Micallef

Full Text Available Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

Conversations With Albert Einstein. II

Science.gov (United States)

Shankland, R. S.

1973-01-01

Discusses Einstein's views on the role of Michelson-Morley, Fizeau, and Miller experiments in the development of relativity and his attitude toward the theories of new quantum mechanics. Indicates that Einstein's opposition to quantum mechanics is beyond dispute. (CC)

Albert Einstein Centenary

CERN Document Server

Amati, Daniele; Weisskopf, Victor Frederick; CERN. Geneva

1979-01-01

The scientist and his work by D. AMATI and S. FUBINI. A socially engaged scientist by V. F. WEISSKOPF. This week, we pay homage to Albert Einstein, the giant of twentieth-century physics born exactly 100 years ago on 14 March 1879 in Ulm, Germany. At the height of his career, Einstein made a whole series of monumental contributions to physics, including the elaborate theories of special and general relativity which revolutionized human thought and marked a major breakthrough in our understanding to the Universe. Along with quantum mechanics, relativity is one of the twin pillars of understanding which allow us here at CERN to study the behaviour of the tiniest components of matter. The development of quantum mechanics took the combined efforts of some of the greatest scientists the world has known, while relativity was developed almost single-handed by Einstein. The centenary of his birth is being commemorated all over the world. Exhibitions and symposia are being organized, books published, postage stamps is...

Boltzmann, Einstein, Natural Law and Evolution

International Nuclear Information System (INIS)

Broda, E.

1980-01-01

Like Boltzmann, Einstein was a protagonist of atomistics. As a physicist, he has been called Boltzmann's true successor. Also in epistemology, after overcoming the positivist influence of Mach, Einstein approached Boltzmann. Any difference between Boltzmann's realism, or even materialism, and Einstein's pantheism may be merely a matter of emphasis. Yet a real difference exists in another respect. Boltzmann explained man's power of thinking and feeling, his morality and his esthetic sense, on an evolutionary, Darwinian, basis. In contrast, evolution had no role in Einstein's thought, though Darwin was accepted by him. This lack of appreciation of the importance of evolution is now attributed to socio-political factors. (author)

Euler's fluid equations: Optimal control vs optimization

Energy Technology Data Exchange (ETDEWEB)

Holm, Darryl D., E-mail: d.holm@ic.ac.u [Department of Mathematics, Imperial College London, SW7 2AZ (United Kingdom)

2009-11-23

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Multistability in an optomechanical system with a two-component Bose-Einstein condensate

International Nuclear Information System (INIS)

Dong Ying; Ye Jinwu; Pu Han

2011-01-01

We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudospin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center-of-mass motion, the atomic collective spin, and the cavity field leads to a strong nonlinearity, resulting in multistable behavior in both matter wave and light wave at the few-photon level.

Discretization vs. Rounding Error in Euler's Method

Science.gov (United States)

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Euler Polynomials, Fourier Series and Zeta Numbers

DEFF Research Database (Denmark)

Scheufens, Ernst E

2012-01-01

Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....

Exact solutions of Einstein and Einstein-Maxwell equations in higher-dimensional spacetime

International Nuclear Information System (INIS)

Xu Dianyan; Beijing Univ., BJ

1988-01-01

The D-dimensional Schwarzschild-de Sitter metric and Reissner-Nordstrom-de-Sitter metric are derived directly by solving the Einstein and Einstein-Maxwell equations. The D-dimensional Kerr metric is rederived by using the complex coordinate transformation method and the D-dimensional Kerr-de Sitter metric is also given. The conjecture about the D-dimensional metric of a rotating charged mass is given at the end of this paper. (author)

When Art Meets Einstein

Science.gov (United States)

Science Scope, 2006

2006-01-01

This article deals with a pale blue sculpture entitled "A New World View", as an homage to the most famous scientist in modern history, Albert Einstein. It has 32 bas-relief squares composed of glass and steel that represent one aspect of the life and legacy of Albert Einstein. Images of children's faces peer out from behind the glass squares,…

Albert Einstein memorial lectures

CERN Document Server

Mechoulam, Raphael; The Israel Academy for Sciences and Humanities

2012-01-01

This volume consists of a selection of the Albert Einstein Memorial Lectures presented annually at the Israel Academy of Sciences and Humanities. Delivered by eminent scientists and scholars, including Nobel laureates, they cover a broad spectrum of subjects in physics, chemistry, life science, mathematics, historiography and social issues. This distinguished memorial lecture series was inaugurated by the Israel Academy of Sciences and Humanities following an international symposium held in Jerusalem in March 1979 to commemorate the centenary of Albert Einstein's birth. Considering that Einstein's interests, activities and influence were not restricted to theoretical physics but spanned broad fields affecting society and the welfare of humankind, it was felt that these memorial lectures should be addressed to scientists, scholars and erudite laypersons rather than to physicists alone.

Global properties of locally rotational symmetric Bianchi I spacetimes in the Einstein-Yang-Mills-dilaton system

Energy Technology Data Exchange (ETDEWEB)

Narita, Makoto [Department of Mathematics, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan (China)

2006-12-21

We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds.

Global properties of locally rotational symmetric Bianchi I spacetimes in the Einstein-Yang-Mills-dilaton system

International Nuclear Information System (INIS)

Narita, Makoto

2006-01-01

We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds

Astrophysical observations: lensing and eclipsing Einstein's theories.

Science.gov (United States)

Bennett, Charles L

2005-02-11

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein provided the framework for understanding modern astrophysical phenomena. Conversely, astrophysical observations provide one of the most effective means for testing Einstein's theories. Here, I review astrophysical advances precipitated by Einstein's insights, including gravitational redshifts, gravitational lensing, gravitational waves, the Lense-Thirring effect, and modern cosmology. A complete understanding of cosmology, from the earliest moments to the ultimate fate of the universe, will require developments in physics beyond Einstein, to a unified theory of gravity and quantum physics.

Contravariant gravity on Poisson manifolds and Einstein gravity

International Nuclear Information System (INIS)

Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi

2017-01-01

A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)

Cavitation Modeling in Euler and Navier-Stokes Codes

Science.gov (United States)

Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.

1993-01-01

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Towards N = 2 SUSY homogeneous quantum cosmology; Einstein-Yang-Mills systems

International Nuclear Information System (INIS)

Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.

1998-01-01

The application of N = 2 supersymmetric Quantum Mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of N = 2 SUSY sigma-model, Hermitian self-adjoint expressions for quantum Hamiltonians and Lagrangians for any signature of a sigma-model metric are obtained. This approach is then applied to coupled SU (2) Einstein-Yang-Mills (EYM) systems in axially-symmetric Bianchi - I,II,VIII, IX, Kantowski-Sachs and closed Friedmann-Robertson-Walker cosmological models. It is shown that all these models admit the embedding into N = 2 SUSY sigma-model with the explicit expressions for superpotentials, being direct sums of gravitational and Yang-Mills (YM) parts. In addition, YM parts of superpotentials exactly coincide with the corresponding Chern-Simons terms. The spontaneous SUSY breaking, caused by YM instantons in EYM systems is discussed in a number of examples

Einstein before Israel Zionist icon or iconoclast?

CERN Document Server

Rosenkranz, Ze’ev

2011-01-01

Albert Einstein was initially skeptical and even disdainful of the Zionist movement, yet he affiliated himself with this controversial political ideology and today is widely seen as an outspoken advocate for a modern Jewish homeland in Palestine. What enticed this renowned scientist and humanitarian, who repeatedly condemned nationalism of all forms, to radically change his views? Was he in fact a Zionist? Einstein Before Israel traces Einstein's involvement with Zionism from his initial contacts with the movement at the end of World War I to his emigration from Germany in 1933 in the wake of Hitler's rise to power. Drawing on a wealth of rare archival evidence--much of it never before published--this book offers the most nuanced picture yet of Einstein's complex and sometimes stormy relationship with Jewish nationalism. Ze'ev Rosenkranz sheds new light on Einstein's encounters with prominent Zionist leaders, and reveals exactly what Einstein did and didn't like about Zionist beliefs, objectives, and methods...

Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model

International Nuclear Information System (INIS)

Peng Mingshu

2004-01-01

A discrete model with a simple cubic nonlinearity term is treated in the study the rich dynamics of a prototype delayed dynamical system under Euler discretization. The effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations

On solutions of Einstein and Einstein-Yang-Mills equations with (maximal) conformal subsymmetries

International Nuclear Information System (INIS)

Sinzinkayo, S.; Demaret, J.

1985-01-01

The maximal subgroups of the conformal group (which have in common as a subgroup the group of pure spatial rotations) are considered as isometry groups of conformally flat space-times. The corresponding cosmological solutions of Einstein's field equations are identified. For each of them, the possibility is investigated that it could be generated by an SU(2) Yang-Mills field built, via the Corrigan-Fairlie-'t Hooft-Wilczek ansatz, from a scalar field identical with the square root of the conformal factor defining the space-time metric tensor. In particular, the Einstein cosmological model can be generated in this manner, but in the framework of strong gravity only, a micro-Einstein universe being then viewed as a possible model for a hadron. (author)

Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations

Science.gov (United States)

Agrawal, S.; Barnett, R. M.; Robinson, B. A.

1991-01-01

A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.

Vortex sorter for Bose-Einstein condensates

International Nuclear Information System (INIS)

Whyte, Graeme; Veitch, John; Courtial, Johannes; Oehberg, Patrik

2004-01-01

We have designed interferometers that sort Bose-Einstein condensates into their vortex components. The Bose-Einstein condensates in the two arms of the interferometer are rotated with respect to each other through fixed angles; different vortex components then exit the interferometer in different directions. The method we use to rotate the Bose-Einstein condensates involves asymmetric phase imprinting and is itself new. We have modeled rotation through fixed angles and sorting into vortex components with even and odd values of the topological charge of two-dimensional Bose-Einstein condensates in a number of states (pure or superposition vortex states for different values of the scattering length). Our scheme may have applications for quantum information processing

Investigation of the Bose–Einstein condensation based on fractality using fractional mathematics

International Nuclear Information System (INIS)

Şirin, Hüseyin; Ertik, Hüseyin; Büyükkiliç, Fevzi; Demirhan, Doğan

2010-01-01

Although atomic Bose gases are investigated in the dilute gas regime, the physical properties of the Bose–Einstein condensates are affected by interparticle interactions and the fractal nature of the space where the Bose systems are evolving. Theoretical predictions of the traditional Bose–Einstein thermostatistics do not account for the deviations from the experimental results, which are related to internal energy, specific heat, transition temperature, etc. On the other hand, in this study, fractional calculus is introduced where effects of the fractality of space are taken into account. Meanwhile, the order of the fractional derivative α is handled as a measure of the fractality of space. In this content, some improvements which take into account the effects of the fractal nature of the system are made in the standard physical results of the Bose–Einstein condensation phenomena. As an example, for the dilute atomic gas 7 Li, the measured transition temperature of Bose–Einstein condensation could be obtained for the value of α ≈ 0.976, and one could predict that the interparticle interactions have a weak attractive nature consistent with experiment (Bradley et al 1995 Phys. Rev. Lett. 75 1687). Thus, a fractional mathematical theory is established in coherence with experimental results of Bose–Einstein condensation

Einstein's Jury The Race to Test Relativity

CERN Document Server

Crelinsten, Jeffrey

2006-01-01

Einstein's Jury is the dramatic story of how astronomers in Germany, England, and America competed to test Einstein's developing theory of relativity. Weaving a rich narrative based on extensive archival research, Jeffrey Crelinsten shows how these early scientific debates shaped cultural attitudes we hold today. The book examines Einstein's theory of general relativity through the eyes of astronomers, many of whom were not convinced of the legitimacy of Einstein's startling breakthrough. These were individuals with international reputations to uphold and benefactors and shareholders to p

Piecewise linear manifolds: Einstein metrics and Ricci flows

International Nuclear Information System (INIS)

Schrader, Robert

2016-01-01

This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field . On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. (paper)

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Directory of Open Access Journals (Sweden)

Zeki Kasap

2015-01-01

Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

Einstein's equivalence principle instead of the inertia forces

International Nuclear Information System (INIS)

Herreros Mateos, F.

1997-01-01

In this article I intend to show that Einstein's equivalence principle substitutes advantageously the inertia forces in the study and resolution of problems in which non-inertial systems appear. (Author) 13 refs

Einstein's universe

CERN Document Server

Calder, Nigel

1979-01-01

This brilliantly written book unlocks the astounding implications of Einstein's revolutionary theories on the nature of science, time and motion. It far surpasses any previous explanation of Relativity for laymen.

Thermal power terms in the Einstein-dilaton system

International Nuclear Information System (INIS)

Zuo, Fen

2014-01-01

We employ the gauge/string duality to study the thermal power terms of various thermodynamic quantities in gauge theories and the renormalized Polyakov loop above the deconfinement phase transition. We restrict ourselves to the five-dimensional Einstein gravity coupled to a single scalar, the dilaton. The asymptotic solutions of the system for a general dilaton potential are employed to study the power contributions of various quantities. If the dilaton is dual to the dimension-4 operator TrF μν 2 , no power corrections would be generated. Then the thermal quantities approach their asymptotic values much more quickly than those observed in lattice simulation. When the dimension of the dual operator is different from 4, various power terms are generated. The lowest power contributions to the thermal quantities are always quadratic in the dilaton, while that of the Polyakov loop is linear. As a result, the quadratic terms in inverse temperature for both the trace anomaly and the Polyakov loop, observed in lattice simulation, cannot be implemented consistently in the system. This is in accordance with the field theory expectation, where no gauge-invariant operator can accommodate such contributions. Two simple models, where the dilaton is dual to operators with different dimensions, are studied in detail to clarify the conclusion.

Numerical solution of Euler's equation by perturbed functionals

Science.gov (United States)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Solutions of Einstein's field equations

Energy Technology Data Exchange (ETDEWEB)

Tomonaga, Y [Utsunomiya Univ. (Japan). Faculty of Education

1978-12-01

In this paper the author investigates the Einstein's field equations of the non-vacuum case and generalizes the solution of Robertson-Walker by the three dimensional Einstein spaces. In Section 2 the author shortly generalizes the dynamic space-time of G. Lemetre and A. Friedmann by a simple transformation.

Coupled Maxwell-pseudoscalar field from the Einstein-Mayer theory

International Nuclear Information System (INIS)

Mahanta, M.N.; Gupta, Y.K.

1987-01-01

A coupled system of field equations representing interacting gravitational, electromagnetic and pseudoscalar fields is obtained using the five-dimensional formalism of Einstein and Mayer (1931-1932). Solutions of the system for concrete cases are under investigation. (author)

Conceptual Development of Einstein's Mass-Energy Relationship

Science.gov (United States)

Wong, Chee Leong; Yap, Kueh Chin

2005-01-01

Einstein's special theory of relativity was published in 1905. It stands as one of the greatest intellectual achievements in the history of human thought. Einstein described the equivalence of mass and energy as "the most important upshot of the special theory of relativity" (Einstein, 1919). In this paper, we will discuss the evolution of the…

Einstein for Schools and the General Public

Science.gov (United States)

Johansson, K. E.; Kozma, C; Nilsson, Ch

2006-01-01

In April 2005 the World Year of Physics (Einstein Year in the UK and Ireland) was celebrated with an Einstein week in Stockholm House of Science. Seven experiments illustrated Einstein's remarkable work in 1905 on Brownian motion, the photoelectric effect and special relativity. Thirteen school classes with 260 pupils, 30 teachers and 25 members…

Series expansion of the modified Einstein Procedure

Science.gov (United States)

Seema Chandrakant Shah-Fairbank

2009-01-01

This study examines calculating total sediment discharge based on the Modified Einstein Procedure (MEP). A new procedure based on the Series Expansion of the Modified Einstein Procedure (SEMEP) has been developed. This procedure contains four main modifications to MEP. First, SEMEP solves the Einstein integrals quickly and accurately based on a series expansion. Next,...

Mileva Maric Einstein vivre avec Albert Einstein

CERN Document Server

Milentijevic, Radmila

2013-01-01

Radmila Milentijevic n’est pas la première à écrire sur les relations entre le génial Albert Einstein et sa première épouse et précieuse collaboratrice durant ses années de recherches, la scientifique serbe Mileva Maric. Mais c’est la première fois qu’un ouvrage traite de cette idylle, puis de ce drame familial qui a duré près de cinquante années, sous une forme quasiment poétique, si rare dans l’historiographie scientifique.Professeur émérite d’histoire à l’université de New York, l’auteur propose ici une monographie riche et vivante, dévoilant une face cachée d’Albert Einstein, et faisant de sa compagne une figure historique de premier plan en même temps qu’un personnage romanesque dont le destin tragique ne laissera aucun lecteur indifférent.

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

International Nuclear Information System (INIS)

Shin, Young Jae; Yun, Jong Hak; Seong, Kyeong Youn; Kim, Jae Ho; Kang, Sung Hwang

2006-01-01

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Paster nak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee

2015-01-01

Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both

Einstein and the "Crucial" Experiment

Science.gov (United States)

Holton, Gerald

1969-01-01

Examines the widespread view that it was the crucial Michelson-Morley experiment that led Einstein to formulate the special relativity theory. From Einstein's writings, evidence is presented that no such direct genetic connection exists. The author suggests that the historian of science must resist the experimenticist's fallacy of imposing a…

2011 Einstein Fellows Chosen

Science.gov (United States)

2011-03-01

ASA has announced the selection of the 2011 Einstein Fellows who will conduct research related to NASA's Physics of the Cosmos program, which aims to expand our knowledge of the origin, evolution, and fate of the Universe. The Einstein Fellowship provides support to the awardees for three years, and the Fellows may pursue their research at a host university or research center of their choosing in the United States. The new Fellows will begin their programs in the fall of 2011. The new Einstein Fellows and their host institutions are listed below: * Akos Bogdan (Smithsonian Astrophysical Observatory, Cambridge, Mass.) * Samuel Gralla (University of Maryland, College Park, Md.) * Philip Hopkins (University of California at Berkeley) * Matthew Kunz (Princeton University, Princeton, N.J.) * Laura Lopez (Massachusetts Institute of Technology, Cambridge, Mass.) * Amy Reines (National Radio Astronomy Observatory, Charlottesville, Virg.) * Rubens Reis (University of Michigan, Ann Arbor) * Ken Shen (Lawrence Berkeley National Laboratory, Berkeley, Calif.) * Jennifer Siegal-Gaskins (California Institute of Technology, Pasadena) * Lorenzo Sironi (Harvard University, Cambridge, Mass.) NASA has two other astrophysics theme-based fellowship programs: the Sagan Fellowship Program, which supports research into exoplanet exploration, and the Hubble Fellowship Program, which supports research into cosmic origins. More information on the Einstein Fellowships can be found at: http://cxc.harvard.edu/fellows/

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

Dynamical systems with classical spin in the Einstein-Maxwell-Cartan theory

International Nuclear Information System (INIS)

Amorin, R.M. de.

1984-01-01

By using variational precedures, spinning charged particles and fluids, with magnetic dipole moment, are analysed. Electromagnetic and gravitational interactions are also dynamically considered. A relativistic formalism which describes the space-time as a Riemann-Cartan manifold caraccterized by curvature and torsion tensors was adopted. The specific features of the Einstein-Maxell-Cartan theory have been analised in detail for the considered models. Also the holonomy of the local Lorentz Frames and constraints has been studied, and as a consequence it has been possible to generate new equations of motion for particles with spin. It has also been possible to derive the complete differential system which includes the fluid, the electromagnetic, the curvature and the torsion fields. (author) [pt

Hamiltonian dynamics of spatially-homogeneous Vlasov-Einstein systems

International Nuclear Information System (INIS)

Okabe, Takahide; Morrison, P. J.; Friedrichsen, J. E. III; Shepley, L. C.

2011-01-01

We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor and their time derivatives yield the canonical coordinates. The evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model, according to its symmetry. For illustrative purposes, we examine the evolution of anisotropy in models with Vlasov matter. The Vlasov content is further simplified by the assumption of cold, counter-streaming matter, a kind of matter that is far from thermal equilibrium and is not describable by an ordinary fluid model nor other more simplistic matter models. Qualitative differences and similarities are found in the dynamics of certain vacuum class A Bianchi models and Bianchi type I models with cold, counter-streaming Vlasov-matter potentials analogous to the curvature potentials of corresponding vacuum models.

Quantum theory and Einstein's general relativity

International Nuclear Information System (INIS)

Borzeszkowski, H.H.v.; Treder, H.J.

1984-01-01

The paper concerns Einstein's general relativity, wave mechanics and the quantization of Einstein's gravitation equations. The principle of equivalence and its association with both wave mechanics and quantum gravity, is discussed. (U.K.)

Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

International Nuclear Information System (INIS)

Barreto, W.; Silva, A. da; Lehner, L.; Gomez, R.; Rosales, L.; Winicour, J.

2005-01-01

We incorporate a massless scalar field into a three-dimensional code for the characteristic evolution of the gravitational field. The extended three-dimensional code for the Einstein-Klein-Gordon system is calibrated to be second-order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the l=2 quasinormal mode

Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations

International Nuclear Information System (INIS)

Arlotti, L.; Lachowicz, M.

1997-01-01

The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics

The world-line. Albert Einstein and modern physics; Die Weltlinie. Albert Einstein und die moderne Physik

Energy Technology Data Exchange (ETDEWEB)

Maalampi, Jukka [Jyvaeskylae Univ. (Finland). Dept. of Physics

2008-07-01

This book is an entertaining and formula-free presentation of modern physics from the 19th century to present. The life of Albert Einstein and his scientific works are drawn as red fathom through the text. The author explains central terms and results of modern physics in populary-scientific form from the historical perspective. To the reader in humorous form an imagination is mediated how modern physics has been developed. We learn from the exciting effects of the ether, we hear from faraday and magnetic needles, from Maxwell's prediction of the electromagnetic waves, from heinrich Hertz and from the photoelectric effect. Was the Michelson-Morley experiment a measurement success or an unsuccess? Why has Einstein abandoned the ether? How has Einstein in the miraculous year 1905 revolutionated physics and why he has begged Newton for excusement? Exist atoms? What is motion? What is light and what is to be understood under ''now'' and ''here''? Light deviation or non-deviation? How act the tidal forces? And above all: How has Einstein answered these questions. We meet Poincare, Lorentz and Hilbert, Boltzmann and Bohr, Minkowski, Planck, de Broglie, Hubble and Weyl, Gamow, Hahn and Meitner, Kapiza and Landau, Fermi and many other famous scientists. What had Eddington against Chandrasekhar and what had Einstein against black holes? Why should space tourists and dream tourists make holiday not on the Loch Ness but on the safe side of a black hole? Why inveighed Pauli against Einstein? Is the concern with the atomic-bomb formula right? Smeared matter, big bang and cosmic background radiation, gravitational waves and double pulsars, the cosmological constant and the expansion of the universe are further themes, which keep the reader in breath and let no mental vacuum arise. [German] Das Buch ist eine unterhaltsame und formelfreie Darstellung der modernen Physik vom 19. Jahrhundert bis zur Gegenwart. Das Leben Albert Einsteins

Conservative numerical schemes for Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

Black hole dynamics in Einstein-Maxwell-dilaton theory

Science.gov (United States)

Hirschmann, Eric W.; Lehner, Luis; Liebling, Steven L.; Palenzuela, Carlos

2018-03-01

We consider the properties and dynamics of black holes within a family of alternative theories of gravity, namely Einstein-Maxwell-dilaton theory. We analyze the dynamical evolution of individual black holes as well as the merger of binary black hole systems. We do this for a wide range of parameter values for the family of Einstein-Maxwell-dilaton theories, investigating, in the process, the stability of these black holes. We examine radiative degrees of freedom, explore the impact of the scalar field on the dynamics of merger, and compare with other scalar-tensor theories. We argue that the dilaton can largely be discounted in understanding merging binary systems and that the end states essentially interpolate between charged and uncharged, rotating black holes. For the relatively small charge values considered here, we conclude that these black hole systems will be difficult to distinguish from their analogs within General Relativity.

Albert Einstein's Magic Mountain: An Aarau Education*

Science.gov (United States)

Hunziker, Herbert

2015-03-01

For economic reasons, the electrotechnical factory J. Einstein & Cie. (co-owned by Albert Einstein's father Hermann) had to be closed in the summer of 1894. While Albert's parents emigrated to Italy to build a new existence, he remained in Munich to complete his studies at the Gymnasium. Left behind, however, he had a difficult time with what he considered the rigid educational practices at the Munich Luitpold-Gymnasium and quit without a diploma. The present article discusses Einstein's richly winding path to the Aargau Cantonal School (Switzerland), especially its history and educational philosophy during the time of his stay in Aarau. There, Einstein met some outstanding teachers, who could serve him as models of scholars and human beings. In spite of Einstein's distinct independence of mind, these personalities may well have had a significant influence on the alignment of his inner compass.

Albert Einstein: A Biographical Sketch

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 4. Albert Einstein: A Biographical Sketch. Maja Winteler-Einstein. Reflections Volume 5 Issue 4 April 2000 pp 111-120. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/005/04/0111-0120 ...

Einstein's Materialism and Modern Tests of Quantum Mechanics

Science.gov (United States)

Vigier, J. P.

After a presentation of Einstein's and Bohr's antagonistic point of view on the interpretation of Quantum Mechanics an illustration of their conflicting positions in the particular case of Young's double slit experiment is presented. It is then shown that in their most recent form (i. e. time dependent neutron interferometry) these experiments suggest (if one accepts absolute energymomentum conservation in all individual microprocesses) that Einstein was right in the Bohr-Einstein controversy.Translated AbstractEinsteins Materialismus und heutige Tests der QuantenmechanikNach einer Darstellung von Einsteins und Bohrs antagonistischen Standpunkten in der Interpretation der Quantenmechanik werden ihre widersprüchlichen Positionen im speziellen Fall des Youngschen Doppelspaltexperiments dargestellt. Es wird dann gezeigt, daß diese Experimente in ihrer neuesten Form (d. h. zeitabhängige Neutroneninterferometrie) Einstein in der Bohr-Einsteinkontroverse recht gaben (wenn man absolute Energie-Impulserhaltung bei allen individuellen Mikroprozessen annimmt).

Revisiting Einstein's brain in Brain Awareness Week.

Science.gov (United States)

Chen, Hao; Chen, Su; Zeng, Lidan; Zhou, Lin; Hou, Shengtao

2014-10-01

Albert Einstein's brain has long been an object of fascination to both neuroscience specialists and the general public. However, without records of advanced neuro-imaging of his brain, conclusions regarding Einstein's extraordinary cognitive capabilities can only be drawn based on the unique external features of his brain and through comparison of the external features with those of other human brain samples. The recent discovery of 14 previously unpublished photographs of Einstein's brain taken at unconventional angles by Dr. Thomas Stoltz Harvey, the pathologist, ignited a renewed frenzy about clues to explain Einstein's genius. Dr. Dean Falk and her colleagues, in their landmark paper published in Brain (2013; 136:1304-1327), described in such details about the unusual features of Einstein's brain, which shed new light on Einstein's intelligence. In this article, we ask what are the unique structures of his brain? What can we learn from this new information? Can we really explain his extraordinary cognitive capabilities based on these unique brain structures? We conclude that studying the brain of a remarkable person like Albert Einstein indeed provides us a better example to comprehensively appreciate the relationship between brain structures and advanced cognitive functions. However, caution must be exercised so as not to over-interpret his intelligence solely based on the understanding of the surface structures of his brain.

BOOK REVIEW: Once Upon Einstein

Science.gov (United States)

Giannetto, E.

2007-07-01

Thibault Damour is a theoretical physicist, and a member of the French Academy of Sciences. This book is the translation, by Eric Novak, of the original French Si Einstein m'etait conté (Le Cherche Midi, 2005). It is neither a book of theoretical physics nor a biography of Einstein. It is not a book of history nor philosophy of science. In Damour's words it was written to encourage the reader to share with Einstein `those times when he understood some part of the hidden order of the universe'. It is a relatively short book, written in a very fluent style, but it deals with all the major problems and achievements of Einstein's works. Starting from special relativity, it continues with general relativity, quantum theories, unified field theory and a brief overview of the actual research related to Einstein's legacy. It is essentially a popular science book with some related exploration in history and philosophy to interpret physical theories. The most important problem discussed by Damour is the nature of time. On this subject, there is a very interesting short paragraph (pp 33--35) dedicated to the reception of the relativity idea by the great writer Marcel Proust and its counterpart within À la Recherche du Temps Perdu. A correct discussion of the implications of a relativistic time should imply the distinction of the different possible interpretations of this concept. Damour seems to conclude that only one interpretation is possible: `time does not exist', flowing of time is an illusion. One has to know that Einstein's ideas on time were related to Spinoza's perspective of a knowledge sub specie aeternitatis. However, other interpretations are possible and are related to the idea of time as an actuality. Damour speaks about the controversy between Einstein and Bergson, but Bergson is considered as a philosopher who did not understand relativity. This philosophical problem of relativistic time is indeed related to a historical problem briefly discussed by Damour

Einstein 1905-1955: His Approach to Physics

Science.gov (United States)

Damour, Thibault

We review Einstein's epistemological conceptions, and indicate their philosophical roots. The particular importance of the ideas of Hume, Kant, Mach, and Poincaré is highlighted. The specific characteristics of Einstein's approach to physics are underlined. Lastly, we consider the practical application of Einstein's methodological principles to the two theories of relativity, and to quantum theory. We emphasize a Kantian approach to quantum theory.

Bose-Einstein Condensation in Complex Networks

International Nuclear Information System (INIS)

Bianconi, Ginestra; Barabasi, Albert-Laszlo

2001-01-01

The evolution of many complex systems, including the World Wide Web, business, and citation networks, is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and nonequilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the 'first-mover-advantage,' 'fit-get-rich,' and 'winner-takes-all' phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks

Distributed adaptive asymptotically consensus tracking control of uncertain Euler-Lagrange systems under directed graph condition.

Science.gov (United States)

Wang, Wei; Wen, Changyun; Huang, Jiangshuai; Fan, Huijin

2017-11-01

In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Euler Strut: A Mechanical Analogy for Dynamics in the Vicinity of a Critical Point

Science.gov (United States)

Bobnar, Jaka; Susman, Katarina; Parsegian, V. Adrian; Rand, Peter R.; Cepic, Mojca; Podgornik, Rudolf

2011-01-01

An anchored elastic filament (Euler strut) under an external point load applied to its free end is a simple model for a second-order phase transition. In the static case, a load greater than the critical load causes a Euler buckling instability, leading to a change in the filament's shape. The analysis of filament dynamics with an external point…

Einstein's first paper on relativity

International Nuclear Information System (INIS)

Schwartz, H.M.

1977-01-01

Because of its exceptional significance in the history of great ideas in science, Einstein's first paper on relativity, especially its first part, deserves a more careful translation into English than presently exists. A new and annotated translation of this first part is presented here, together with a brief discussion of certain aspects of Einstein's paper

Kopernik, Einstein and evolution of a logic structure of relativity principle

International Nuclear Information System (INIS)

Kruczek, W.

1986-01-01

This paper shown that the development of physics as a logic structure was begun by Mikolaj Kopernik. It was consequently presented that the whole period of physic evolution, since Kopernik times through Einstein and also later, was determined by the relativity principle. That principle in this primary version was used for scienific justification of heliocentric system. As a consequence it caused the development of research on the motion, the time and the space (Gallileo, Newton and others). The article presents successive stages of the evolution of those motions, explaining the difference between Einstein's and Poincare's interpretation of them. The methodologic background of Einstein's measuring procedures was also explained. 10 refs., 7 figs. (author)

The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks.

Science.gov (United States)

Guo, Jin-Li; Suo, Qi; Shen, Ai-Zhong; Forrest, Jeffrey

2016-09-27

To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to describe the arrival process of new node batches. And, by using the Poisson process theory and a continuity technique, the hypernetwork is analyzed and the characteristic equation of hyperedge cardinalities is obtained. Additionally, an analytical expression for the stationary average hyperedge cardinality distribution is derived by employing the characteristic equation, from which Bose-Einstein condensation in the hypernetwork is obtained. The theoretical analyses in this paper agree with the conducted numerical simulations. This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Moreover, a condensation degree is also discussed with which Bose-Einstein condensation can be classified.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

Science.gov (United States)

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

Directory of Open Access Journals (Sweden)

Ling Zhang

2017-10-01

Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Correct Linearization of Einstein's Equations

Directory of Open Access Journals (Sweden)

Rabounski D.

2006-06-01

Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

Construction of Einstein-Sasaki metrics in D≥7

International Nuclear Information System (INIS)

Lue, H.; Pope, C. N.; Vazquez-Poritz, J. F.

2007-01-01

We construct explicit Einstein-Kaehler metrics in all even dimensions D=2n+4≥6, in terms of a 2n-dimensional Einstein-Kaehler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, or gravomagnetic charge, in addition to..' in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5≥7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and nonsingular manifolds, even though the underlying Einstein-Kaehler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M theory, which play a role in the AdS 4 /CFT 3 correspondence

Books on Einstein--Collectors' Delight

Science.gov (United States)

Khoon, Koh Aik; Jalal, Azman; Abd-Shukor, R.; Yatim, Baharudin; Talib, Ibrahim Abu; Daud, Abdul Razak; Samat, Supian

2009-01-01

A survey of thirteen books on Einstein is presented. Its gives an idea on how much is written about the man and how frequent are the publications. The year 2005 saw the most publications. It is the centenary for the Miraculous Year. Interestingly some books can just sustain their readers' interest with just words. Einstein comes alive with the…

Motion of spinning particles. Post-Newtonian approximation in the Einstein-Cartan theory

Energy Technology Data Exchange (ETDEWEB)

Boccaletti, D; Agostini, W; Festa, P [Rome Univ. (Italy). Ist. di Matematica

1979-01-11

The equations of motion of spinning particles are obtained in the post-Newtonian approximation of the Einstein-Cartan theory. The starting point of the calculation is the Hehl combined equation and a semi-classical model is assumed for the system of spinning particles. Comparison is made with an analogous quantum result obtained in the context of Gupta quantization of the linearized Einstein theory.

Particlelike solutions of the Einstein-Dirac equations

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-05-01

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

Einstein pictures the x-ray sky

International Nuclear Information System (INIS)

Hartline, B.K.

1979-01-01

The second High Energy Astronomy Observatory (HEAO-2, Einstein) is revolutionizing x-ray astronomy just as its namesake revolutionized physics. Earlier x-ray observatories, including HEAO-1, were designed to scan the sky for x-ray emitters. With Einstein, the challenge has shifted from discovering x-ray sources to understanding the processes producing the x-rays. But having 500 times the sensitivity of previous detectors, Einstein makes more than its share of discoveries, too. For example, it sees distant quasars and clusters of galaxies that can barely be detected by the largest optical telescopes

Soliton resonance in bose-einstein condensate

Science.gov (United States)

Zak, Michail; Kulikov, I.

2002-01-01

A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

A student's guide to Einstein's major papers

CERN Document Server

Kennedy, Robert E

2012-01-01

Our understanding of the physical universe underwent a revolution in the early twentieth century - evolving from the classical physics of Newton, Galileo, and Maxwell to the modern physics of relativity and quantum mechanics. The dominant figure in this revolutionary change was Albert Einstein. In a single year, 1905, Einstein produced breakthrough works in three areas of physics: on the size and the effects of atoms; on the quantization of the electromagnetic field; and on the special theory of relativity. In 1916 he produced a fourth breakthrough work, the general theory of relativity. A Student's Guide to Einstein's Major Papers focuses on Einstein's contributions, setting his major works into their historical context, and then takes the reader through the details of each paper, including the mathematics. This book helps the reader appreciate the simplicity and insightfulness of Einstein's ideas and how revolutionary his work was, and locate it in the evolution of scientific thought begun by the ancient...

Secrets of the old one Einstein, 1905

CERN Document Server

Bernstein, Jeremy

2006-01-01

In March 1905, at approximately eight week intervals, the Editor of the noted German physics journal, Annalen der Physik, received three hand-written manuscripts from a relatively unknown patent examiner in Bern, Switzerland. This patent examiner was the twenty-six year old Albert Einstein and the three papers would set the agenda for twentieth century physics. A fourth short paper was received in September 1905 and contained Einstein's derivation of the formula E=mc^2. These papers changed our lives in the twentieth century and beyond. While to a professional physicist the mathematics in these papers are quite straight forward, the ideas behind them are not. In fact, none of Einstein's contemporaries fully understood what he had done. In SECRETS OF THE OLD ONE: Einstein, 1905, renowned science writer Jeremy Bernstein makes these ideas accessible to a general reader with a limited background in mathematics. After reading this book, you will understand why 1905 is often designated as Einstein's miracle year.

Einstein's Mirror

Science.gov (United States)

Gjurchinovski, Aleksandar; Skeparovski, Aleksandar

2008-10-01

Reflection of light from a plane mirror in uniform rectilinear motion is a century-old problem, intimately related to the foundations of special relativity.1-4 The problem was first investigated by Einstein in his famous 1905 paper by using the Lorentz transformations to switch from the mirror's rest frame to the frame where the mirror moves at a constant velocity.5 Einstein showed an intriguing fact that the usual law of reflection would not hold in the case of a uniformly moving mirror, that is, the angles of incidence and reflection of the light would not equal each other. Later on, it has been shown that the law of reflection at a moving mirror can be obtained in various alternative ways,6-10 but none of them seems suitable for bringing this interesting subject into the high school classroom.

The Einstein-Podolsky-Rosen paradox

International Nuclear Information System (INIS)

Roy, S.M.

1980-01-01

The celebrated arguments of Einstein, Podolsky and Rosen claiming that quantum mechanics cannot be a complete theory are reviewed. Recent research climaxed by Bell's theorem shows that Einstein's locality or ''no telepathy'' postulate conflicts with quantum theory. It adds a new dimension to the paradox by catapulting the problem from the domain of metaphysics into that of experimental physics. (auth.)

The times of Albert Einstein

International Nuclear Information System (INIS)

Ahmad, S.M.W.

1990-09-01

''The life of Albert Einstein has a dramatic quality that does not rest exclusively on his theory of relativity. The extravagant timing of history linked him with three shattering developments of the twentieth century: the rise and fall of Nazi Germany, the birth of nuclear weapons, and the birth of zionism (and Israel). Their impact on Einstein's genius combined to drive him into a contact with the affairs of the world for which Einstein had little taste''. This article is the result of my lecture delivered at ICTP on 17 August, 1990 before a knowledgable audience that included scientists from many countries including the third world countries. This one and half hour lecture was organised by Dr. A.M. Hamende and Dr. H.R. Dalafi. 10 refs

Albert Einstein, Analogizer Extraordinaire

CERN Multimedia

CERN. Geneva

2007-01-01

Where does deep insight in physics come from? It is tempting to think that it comes from the purest and most precise of reasoning, following ironclad laws of thought that compel the clear mind completely rigidly. And yet the truth is quite otherwise. One finds, when one looks closely at any major discovery, that the greatest of physicists are, in some sense, the most crazily daring and irrational of all physicists. Albert Einstein exemplifies this thesis in spades. In this talk I will describe the key role, throughout Albert Einstein's fabulously creative life, played by wild guesses made by analogy lacking any basis whatsoever in pure reasoning. In particular, in this year of 2007, the centenary of 1907, I will describe how over the course of two years (1905 through 1907) of pondering, Einstein slowly came, via analogy, to understand the full, radical consequences of the equation that he had first discovered and published in 1905, arguably the most famous equation of all time: E = mc2.

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

Einstein in love a scientific romance

CERN Document Server

Overbye, Dennis

2000-01-01

At its height, Einstein's marriage to Mileva was an extraordinary one - a colleague and often fierce adversary, Mileva was brilliantly matched with the scientific genius. Dennis Overbye seeks to present this scientific romance in a vivid light, telling the private story of the young Einstein.

Einstein, Kant, and Taoism

OpenAIRE

Kim, Y. S.

2006-01-01

It is said that Einstein's conceptual base for the theory of relativity was the philosophy formulated by Immanuel Kant. Then, is it possible to see how Kant played a role in Einstein's thinking without reading Kant's books? This question arises because it is not possible for physicists to read Kant's writings. Yes, it is possible if we use the method of physics. It is known also that Kant's mode of thinking was profoundly affected by the geography of Koenigsberg where he spent eighty years of...

Ceremony marking Einstein Year

CERN Multimedia

2005-01-01

Sunday 13th November at 10:00amat Geneva's St. Peter's Cathedral To mark Einstein Year and the importance of the intercultural dialogue of which it forms a part, a religious service will take place on Sunday 13 November at 10 a.m. in St. Peter's Cathedral, to which CERN members and colleagues are warmly welcomed. Pastor Henry Babel, senior minister at the Cathedral, will speak on the theme: 'God in Einstein's Universe'. Diether Blechschmidt will convey a message on behalf of the scientific community.

Quantum theory and Einstein's general relativity

International Nuclear Information System (INIS)

Borzeszkowski, H. von; Treder, H.

1982-01-01

We dicusss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Einstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a ''quantization of geometry.'' However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies

Wormhole instanton solution in the Einstein-Yang-Mills system

International Nuclear Information System (INIS)

Hosoya, Akio; Ogura, Waichi.

1989-01-01

A spherical symmetric classical solution of the Einstein and the SU(2) Yang-Mills equations is found in the four dimensional Euclidean space-time with the cosmological constant. The isospinor fermion has zero modes. Their cosmological implications are also discussed with an emphasis on the fact that wormhole instantons in general can be found not only in the sub-Planck physics but also in almost all the stages in lower energy physics. (author)

Left-invariant Einstein metrics on S3 ×S3

Science.gov (United States)

Belgun, Florin; Cortés, Vicente; Haupt, Alexander S.; Lindemann, David

2018-06-01

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics g on G = SU(2) × SU(2) =S3 ×S3. Einstein metrics are critical points of the total scalar curvature functional for fixed volume. The scalar curvature S of a left-invariant metric g is constant and can be expressed as a rational function in the parameters determining the metric. The critical points of S, subject to the volume constraint, are given by the zero locus of a system of polynomials in the parameters. In general, however, the determination of the zero locus is apparently out of reach. Instead, we consider the case where the isotropy group K of g in the group of motions is non-trivial. When K ≇Z2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kähler metric, based on representation-theoretic arguments and computer algebra. For the remaining case K ≅Z2 we present partial results.

Correspondence passed between Einstein and Schroedinger

International Nuclear Information System (INIS)

Balibar, F.

1992-01-01

The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories

Exact solutions of Einstein and Einstein-scalar equations in 2+1 dimensions

International Nuclear Information System (INIS)

Virbhadra, K.S.

1995-01-01

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant Λ and null fluid) in 2 + 1 dimensions is given. This is a nonstatic generalization of the uncharged spinless Bandos Teitelboim Zanelli (BTZ) metric. For Λ = 0, spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at r=0 and the scalar field diverges at r=0 as well as at infinity. (author). 12 refs

Static Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Das, A.

1979-01-01

The static Einstein--Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein--Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein--Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque

Bose-Einstein condensation in microgravity.

Science.gov (United States)

van Zoest, T; Gaaloul, N; Singh, Y; Ahlers, H; Herr, W; Seidel, S T; Ertmer, W; Rasel, E; Eckart, M; Kajari, E; Arnold, S; Nandi, G; Schleich, W P; Walser, R; Vogel, A; Sengstock, K; Bongs, K; Lewoczko-Adamczyk, W; Schiemangk, M; Schuldt, T; Peters, A; Könemann, T; Müntinga, H; Lämmerzahl, C; Dittus, H; Steinmetz, T; Hänsch, T W; Reichel, J

2010-06-18

Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Investigation of source location determination from Magsat magnetic anomalies: The Euler method approach

Science.gov (United States)

Ravat, Dhananjay

1996-01-01

The applicability of the Euler method of source location determination was investigated on several model situations pertinent to satellite-data scale situations as well as Magsat data of Europe. Our investigations enabled us to understand the end-member cases for which the Euler method will work with the present satellite magnetic data and also the cases for which the assumptions implicit in the Euler method will not be met by the present satellite magnetic data. These results have been presented in one invited lecture at the Indo-US workshop on Geomagnetism in Studies of the Earth's Interior in August 1994 in Pune, India, and at one presentation at the 21st General Assembly of the IUGG in July 1995 in Boulder, CO. A new method, called Anomaly Attenuation Rate (AAR) Method (based on the Euler method), was developed during this study. This method is scale-independent and is appropriate to locate centroids of semi-compact three dimensional sources of gravity and magnetic anomalies. The method was presented during 1996 Spring AGU meeting and a manuscript describing this method is being prepared for its submission to a high-ranking journal. The grant has resulted in 3 papers and presentations at national and international meetings and one manuscript of a paper (to be submitted shortly to a reputable journal).

Bose-Einstein condensation of a relativistic Bose gas trapped in a general external potential

International Nuclear Information System (INIS)

Su Guozhen; Chen Jincan; Chen Lixuan

2006-01-01

Bose-Einstein condensation of an ideal relativistic Bose gas trapped in a generic power-law potential is investigated. The analytical expressions for some important parameters such as the critical temperature, ground-state fraction and heat capacity are derived. The general criteria on the occurrence of Bose-Einstein condensation and the discontinuity of heat capacity at the critical temperature are obtained. The results obtained here present a unified description for the Bose-Einstein condensation of a class of ideal Bose systems so that many important conclusions in the literature are included in this paper

An improved front tracking method for the Euler equations

NARCIS (Netherlands)

Witteveen, J.A.S.; Koren, B.; Bakker, P.G.

2007-01-01

An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as

On the hyperbolicity of Einstein's and other gauge field equations

International Nuclear Information System (INIS)

Friedrich, H.

1985-01-01

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)

Einstein's essays in science

CERN Document Server

Einstein, Albert

2009-01-01

His name is synonymous with ""genius,"" but these essays by the renowned physicist and scholar are accessible to any reader. In addition to outlining the core of relativity theory in everyday language, Albert Einstein presents fascinating discussions of other scientific fields to which he made significant contributions. The Nobel Laureate also profiles some of history's most influential physicists, upon whose studies his own work was based.Assembled during Einstein's lifetime from his speeches and essays, this book marks the first presentation to the wider world of the scientist's accomplishme

Ethic and Evolution in Boltzmann's and Einstein's Thought

Energy Technology Data Exchange (ETDEWEB)

Broda, E.

1980-07-01

In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

Ethic and Evolution in Boltzmann's and Einstein's Thought

International Nuclear Information System (INIS)

Broda, E.

1980-01-01

In physics and to a large extent in epistomology, Einstein was the natural successor to Boltzmann. But while Boltzmann was an ardent evolutionist, Einstein cared little for biology. Boltzmann applied Darwinian principles also to ethics, but remained aloof from politics. In contrast, Einstein's morality, though expressed in magnificent and selfless activity, lacked a firm theoretical basis. (author)

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R

Directory of Open Access Journals (Sweden)

Boutros Paul C

2011-01-01

Full Text Available Abstract Background Visualization of orthogonal (disjoint or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. Results The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. Conclusions The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R.

Science.gov (United States)

Chen, Hanbo; Boutros, Paul C

2011-01-26

Visualization of orthogonal (disjoint) or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor

International Nuclear Information System (INIS)

So, Lau Loi

2008-01-01

The energy-momentum for a gravitating system can be considered using the tetrad teleparallel gauge current in orthonormal frames, instead of the more commonly used Einstein pseudotensor, which makes use of holonomic frames. The tetrad expression itself gives a better result for gravitational energy than Einstein's in that it gives a positive gravitational energy in the small sphere approximation. Inspired by an idea of Deser, we propose an alternative quasilocal gravitational energy expression in the small sphere limit which also enjoys the positive energy property by combining the tetrad expression and the Einstein pseudotensor, such that the connection coefficient has a form appropriate to a suitable intermediate between orthonormal and holonomic frames

Einstein and solid-state physics

International Nuclear Information System (INIS)

Aut, I.

1982-01-01

A connection between the development of solid-state physics and the works and activity of Albert Einstein is traced. A tremendous Einstein contribution to solid state physics is marked. A strict establishment of particle-wave dualism; a conclusion about the applicability of the Plank radiation law not only to black body radiation; finding out particles indistinguishability - all three discoveries have a principle significance for solid state physics too

Einstein and the twin paradox

International Nuclear Information System (INIS)

Pesic, Peter

2003-01-01

Einstein was the first to discuss and resolve the 'twin paradox', which in 1905 he did not consider paradoxical and treated as a consequence of lack of simultaneity. He maintained this view until at least 1914. However, in 1918 Einstein brought forward arguments about accelerated frames of reference that tended to overshadow his initial resolution. His earlier arguments were gradually rediscovered during the subsequent controversy about this 'paradox'

Bose-Einstein condensation of photons in a 'white-wall' photon box

International Nuclear Information System (INIS)

Klaers, Jan; Schmitt, Julian; Vewinger, Frank; Weitz, Martin

2011-01-01

Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a 'white-wall' photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.

Bose-Einstein condensation of photons in a 'white-wall' photon box

Science.gov (United States)

Klärs, Jan; Schmitt, Julian; Vewinger, Frank; Weitz, Martin

2011-01-01

Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a "white-wall" photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.

Entanglement Equilibrium and the Einstein Equation.

Science.gov (United States)

Jacobson, Ted

2016-05-20

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

An Einstein-Cartan Fine Structure Constant Definition

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Stone R. A. Jr.

2010-01-01

Full Text Available The fine structure constant definition given in Stone R.A. Jr. Progress in Physics, 2010, v.1, 11-13 is compared to an Einstein-Cartan fine structure constant definition. It is shown that the Einstein-Cartan definition produces the correct pure theory value, just not the measure value. To produce the measured value, the pure theory Einstein-Cartan fine structure constant requires only the new variables and spin coupling of the fine structure constant definition in [1].

Albert Einstein and the relativity theory

International Nuclear Information System (INIS)

Pavlickova, E.

1975-01-01

A bibliography is presented of Albert Einstein's works, listing his correspondence, biographical literature, articles on A. Einstein published in Czech journals, principal relativity theory monographs and popular, historical and philosophical publications. The bibliographical records are listed alphabetically. Most references give the abbreviations of libraries where the publications are available. (J.P.)

BOOK REVIEW: A Student's Guide to Einstein's Major Papers A Student's Guide to Einstein's Major Papers

Science.gov (United States)

Janssen, Michel

2013-12-01

The core of this volume is formed by four chapters (2-5) with detailed reconstructions of the arguments and derivations in four of Einstein's most important papers, the three main papers of his annus mirabilis 1905 (on the light quantum, Brownian motion, and special relativity) and his first systematic exposition of general relativity of 1916. The derivations are given in sufficient detail and in sufficiently modernized notation (without any serious distortion of the originals) for an undergraduate physics major to read and understand them with far less effort than it would take him or her to understand (English translations of) Einstein's original papers. Each of these four papers is accompanied by a detailed introduction, which covers the conceptual development of the relevant field prior to Einstein's contribution to it and corrects some of the myths surrounding these papers that still have not been fully eradicated among physicists. (One quibble: though Kennedy correctly points out that the goal of the light quantum paper was not to explain the photoelectric effect, it is also not quite right to say that 'it was written to explain the Wien region of blackbody radiation' (p. xv). Einstein used this explanatory feat as the central argument for his light quantum hypothesis.) These four chapters then are the most valuable part of the volume. They could be used, independently of one another, but preferably in conjunction with Einstein's original texts, in courses on quantum mechanics, statistical mechanics, electrodynamics, and general relativity, respectively, to add a historical component to such courses. As a historian of science embedded in a physics department who is regularly called upon to give guest lectures in such courses on the history of their subjects, I can highly recommend the volume for this purpose. However, I would not adopt this volume as (one of) the central text(s) for a course on the history of modern physics. For one thing, chapter 1, which in

Axially symmetric stationary black-hole states of the Einstein gravitational theory

International Nuclear Information System (INIS)

Meinhardt, R.

1976-01-01

Some aspects of the thepry of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology

Axially symmetric stationary black-hole states of the Einstein gravitational theory

Energy Technology Data Exchange (ETDEWEB)

Meinhardt, R [Chile Univ., Santiago. Departamento de Fisica

1976-01-01

Some aspects of the theory of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology.

Using Euler buckling springs for vibration isolation

CERN Document Server

Winterflood, J; Blair, D G

2002-01-01

Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance.

Using Euler buckling springs for vibration isolation

International Nuclear Information System (INIS)

Winterflood, J; Barber, T; Blair, D G

2002-01-01

Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance

Linear Einstein equations and Kerr-Schild maps

International Nuclear Information System (INIS)

Gergely, Laszlo A

2002-01-01

We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

On the Local Type I Conditions for the 3D Euler Equations

Science.gov (United States)

Chae, Dongho; Wolf, Jörg

2018-05-01

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution {v\\in L^∞ (-1,0; L^2 ( B(x_0,r)))\\cap L^∞_{loc} (-1,0; W^{1, ∞} (B(x_0, r)))} of the 3D Euler equations, where {B(x_0,r)} is the ball with radius r and the center at x 0, if the limiting values of certain scale invariant quantities for a solution v(·, t) as {t\\to 0} are small enough, then { \

Symmetries of the Euler compressible flow equations for general equation of state

Energy Technology Data Exchange (ETDEWEB)

Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-10-15

The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

Science.gov (United States)

Dadhich, Naresh; Pons, Josep M

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.

Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

CERN physicist receives Einstein Medal

CERN Multimedia

2006-01-01

On 29 June the CERN theorist Gabriele Veneziano was awarded the prestigious Albert Einstein Medal for significant contributions to the understanding of string theory. This award is given by the Albert Einstein Society in Bern to individuals whose scientific contributions relate to the work of Einstein. Former recipients include exceptional physicists such as Murray Gell-Mann last year, but also Stephen Hawking and Victor Weisskopf. Gabriele Veneziano, a member of the integrated CERN Theory Team since 1977, led the Theory Division from 1994 to 1997 and has already received many prestigious prizes for his outstanding work, including the Enrico Fermi Prize (see CERN Courier, November 2005), the Dannie Heineman Prize for mathematical physics of the American Physical Society in 2004 (see Bulletin No. 47/2003), and the I. Ya. Pomeranchuk Prize of the Institute of Theoretical and Experimental Physics (Moscow) in 1999.

Einstein as a Missionary of Science

Science.gov (United States)

Renn, Jürgen

2013-01-01

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed…

Linearized pseudo-Einstein equations on the Heisenberg group

Science.gov (United States)

Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard

2017-02-01

We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.

Einstein y la complejidad

Directory of Open Access Journals (Sweden)

Jou, David

2007-12-01

Full Text Available We study Einstein’s contributions to thermodynamics and statistical physics and their influence on some fields of physics which have led to current studies on complexity. We focus our attention on the use of fluctuations and entropy as a common framework for light and matter, whcich leds him to some of his fundamental contributions (phtoelectric effect, Brownian motion, specific heat of solids, stimulated light emission, Bose-Einstein condensation. We underline some aspects of Einstein’s research style: extrapolations, analogies, simplifications. We underline the relationship between light and matter as a common link of his researches in statistical physics.Presentamos las contribuciones de Einstein a la termodinámica y la mecánica estadística y su resonancia en ramas de la física que han conducido hasta la consideración actual de lo complejo. Nos referimos especialmente al uso de las fluctuaciones y de la entropía como marco común y nexo de unión entre luz y materia, que le conducen a algunas de sus aportaciones fundamentales (efecto fotoeléctrico, movimiento browniano, calor específico de los sólidos, emisión estimulada de la luz, condensación de Bose-Einstein. Consideramos también algunas facetas del estilo de investigación de Einstein, que se manifiestan con especial claridad en este campo: extrapolaciones, analogías, simplificaciones. Destacamos especialmente la importancia de la relación entre luz y materia en sus investigaciones.

The Einstein-Brazil Fogarty: A decade of synergy.

Science.gov (United States)

Nosanchuk, Joshua D; Nosanchuk, Murphy D; Rodrigues, Marcio L; Nimrichter, Leonardo; Carvalho, Antonio C Campos de; Weiss, Louis M; Spray, David C; Tanowitz, Herbert B

2015-01-01

A rich, collaborative program funded by the US NIH Fogarty program in 2004 has provided for a decade of remarkable opportunities for scientific advancement through the training of Brazilian undergraduate, graduate and postdoctoral students from the Federal University and Oswaldo Cruz Foundation systems at Albert Einstein College of Medicine. The focus of the program has been on the development of trainees in the broad field of Infectious Diseases, with a particular focus on diseases of importance to the Brazilian population. Talented trainees from various regions in Brazil came to Einstein to learn techniques and study fungal, parasitic and bacterial pathogens. In total, 43 trainees enthusiastically participated in the program. In addition to laboratory work, these students took a variety of courses at Einstein, presented their results at local, national and international meetings, and productively published their findings. This program has led to a remarkable synergy of scientific discovery for the participants during a time of rapid acceleration of the scientific growth in Brazil. This collaboration between Brazilian and US scientists has benefitted both countries and serves as a model for future training programs between these countries.

EXTENDED EINSTEIN`S THEORY OF WAVES IN THE PRESENCE OF TENSIONS IN SPACE-TIME TENSIONS TEORÍA EXTENDIDA DE ONDAS DE EINSTEIN EN LA PRESENCIA DE TENSIONES EN EL ESPACIO-TIEMPO

Directory of Open Access Journals (Sweden)

Héctor Torres-Silva

2008-11-01

Full Text Available A modification of Einstein's dynamics in the presence of certain states of space-time tension is proposed. The structure of the equations of motion for gravitational disturbances is very similar to Maxwell's equations for micro and macroscopic chiral bodies characterized by T, when the operators and are like . The unification limit between the electromagnetism and gravity is discussed. As an application of this theory we mention the birefringence effect in GPS (Global Positioning Systems systems.Se propone una modificación a la dinámica de Einstein en presencia de ciertos tipos de tensión del espacio tiempo. La estructura de las ecuaciones de movimiento para las perturbaciones gravitacionales es muy similar a las ecuaciones de Maxwell para cuerpos quirales micro y macroscópicos caracterizados por T, cuando los operadores de y son como . Se discute el límite de unificación del electromagnetismo y la gravitación en el tiempo de Planck. Como aplicación de esta teoría se menciona el efecto de la birrefringencia en sistemas GPS (Global Positioning Systems.

Multi-dimensional Fuzzy Euler Approximation

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Yangyang Hao

2017-05-01

Full Text Available Multi-dimensional Fuzzy differential equations driven by multi-dimen-sional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differential equations. The multi-dimensional fuzzy Taylor expansion is given, based on this expansion, a numerical method which is designed for giving the solution of multi-dimensional fuzzy differential equation via multi-dimensional Euler method will be presented, and its local convergence also will be discussed.

Euler y la Conjetura de Fermat sobre Números Triangulares

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José Manuel Sánchez Muñoz

2011-04-01

Full Text Available Este artículo describe la historia de como Euler demostró la existencia de infinitos números triangulares bicuadráticos, desde su correspondencia con su amigo Christian Goldbach hasta la publicación de sus resultados en la Academia de San Petesburgo.

Multipliers for the Absolute Euler Summability of Fourier Series

Indian Academy of Sciences (India)

In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.

Solitons, gauge theories and the 'great Einstein theorem'

International Nuclear Information System (INIS)

Dresden, M.; Chen, S.F.

1976-01-01

A field theory is said to be of 'Einstein type' if it has the property that the field equations imply the equations of motion. It is known that general relativity is of Einstein type, it is demonstrated here that the Yang-Mills gauge theory is of Einstein type. The relationship between the singularities in the solutions of the field equations and soliton type is analyzed. (Auth.)

From Petrov-Einstein to Navier-Stokes

Science.gov (United States)

Lysov, Vyacheslav

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics. We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p+1 dimensions, there is an associated "dual" solution of the vacuum Einstein equations in p+2 dimensions. The dual geometry has an intrinsically flat time-like boundary segment whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which hypersurface becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. It is shown that imposing a Petrov type I condition on the hypersurface geometry reduces the degrees of freedom in the extrinsic curvature to those of a fluid. Moreover, expanding around a limit in which the mean curvature of the embedding diverges, the leading-order Einstein constraint equations on hypersurface are shown to reduce to the non-linear incompressible Navier-Stokes equation for a fluid moving in hypersurface. We extend the fluid/gravity correspondence to include the magnetohydrodynamics/gravity correspondence, which translates solutions of the equations of magnetohydrodynamics (describing charged fluids) into geometries that satisfy the Einstein-Maxwell equations. We present an explicit example of this new correspondence in the context of flat Minkowski space. We show that a perturbative deformation of the Rindler wedge satisfies the Einstein-Maxwell equations provided that the parameters appearing in the expansion, which we interpret as fluid fields, satisfy the

New facets of the Einstein-Podolsky-Rosen paradox from elementary particle physics

International Nuclear Information System (INIS)

Home, Dipankar

1988-01-01

It is pointed out that the K 0 anti-K 0 and B 0 anti-B 0 systems provide a new arena for exploring the intricacies of the Einstein-Podolsky-Rosen (EPR) type example. This also provides clues for experimental discrimination between quantum mechanics and local realism. Consideration of the effect of CP non-invariance in the conext of such systems leads to the intriguing possibility, at least in principle, of an incompatibility between quantum mechanics and Einstein's locality condition at the statistical level. This calls for further investigations to clarify the subtleties involved. (author). 22 refs

Sky surveys with Einstein

International Nuclear Information System (INIS)

Gioia, I.M.

1990-01-01

Since the early times after the launch of the Einstein Observatory, systematic studies of serendipitous Einstein x-ray sources have been carried out by several observers with interests in both galactic and extragalactic astronomy. The majority of these studies were not surveys in the strict sense of the word: in several cases no analyses requiring flux completeness were performed. However, these systematic searches for sources added much to our knowledge of the behaviour in the X-ray domain of the different classes of astronomical objects and in many instances led to the study of their properties at different wavebands. (author)

Einstein and modern cosmology

International Nuclear Information System (INIS)

Stabell, R.

1979-01-01

Einstein applied his gravitation theory to a universe model with positively curved space in 1917. In order to maintain a static universe he introduced the cosmological constant, which in the light of later nonstatic universe models, he described as his life's greatest mistake. The best known such model is the Einstein-de Sitter model, which is here discussed in some detail. The 'big bang' theory is also discussed leading to the cosmic background radiation. The early phase of the 'big bang' cosmology, the first ten seconds, and the first minutes are discussed, leading to the transparent stage. (JIW)

The intellectual quadrangle: Mach-Boltzmann-Planck-Einstein

International Nuclear Information System (INIS)

Broda, E.

1981-01-01

These four men were influential in the transition from classical to modern physics. They interacted as scientists, often antagonistically. Thus Boltzmann was the greatest champion of the atom, while Mach remained unconvinced all his life. As a aphysicist, Einstein was greatly influenced by both Mach and Boltzmann, although Mach in the end rejected relativity as well. Because of his work on statistical mechanics, fluctuations, and quantum theory, Einstein has been called the natural successor to Boltzmann. Planck also was influenced by Mach at first. Hence he and Boltzmann were adversaries antil Planck converted to atomistics in 1900 and used the statistical interpretation of entropy to establish his radiation law. Planck accepted relativity early, but in quantum theory he was for a long time partly opposed to Einstein, and vice versa - Einstein considered Planck's derivation of his radiation law as unsound, while Planck could not accept the light quantum. In the case of all four physicists, science was interwoven with philosophy. Boltzmann consistently fought Mach's positivism, while Planck and Einstein moved from positivism to realism. All were also, though in very different ways, actively interested in public affairs. (orig.)

How History Helped Einstein in Special Relativity

Science.gov (United States)

Martinez, Alberto

2013-04-01

I will discuss how the German intellectual movement known as ``critical history'' motivated several physicists in the late 1900s to radically analyze the fundamental principles of mechanics, leading eventually to Einstein's special theory of relativity. Eugen Karl Dühring, Johann Bernhard Stallo, Ludwig Lange, and Ernst Mach wrote critical histories of mechanics, some of which emphasized notions of relativity and observation, in opposition to old metaphysical concepts that seemed to infect the foundations of physics. This strand of critical history included the ``genetic method'' of analyzing how concepts develop over time, in our minds, by way of ordinary experiences, which by 1904 was young Albert Einstein's favorite approach for examining fundamental notions. Thus I will discuss how history contributed in Einstein's path to relativity, as well as comment more generally on Einstein's views on history.

Development of Einstein's general theory of relativity

International Nuclear Information System (INIS)

Datta, B.K.

1980-01-01

Starting from Poincare's Lorentz-invariant theory of gravity formulated in 1906, development of Einstein's general theory of relativity during 1906-1916 is discussed. Three stages in this development are recognised. In the first stage during 1907-1914, Einstein tried to extend the relativity principle of uniform motion to the frames in non-uniform motion. For this purpose, he introduced the principle of equivalence which made it possible to calculate the effect of homogeneous gravitational field on arbitrary physical processes. During the second stage comprising years 1912-1914 overlapping the first stage, Einstein and Grossmann were struggling to translate physical postulates into the language of the absolute differential calculus. In the period 1915-1916, Einstein formulated the field equations of general relativity. While discussing these developmental stages, theories of gravitation formulated by Abraham, Nordstroem and Mie are also discussed. (M.G.B.)

Ehrenfest en Einstein. Menselijke katalysator van het heldere denken

Directory of Open Access Journals (Sweden)

Marijn J. Hollestelle

2016-10-01

Full Text Available Ehrenfest and EinsteinEhrenfest and Einstein met just before Ehrenfest became professor at Leiden University. They had much in common and became best friends. Ehrenfest shed light on some problematic aspects of Einstein’s work and during the years acted as an important sparring partner for Einstein. Ehrenfest also explained difficult aspects of Einstein’s work to the physics community. He set others on the track of working on general relativity and made Leiden an international centre for these developments during the years 1912–1920. Ehrenfest made sure Einstein was appointed part-time professor at Leiden, from which Leiden physics profited. He also aided Bohr and Einstein during their notorious debates. Ehrenfest struggled with depression his whole life. The rapid developments and mathematicising of quantum physics, Hitler’s appointment as Reichs Chancellor, money and marriage problems worsened his depressions. In 1933 Ehrenfest committed suicide, and Einstein moved to the United States and away from the study on quantum physics.

Quantum tunneling of Bose-Einstein condensates in optical lattices

CERN Document Server

Fan Wen Bin

2003-01-01

In quantum tunneling a particle with energy E can pass through a high potential barrier V(>E) due to the wave character of the particle. Bose-Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double-well or optical lattices. The employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose-Einstein condensates in optical lattices. The results show that there are two kinds of tunneling in this system, Landau-Zener tunneling between extended states of the system and Wannier-Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. The also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. The results agree with experimental data in references. Finally, the propose an experimental protocol to observe this new phenomenon in future experiments

A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef

2014-01-01

The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations...

Test of Einstein-Podolsky-Rosen steering based on the all-versus-nothing proof.

Science.gov (United States)

Wu, Chunfeng; Chen, Jing-Ling; Ye, Xiang-Jun; Su, Hong-Yi; Deng, Dong-Ling; Wang, Zhenghan; Oh, C H

2014-03-06

In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.

Contact discontinuities in multi-dimensional isentropic Euler equations

Czech Academy of Sciences Publication Activity Database

Březina, J.; Chiodaroli, E.; Kreml, Ondřej

2018-01-01

Roč. 2018 (2018), č. článku 94. ISSN 1072-6691 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : isentropic Euler equations * non-uniqueness * Riemann problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/94/abstr.html

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

Science.gov (United States)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...

African Journals Online (AJOL)

This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...

Einstein, Ethics and the Atomic Bomb

Science.gov (United States)

Rife, Patricia

2005-03-01

Einstein voiced his ethical views against war as well as fascism via venues and alliances with a variety of organizations still debated today. In 1939, he signed a letter to President Roosevelt (drafted by younger colleagues Szilard, Wigner and others) warning the U.S.government about the danger of Nazi Germany gaining control of uranium in the Belgian-controlled Congo in order to develop atomic weapons, based on the discovery of fission by Otto Hahn and Lise Meitner. In 1945, he became a member of the Princeton-based ``Emergency Committee for Atomic Scientists'' organized by Bethe, Condon, Bacher, Urey, Szilard and Weisskopf. Rare Einstein slides will illustrate Dr.Rife's presentation on Albert Einstein's philosophic and ethical convictions about peace, and public stance against war (1914-1950).

Einstein wrote back my life in physics

CERN Document Server

Moffat, John W

2012-01-01

John W. Moffat was a poor student of math and science. That is, until he read Einstein's famous paper on general relativity. Realizing instantly that he had an unusual and unexplained aptitude for understanding the complex physics described in the paper, Moffat wrote a letter to Einstein that would change the course of his life. Einstein Wrote Back tells the story of Moffat's unusual entry into the world of academia and documents his career at the frontlines of twentieth-century physics as he worked and associated with some of the greatest minds in scientific history, including Niels Bohr,

Einstein constraints in the Yang-Mills form

International Nuclear Information System (INIS)

Ashtekar, A.

1987-01-01

It is pointed out that constraints of Einstein's theory play a powerful role in both classical and quantum theory because they generate motions in spacetime, rather than in an internal space. New variables are then introduced on the Einstein phase space in terms of which constraints simplify considerably. In particular, the use of these variables enables one to imbed the constraint surface of Einstein's theory into that of Yang-Mills. The imbedding suggests new lines of attack to a number of problems in classical and quantum gravity and provides new concepts and tools to investigate the microscopic structure of space-time geometry

Einstein's Riddle as a Tool for Profiling Students

Science.gov (United States)

Özeke, Vildan; Akçapina, Gökhan

2016-01-01

There are many computer games, learning environments, online tutoring systems or computerized tools which keeps the track of the user while learning or engaging in the activities. This paper presents results from an exploratory study and aims to group students regarding their behavior data while solving the Einstein's riddle. 45 undergraduate…

Effective equivalence of the Einstein-Cartan and Einstein theories of gravity

International Nuclear Information System (INIS)

Nester, J.M.

1977-01-01

I prove that, for any choice of minimally coupled source field Lagrangian for the Einstein-Cartan-Sciama-Kibble theory of gravity, there exists a related minimally coupled source field Lagrangian for the Einstein theory which produces the same field equations for the metric and source field. By using a standard first-order form for source Lagrangians, the converse is also demonstrated. This establishes a one-to-one correspondence between source Lagrangians for the two theories which clearly reveals their similarities and their differences. Because of this ''equivalence,'' one can view either theory, in terms of the other, as minimal coupling for a related Minkowski source Lagrangian or as nonminimal coupling for the same Minkowski source Lagrangian. Consequently the two theories are, in this sense, indistinguishable. Some other implications of this ''equivalence'' are discussed

First integrals of geodesics in the Einstein-Schwarzschild space

International Nuclear Information System (INIS)

Meshkov, A.G.; Dordzhiev, P.B.

1984-01-01

Linear and quadratic velocity integrals of geodesics in the Einstein-Schwarzschild space are calculated. The Schwarzschild geodesics equations have only four independent linear integrals. Quadratic integrals are polynomials from linear ones with constant coefficients. Total separation of variables in the Hamilton-Jacobi equation with Schwarzschild metric is possible only in two coordinate systems: ''spherical'' and ''conic'' systems

Self Completeness of Einstein Gravity

CERN Document Server

Dvali, Gia

2010-01-01

We argue, that in Einsteinian gravity the Planck length is the shortest length of nature, and any attempt of resolving trans-Planckian physics bounces back to macroscopic distances due to black hole formation. In Einstein gravity trans-Planckian propagating quantum degrees of freedom cannot exist, instead they are equivalent to the classical black holes that are fully described by lighter infra-red degrees of freedom and give exponentially-soft contribution into the virtual processes. Based on this property we argue that pure-Einstein (super)gravity and its high-dimensional generalizations are self-complete in deep-UV, but not in standard Wilsonian sense. We suggest that certain strong-coupling limit of string theory is built-in in pure Einstein gravity, whereas the role of weakly-coupled string theory limit is to consistently couple gravity to other particle species, with their number being set by the inverse string coupling. We also discuss some speculative ideas generalizing the notion of non-Wilsonian sel...

The symplectic structure of Euler-Lagrange superequations and Batalin-Vilkoviski formalism

CERN Document Server

Monterde, J

2003-01-01

We study the graded Euler-Lagrange equations from the viewpoint of graded Poincare-Cartan forms. An application to a certain class of solutions of the Batalin-Vilkoviski master equation is also given.

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Science.gov (United States)

Mitra, Sukanya

2018-01-01

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

Directory of Open Access Journals (Sweden)

Ma Yanfeng

2016-10-01

Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

Albert Einstein and 20th century's physics

International Nuclear Information System (INIS)

Zajac, R.

1979-01-01

Albert Einstein's teaching and his three fundamental works are discussed dealing with the molecular theory of heat applied to the motion of suspended particles in liquids at rest, the photoelectric effect, and the theory of relativity. Albert Einstein's impact on contemporary physics is evaluated. (J.P.)

Optomechanically induced transparency with Bose–Einstein condensate in double-cavity optomechanical system

Science.gov (United States)

Liu, Li-Wei; Gengzang, Duo-Jie; An, Xiu-Jia; Wang, Pei-Yu

2018-03-01

We propose a novel technique of generating multiple optomechanically induced transparency (OMIT) of a weak probe field in hybrid optomechanical system. This system consists of a cigar-shaped Bose–Einstein condensate (BEC), trapped inside each high finesse Fabry-Pérot cavity. In the resolved sideband regime, the analytic solutions of the absorption and the dispersion spectrum are given. The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum. Furthermore, whether there is BEC in each cavity is a key factor in the number of OMIT windows determination. The technique presented may have potential applications in quantum engineering and quantum information networks. Project supported by the National Natural Science Foundation of China (Grant Nos. 11564034, 11105062, and 21663026) and the Scientific Research Funds of College of Electrical Engineering, Northwest University, China (Grant No. xbmuyjrc201115).

Newton's Laws, Euler's Laws and the Speed of Light

Science.gov (United States)

Whitaker, Stephen

2009-01-01

Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…

A Short Proof of Euler's Inequality R ≥ 2r Theorem. Let ∆ ABC be an ...

Indian Academy of Sciences (India)

IAS Admin

A Short Proof of Euler's Inequality R ≥ 2r. Theorem. Let ∆ ABC be an arbitrary triangle with circumradius R and inradius r. Then R ≥ 2r with equality holding if and only if ∆ABC is equilateral. This was first published by Euler in 1765. Since then several proofs have followed, some geometric and some algebraic. We will use ...

Parallel computation of Euler and Navier-Stokes flows

International Nuclear Information System (INIS)

Swisshelm, J.M.; Johnson, G.M.; Kumar, S.P.

1986-01-01

A multigrid technique useful for accelerating the convergence of Euler and Navier-Stokes flow computations has been restructured to improve its performance on both SIMD and MIMD computers. The new algorithm allows both the construction of longer coarse-grid vectors and the multitasking of entire grids. Computational results are presented for the CDC Cyber 205, Cray X-MP, and Denelcor HEP I. 15 references

Spectroscopy of dark soliton states in Bose-Einstein condensates

International Nuclear Information System (INIS)

Bongs, K; Burger, S; Hellweg, D; Kottke, M; Dettmer, S; Rinkleff, T; Cacciapuoti, L; Arlt, J; Sengstock, K; Ertmer, W

2003-01-01

Experimental and numerical studies of the velocity field of dark solitons in Bose-Einstein condensates are presented. The formation process after phase imprinting as well as the propagation of the emerging soliton are investigated using spatially resolved Bragg spectroscopy of soliton states in Bose-Einstein condensates of 87 Rb. A comparison of experimental data to results from numerical simulations of the Gross-Pitaevskii equation clearly identifies the flux underlying a dark soliton propagating in a Bose-Einstein condensate. The results allow further optimization of the phase imprinting method for creating collective excitations of Bose-Einstein condensates

Large Scale Simulations of the Euler Equations on GPU Clusters

KAUST Repository

Liebmann, Manfred; Douglas, Craig C.; Haase, Gundolf; Horvá th, Zoltá n

2010-01-01

The paper investigates the scalability of a parallel Euler solver, using the Vijayasundaram method, on a GPU cluster with 32 Nvidia Geforce GTX 295 boards. The aim of this research is to enable large scale fluid dynamics simulations with up to one

Stationary axisymmetric Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Catenacci, R.; Diaz Alonso, J.

1976-01-01

We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known

Einstein Ring in Distant Universe

Science.gov (United States)

2005-06-01

on the newly discovered Einstein ring. The image quality ("seeing") of the R-band image is exceptional (0.5") and the image reveals the lensing system in stunning details. The central dot is the lens, a quiescent massive galaxy that distort the light emitted by background sources. The large arc surrounding the central lens is a part of the Einstein-ring created by a background source finely aligned with the lens. The reddish colour indicates that the redshift of the system is very large. FORS2 spectroscopy of the lensing system yield a redshift close to 1 for the lens (we see the lens as it was when the universe was half its present size), and a record-breaking redshift z=3.8 for a background source of such brightness, hence we see the object (a star forming galaxy) as it was when the universe was only 12% of its present age. The lensing model indicates that the light of the source is magnified at least 13 times. The right panel shows the reconstructed image based on the model of the lens and the source, showing the ring to extend over 3/4 of a circle. "There are only a very few optical rings or arcs known, and even less so in which the lens and the source are at large distance, i.e. more than about 7,000 million light-years away (or half the present age of the Universe)", says Rémi Cabanac, former ESO Fellow and now working at the Canada-France-Hawaii Telescope. "Moreover, very few are nearly complete", he adds. But in the case of this newly found cosmic ring, the images show it to extend to almost 3/4 of a circle. The lensing galaxy is located at a distance of about 8,000 million light-years from us, while the source galaxy whose light is distorted, is much farther away, at 12,000 million light-years. Thus, we see this galaxy as it was when the universe was only 12% of its present age. The lens magnifies the source almost 13 times. The observations reveal the galaxy acting as a lens to be a rather quiet galaxy, 40,000 light-years wide, with an old stellar

On Certain Conceptual Anomalies in Einstein's Theory of Relativity

Directory of Open Access Journals (Sweden)

Crothers S. J.

2008-01-01

Full Text Available There are a number of conceptual anomalies occurring in the Standard exposition of Einstein's Theory of Relativity. These anomalies relate to issues in both mathematics and in physics and penetrate to the very heart of Einstein's theory. This paper reveals and amplifies a few such anomalies, including the fact that Einstein's field equations for the so-called static vacuum configuration, $R_{mu u} = 0$, violates his Principle of Equivalence, and is therefore erroneous. This has a direct bearing on the usual concept of conservation of energy for the gravitational field and the conventional formulation for localisation of energy using Einstein's pseudo-tensor. Misconceptions as to the relationship between Minkowski spacetime and Special Relativity are also discussed, along with their relationships to the pseudo-Riemannian metric manifold of Einstein's gravitational field, and their fundamental geometric structures pertaining to spherical symmetry.

Bose-Einstein correlation in Landau's model

International Nuclear Information System (INIS)

Hama, Y.; Padula, S.S.

1986-01-01

Bose-Einstein correlation is studied by taking an expanding fluid given by Landau's model as the source, where each space-time point is considered as an independent and chaotic emitting center with Planck's spectral distribution. As expected, the correlation depends on the relative angular positions as well as on the overall localization of the measuring system and it turns out that the average dimension of the source increases with the multiplicity N/sub ch/

What about Albert Einstein? Using Biographies to Promote Students' Scientific Thinking

Science.gov (United States)

Fingon, Joan C.; Fingon, Shallon D.

2009-01-01

Who hasn't heard of Einstein? Science educators everywhere are familiar with Einstein's genius and general theory of relativity. Students easily recognize Einstein's image by his white flyaway hair and bushy mustache. It is well known that Einstein was a brilliant physicist and an abstract thinker who often used his creativity and imagination in…

Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian

International Nuclear Information System (INIS)

Edelstein, Jose D.; Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge

2006-01-01

Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions

Spatial interference patterns in the dynamics of a 2D Bose-Einstein condensate

Science.gov (United States)

Bera, Jayanta; Roy, Utpal

2018-05-01

Bose-Einstein condensate has become a highly tunable physical system, which is proven to mimic a number of interesting physical phenomena in condensed matter physics. We study the dynamics of a two-dimensional Bose Einstein condensate (BEC) in the presence of a flat harmonic confinement and time-dependent sharp potential peak. Condensate density can be meticulously controlled with time by tuning the physically relevant parameters: frequency of the harmonic trap, width of the peaks, frequency of their oscillations, initial density etc. By engineering various trap profile, we solve the system, numerically, and explore the resulting spatial interference patters.

Bose-Einstein Condensation

Indian Academy of Sciences (India)

absolute zero. These ideas had ... Everybody is talking about Bose-Einstein condensation. This discovery ... needed if we want to find the probability distribution of the x- ... Boltzmann took two approaches to the problem, both of them deep and ...

Competition between Bose-Einstein Condensation and Spin Dynamics.

Science.gov (United States)

Naylor, B; Brewczyk, M; Gajda, M; Gorceix, O; Maréchal, E; Vernac, L; Laburthe-Tolra, B

2016-10-28

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Existence of Bose-Einstein condensation in one and two dimensions

International Nuclear Information System (INIS)

Olinto, A.C.

1988-10-01

It is shown that in Bose Condensed systems the γ-sum rule has an additional term due to the condensate reservoir. As a result of this new sum rule and an exact Bogoliubov inequality, Bose-Einstein condensation in repulsively interacting systems may occur in one and two dimensions. (author) [pt

Einstein's Mirror

Science.gov (United States)

Gjurchinovski, Aleksandar; Skeparovski, Aleksandar

2008-01-01

Reflection of light from a plane mirror in uniform rectilinear motion is a century-old problem, intimately related to the foundations of special relativity. The problem was first investigated by Einstein in his famous 1905 paper by using the Lorentz transformations to switch from the mirror's rest frame to the frame where the mirror moves at a…

Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method; Diferentes semillas para solucionar las ecuaciones de la cinetica puntual estocastica empleando el metodo de Euler-Maruyama

Energy Technology Data Exchange (ETDEWEB)

Suescun D, D.; Oviedo T, M., E-mail: daniel.suescun@usco.edu.co [Universidad Surcolombiana, Av. Pastrana Borrero - Carrera 1, Neiva, Huila (Colombia)

2017-09-15

In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

Regularity and energy conservation for the compressible Euler equations

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.; Wiedemann, E.

2017-01-01

Roč. 223, č. 3 (2017), s. 1375-1395 ISSN 0003-9527 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.392, year: 2016 http://link.springer.com/article/10.1007%2Fs00205-016-1060-5

A non-linear multigrid method for the steady Euler equations

NARCIS (Netherlands)

Hemker, P.W.; Koren, B.; Dervieux, A.; Leer, van B.; Periaux, J.; Rizzi, A.

1989-01-01

Higher-order accurate Euler-flow solutions are presented for some airfoil test cases. Second-order accurate solutions are computed by an Iterative Defect Correction process. For two test cases even higher accuracy is obtained by the additional use of a ~xtrapolation technique. Finite volume

Euler-Lagrange modeling of the hydrodynamics of dense multiphase flows

NARCIS (Netherlands)

Padding, J.T.; Deen, N.G.; Peters, E. A. J. F.; Kuipers, J. A. M.

2015-01-01

The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are

Iterative methods for compressible Navier-Stokes and Euler equations

Energy Technology Data Exchange (ETDEWEB)

Tang, W.P.; Forsyth, P.A.

1996-12-31

This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.

You err, Einstein.. Newton, Einstein, Heisenberg, and Feynman discuss quantum physics

International Nuclear Information System (INIS)

Fritzsch, Harald

2008-01-01

Harald Fritzsch and his star physicists Einstein, Heisenberg, and Feynman explain the central concept of nowadays physics, quantum mechanics, without it nothing goes in modern world. And the great Isaac newton puts the questions, which all would put

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

Science.gov (United States)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Theory of a gauge gravitational field at localization of the Einstein group

International Nuclear Information System (INIS)

Tunyak, V.N.

1985-01-01

Theory of a gauge gravitational field when localizing a group of movements of the Einstein homogeneous static Universe (the R x SO Einstein group (4)) has been formulated. Proceeding from tetrade components of the Einstein Universe the relation between the Riemann metrics and gauge fields of the Einstein group has been established. Metric coherence with torsion transforming to the Kristoffel coherence of the Einstein Universe has been found when switching out gauge fields. It is shown that within the limit of infinite radius of the Einstein Universe curvature the given Einstein-invariant gauge theory transforms to the tetrade gravitation theory with localized triade rotations. Exact solutions in the form of nonsingular cosmological models have been obtained

Wetting phase transition of two segregated Bose–Einstein condensates restricted by a hard wall

Energy Technology Data Exchange (ETDEWEB)

Thu, Nguyen Van [Department of Physics, Hanoi Pedagogical University No. 2, Hanoi (Viet Nam); Phat, Tran Huu [Vietnam Atomic Energy Commission, 59 Ly Thuong Kiet, Hanoi (Viet Nam); Song, Pham The, E-mail: thesong80@icloud.com [Tay Bac University, Son La (Viet Nam)

2016-04-01

Highlights: • System of two segregated Bose–Einstein condensates limited by a wall is studied. • Double-parabola approximation is applied to Gross–Pitaevskii theory. • Interface tension and wetting phase diagram are established. - Abstract: The wetting phase transition in the system of two segregated Bose–Einstein condensates (BECs) restricted by a hard wall is studied by means of the double-parabola approximation (DPA) applied to the Gross–Pitaevskii (GP) theory. We found the interfacial tension and the wetting phase diagram which depend weakly on the spatial restriction.

EINSTEIN EQUATIONS FOR TETRAD FIELDS ECUACIONES DE EINSTEIN PARA CAMPOS TETRADOS

Directory of Open Access Journals (Sweden)

Héctor Torres-Silva

2008-11-01

Full Text Available Every metric tensor can be expressed by the inner product of tetrad fields. We prove that Einstein's equations for these fields have the same form as the stress-energy tensor of electromagnetism if the total external current . Using the Evans' unified field theory, we show that the true unification of gravity and electromagnetism is with source-free Maxwell equations.Todo tensor métrico puede ser expresado por el producto interno de campos tetrados. Se prueba que las ecuaciones de Einstein para esos campos tienen la misma forma que el tensor electromagnético de momento-energía si la corriente externa total es igual a cero. Usando la teoría de campo unificado de Evans se muestra que la verdadera unificación de la gravedad y el electromagnetismo es con las ecuaciones de Maxwell sin fuentes.

The role of Euler buckling instability in the fabrication of nanoelectromechanical systems on the basis of GaAs/AlGaAs heterostructures

Science.gov (United States)

Shevyrin, A. A.; Pogosov, A. G.; Budantsev, M. V.; Bakarov, A. K.; Toropov, A. I.; Ishutkin, S. V.; Shesterikov, E. V.; Kozhukhov, A. S.; Kosolobov, S. S.; Gavrilova, T. A.

2012-12-01

Mechanical stresses are investigated in suspended nanowires made on the basis of GaAs/AlGaAs heterostructures. Though there are no intentionally introduced stressor layers in the heterostructure, the nanowires are subject to Euler buckling instability. In the wide nanowires, the out-of-plane buckling is observed at length significantly smaller (3 times) than the theoretically estimated critical value, while in the narrow nanowires, the experimentally measured critical length of the in-plane buckling coincides with the theoretical estimation. The possible reasons for the obtained discrepancy are considered. The observed peculiarities should be taken into account in the fabrication of nanomechanical and nanoelectromechanical systems.

Leonhardi Euleri Opera omnia: Editing the works and correspondence of Leonhard Euler

Directory of Open Access Journals (Sweden)

Andreas KLEINERT

2015-12-01

Full Text Available The paper gives an overview on the history and present state of the edition of the complete works of Leonhard Euler (1707–1783. After several failed initiatives in the 19th century, the project began in 1907 with the edition of Euler’s printed works. The works were divided into three series: I. Mathematics (29 volumes; II. Mechanics and Astronomy (31 volumes; and III. Physics and Miscellaneous (12 volumes. After several ups and downs due to two World Wars and economic problems, the publication of the printed works with a total of 72 volumes is nearly finished. Only two volumes on perturbation theory in astronomy are still missing. The publication of series IV (manuscripts and correspondence started in 1967 as a joint project of the Swiss and the Soviet academies of sciences. The manuscript edition was postponed, and the project focussed on Euler’s correspondence which contains approximately 3000 letters, 1000 of them written by Euler. The correspondents include famous mathematicians of the 18th century like d’Alembert, Clairaut and the Bernoullis, but also many less-known people with whom Euler corresponded on a great variety of subjects. A major problem is to find and to finance appropriate editors who are able to read French, Latin, and the old German handwriting, and who are acquainted with history, culture and science of the 18th century. During the last 50 years, the editors gathered copies or scans of most of the preserved Euler’s letters. The original letters addressed to Euler were made available to the editorial group in Switzerland by the Russian Academy of Sciences before World War I, and before their restitution in 1947 the editors made fairly good photographs that are now an important part of the material basis of the edition. Each volume of the letter series (VIA contains Euler’s correspondence with one or more of his contemporaries, presented in a chronological order. Up to the present day, four volumes of the

Bose-Einstein condensates form in heuristics learned by ciliates deciding to signal 'social' commitments.

Science.gov (United States)

Clark, Kevin B

2010-03-01

Fringe quantum biology theories often adopt the concept of Bose-Einstein condensation when explaining how consciousness, emotion, perception, learning, and reasoning emerge from operations of intact animal nervous systems and other computational media. However, controversial empirical evidence and mathematical formalism concerning decoherence rates of bioprocesses keep these frameworks from satisfactorily accounting for the physical nature of cognitive-like events. This study, inspired by the discovery that preferential attachment rules computed by complex technological networks obey Bose-Einstein statistics, is the first rigorous attempt to examine whether analogues of Bose-Einstein condensation precipitate learned decision making in live biological systems as bioenergetics optimization predicts. By exploiting the ciliate Spirostomum ambiguum's capacity to learn and store behavioral strategies advertising mating availability into heuristics of topologically invariant computational networks, three distinct phases of strategy use were found to map onto statistical distributions described by Bose-Einstein, Fermi-Dirac, and classical Maxwell-Boltzmann behavior. Ciliates that sensitized or habituated signaling patterns to emit brief periods of either deceptive 'harder-to-get' or altruistic 'easier-to-get' serial escape reactions began testing condensed on initially perceived fittest 'courting' solutions. When these ciliates switched from their first strategy choices, Bose-Einstein condensation of strategy use abruptly dissipated into a Maxwell-Boltzmann computational phase no longer dominated by a single fittest strategy. Recursive trial-and-error strategy searches annealed strategy use back into a condensed phase consistent with performance optimization. 'Social' decisions performed by ciliates showing no nonassociative learning were largely governed by Fermi-Dirac statistics, resulting in degenerate distributions of strategy choices. These findings corroborate

Einstein's Years in Switzerland

Science.gov (United States)

Plendl, Hans S.

2005-11-01

Albert Einstein left Germany, the country of his birth, in 1894 and moved to Switzerland in 1895. He studied, worked and taught there, except for a year's stay in Prague, until1914. That year he returned to Germany, where he lived until his emigration to the United States in 1933. In 1905, while living with his wife Mileva and their first son Hans Albert in Bern and working as a technical expert at the Swiss Patent Office, he published his dissertation on the determination of molecular dimensions, his papers on Brownian Motion that helped to establish the Kinetic Theory of Heat and on the Photo-Electric Effect that validated the Quantum Theory of Light, and the two papers introducing the Special Theory of Relativity. How the young Einstein could help to lay the foundations of these theories while still working on his dissertation, holding a full-time job and helping to raise a family has evoked much discussion among his biographers. In this contribution, the extent to which living within Swiss society and culture could have made this feat possible will be examined. Old and recent photos of places in Switzerland where Einstein has lived and worked will be shown.

What Einstein Can Teach Us about Education

Science.gov (United States)

Hayes, Denis

2007-01-01

People are more likely to associate Einstein with complex scientific theories and mathematical calculations than with education theory. In fact, Einstein's own experiences of schooling and his reflections on the meaning of life and the significance of education are profound and oddly relevant to the situation that pertains in England today. It is…

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

Science.gov (United States)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.

2015-09-30

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

Stability of the graviton Bose–Einstein condensate in the brane-world

Energy Technology Data Exchange (ETDEWEB)

Casadio, Roberto, E-mail: casadio@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna (Italy); INFN, Sezione di Bologna, viale B. Pichat 6, 40127 Bologna (Italy); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, 09210-580, Santo André, SP (Brazil)

2016-12-10

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic Eötvös brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose–Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.

Die Leben Einsteins eine Reise durch die Geschichte der Physik

CERN Document Server

Fiami

2005-01-01

Jeder kennt die Namen Einstein, Newton oder Galilei. aber was weiss man über sie? Hier ein Porträt Einsteins anhand von sechs Meilensteinen aus der Geschichte der Physik. Einstein tritt auf als Protagonist in verschiedenen Epochen und bei verschiedenen Entdeckungen, die die Welt verändert haben.

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Energy Technology Data Exchange (ETDEWEB)

Mitra, Sukanya [Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat (India)

2018-01-15

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system. (orig.)

Derivation of Einstein-Cartan theory from general relativity

Science.gov (United States)

Petti, Richard

2015-04-01

General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.

Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

International Nuclear Information System (INIS)

Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.

2011-01-01

Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.

EINSTEIN - Expert system for an Intelligent Supply of Thermal Energy in Industry. Audit methodology and software tool

Energy Technology Data Exchange (ETDEWEB)

Schweiger, Hans; Danov, Stoyan (energyXperts.NET (Spain)); Vannoni, Claudia; Facci, Enrico (Sapienza Univ. of Rome, Dept. of Mechanics and Aeronautics, Rome (Italy)); Brunner, Christoph; Slawitsch, Bettina (Joanneum Research, Inst. of Sustainable Techniques and Systems - JOINTS, Graz (Austria))

2009-07-01

For optimising thermal energy supply in industry, a holistic integral approach is required that includes possibilities of demand reduction by heat recovery and process integration, and by an intelligent combination of efficient heat and cold supply technologies. EINSTEIN is a tool-kit for fast and high quality thermal energy audits in industry, composed by an audit guide describing the methodology and by a software tool that guides the auditor through all the audit steps. The main features of EINSTEIN are: (1) a basic questionnaire helps for systematic collection of the necessary information with the possibility to acquire data by distance; (2) special tools allow for fast consistency checking and estimation of missing data, so that already with very few data some first predictions can be made; (3) the data processing is based on standardised models for industrial processes and industrial heat supply systems; (4) semi-automatization: the software tool gives support to decision making for the generation of alternative heat and cold supply proposals, carries out automatically all the necessary calculations, including dynamic simulation of the heat supply system, and creates a standard audit report. The software tool includes modules for benchmarking, automatic design of heat exchanger networks, and design assistants for the heat and cold supply system. The core of the expert system software tool is available for free, as an open source software project. This type of software development has shown to be very efficient for dissemination of knowledge and for the continuous maintenance and improvement thanks to user contributions.

Elastic scattering of a Bose-Einstein condensate at a potential landscape

International Nuclear Information System (INIS)

Březinová, Iva; Burgdörfer, Joachim; Lode, Axel U J; Streltsov, Alexej I; Cederbaum, Lorenz S; Alon, Ofir E; Collins, Lee A; Schneider, Barry I

2014-01-01

We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Science.gov (United States)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Interactions of Ultracold Impurity Particles with Bose-Einstein Condensates

Science.gov (United States)

2015-06-23

AFRL-OSR-VA-TR-2015-0141 INTERACTIONS OF ULTRACOLD IMPURITY PARTICLES WITH BOSE- EINSTEIN CONDENSATES Georg Raithel UNIVERSITY OF MICHIGAN Final...SUBTITLE Interactions of ultracold impurity particles with Bose- Einstein Condensates 5a. CONTRACT NUMBER FA9550-10-1-0453 5b. GRANT NUMBER 5c...Interactions of ultracold impurity particles with Bose- Einstein Condensates Contract/Grant #: FA9550-10-1-0453 Reporting Period: 8/15/2010 to 2/14

[Photoeffects, Einstein's light quanta and the history of their acceptance].

Science.gov (United States)

Wiederkehr, Karl Heinrich

2006-01-01

It is generally supposed, that the discovery of the efficacy-quantum by Planck was the impetus to Einstein's hypothesis of lightquanta. With its help Einstein could explain the external light-electrical effect. But even years before Einstein had worked at the photoeffect and already made experiments on it. For that reason the article gives a short survey about the history of the lightelectric effects. Lenard's basical work about the release of the photoelectrons is dealt with in detail, without which Einstein would scarcely have found his lightquanta. Furthermore it is shown how difficult it was for the physicists to give up--at least partially--the traditional view of the undulation-nature of light, and how they searched to explain the great energies of the photoelectrons. On the other side it is set forth how Einstein's formula of lightquanta was gradually confirmed. The tragical development of Einstein's personal relations with Johannes Stark and Philipp Lenard are briefly described. Stark was one of the few who supported Einstein's ideas at the beginning. Only with the Compton-effect, which could only be quantitatively interpreted by means of lightquanta and the special theory of relativity 1923, the way was free for the general acceptance of the lightquanta. Einstein did not agree to the obtained dualism of undulation and corpuscle; he had a different solution in mind about the fusion of the two forms of appearance of light.

Approximate radiative solutions of the Einstein equations

International Nuclear Information System (INIS)

Kuusk, P.; Unt, V.

1976-01-01

In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)

Automatic interpretation of magnetic data using Euler deconvolution with nonlinear background

Digital Repository Service at National Institute of Oceanography (India)

Dewangan, P.; Ramprasad, T.; Ramana, M.V.; Desa, M.; Shailaja, B.

are close to each other. A possible solution to these problems is prposed by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization...

Academic Training: Einstein and beyond: Introduction to General relativity

CERN Multimedia

Françoise Benz

2005-01-01

2005-2006 ACADEMIC TRAINING PROGRAMME LECTURE SERIES 3, 4, 5, 6, 7 October from 11:00 to 12:00 - Main Auditorium, bldg. 500 Einstein and beyond: Introduction to General relativity by N. Straumann / Institut fur theoretische physics, Univ. Zürich We review the enduring achievements of Einstein's papers of 1905 and their impact on the further developments in physics. Program : Lectures I and II:Einstein's Contributions to Statistical Mechanics and Quantum Theory Lecture III:Einstein's Thesis at the University of Zürich Lecture IV: From Special to General Relativity Lecture V: The History and the Mystery of the Cosmological Constant ENSEIGNEMENT ACADEMIQUE ACADEMIC TRAINING Françoise Benz 73127 academic.training@cern.ch

An addendum to the Heisenberg-Euler effective action beyond one loop

Energy Technology Data Exchange (ETDEWEB)

Gies, Holger; Karbstein, Felix [Helmholtz-Institut Jena,Fröbelstieg 3, 07743 Jena (Germany); Theoretisch-Physikalisches Institut, Abbe Center of Photonics,Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena (Germany)

2017-03-21

We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields.

Einstein was right!

CERN Multimedia

2003-01-01

For the first time scientists have succeeded in measuring the speed of gravity. They took advantage of a rare alignment of Jupiter against a far-off quasar to measure the fundamental constant described by Albert Einstein in his general theory of relativity (2 pages).

New details emerge from the Einstein files

CERN Multimedia

Overbye, D

2002-01-01

For many years the FBI spied on Einstein. New details of this surveilance are emerging in "The Einstein File: J. Edgar Hoover's Secret War Against the World's Most Famous Scientist," by Fred Jerome, who sued the government with the help of the Public Citizen Litigation Group to obtain a less censored version of the file (1 page).

EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited

Science.gov (United States)

Nikolic, Hrvoje

2012-01-01

In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…

A Student's Guide to Einstein's Major Papers

International Nuclear Information System (INIS)

Janssen, Michel

2013-01-01

The core of this volume is formed by four chapters (2–5) with detailed reconstructions of the arguments and derivations in four of Einstein's most important papers, the three main papers of his annus mirabilis 1905 (on the light quantum, Brownian motion, and special relativity) and his first systematic exposition of general relativity of 1916. The derivations are given in sufficient detail and in sufficiently modernized notation (without any serious distortion of the originals) for an undergraduate physics major to read and understand them with far less effort than it would take him or her to understand (English translations of) Einstein's original papers. Each of these four papers is accompanied by a detailed introduction, which covers the conceptual development of the relevant field prior to Einstein's contribution to it and corrects some of the myths surrounding these papers that still have not been fully eradicated among physicists. (One quibble: though Kennedy correctly points out that the goal of the light quantum paper was not to explain the photoelectric effect, it is also not quite right to say that 'it was written to explain the Wien region of blackbody radiation' (p. xv). Einstein used this explanatory feat as the central argument for his light quantum hypothesis.) These four chapters then are the most valuable part of the volume. They could be used, independently of one another, but preferably in conjunction with Einstein's original texts, in courses on quantum mechanics, statistical mechanics, electrodynamics, and general relativity, respectively, to add a historical component to such courses. As a historian of science embedded in a physics department who is regularly called upon to give guest lectures in such courses on the history of their subjects, I can highly recommend the volume for this purpose. However, I would not adopt this volume as (one of) the central text(s) for a course on the history of modern physics. For one thing, chapter 1, which

Flow fields in the supersonic through-flow fan. Comparison of the solutions of the linear potential theory and the numerical solution of the Euler equations; Choonsoku tsukaryu fan nai no nagareba. Senkei potential rironkai to Euler hoteishiki no suchikai no hikaku

Energy Technology Data Exchange (ETDEWEB)

Yamasaki, N; Nanba, M; Tashiro, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1996-03-27

Comparison study between solutions of a linear potential theory and numerical solution of Euler equations was made for flow in a supersonic through-flow fan. In numerical fluid dynamic technique, Euler equations are solved by finite difference method under the assumption of air and perfect gas fluid, and neglected viscosity and thermal conductivity of fluid. As a result, in a linear potential theory, expansion wave was regarded as equipotential discontinuous surface, while in Euler numerical solution, it was regarded as finite pressure gradient where a wave front fans out toward downstream. The latter reflection point of shock wave on a wing existed upstream as compared with the former reflection point. The shock wave angle was dominated by Euler equations, and different from the Mach line of a linear potential theory in both angle and discontinuous quantities in front and behind. Both calculated solutions well agreed with each other until the first reflection point of the Mach line, however, thereafter the difference between them increased toward downstream. 5 refs., 5 figs., 1 tab.

Bose-Einstein condensation in a general static homogeneous magnetic fieldinebreak and the effective action: The nonrelativistic ideal gas

International Nuclear Information System (INIS)

Toms, D.J.

1995-01-01

We consider the problem of Bose-Einstein condensation for a system of nonrelativistic spin-0 bosons in a space of arbitrary dimension D. A general static homogeneous magnetic field is imposed. The effective action approach and ζ-function regularization are used. If D=2δ or 2δ+1, a constant magnetic field is characterized by δ independent components. If p≤δ of these components are nonzero, the condition for Bose-Einstein condensation to occur is D-2p≥3. This means that if D=2δ, then Bose-Einstein condensation never occurs for p=δ-1 or δ. If D=2δ+1, Bose-Einstein condensation never occurs for p=δ. For D-2p≥3, Bose-Einstein condensation does occur, and we show how it may be interpreted as symmetry breaking to give a ground state which is not constant

Controlling chaos in the Bose-Einstein condensate

Energy Technology Data Exchange (ETDEWEB)

Cong Fuzhong, E-mail: wzx2007111@126.com; Wang Zhixia; Hua Hongtu; Pang Shichun; Tong Shouyu [Aviation University of Air Force (China)

2012-03-15

The spatial structure of the Bose-Einstein condensate (BEC) is investigated and spatially chaotic distributions of the condensates are revealed. By means of changing the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the Lyapunov exponent of the system is negative.

Modified Einstein and Navier–Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Modified Einstein and Navier-Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

International Nuclear Information System (INIS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

The Stokes-Einstein relation at moderate Schmidt number.

Science.gov (United States)

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Discovering Euler Circuits and Paths through a Culturally Relevant Lesson

Science.gov (United States)

Robichaux, Rebecca R.; Rodrigue, Paulette R.

2006-01-01

This article describes a middle school discrete mathematics lesson that uses the context of catching crawfish to provide students with a hands-on experience related to Euler circuits and paths. The lesson promotes mathematical communication through the use of cooperative learning as well as connections between mathematics and the real world…

Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we prove the long-time existence of the Hermitian-Einstein flow on a holomorphic vector bundle over a compact Hermitian (non-kaehler) manifold, and solve the Dirichlet problem for the Hermitian-Einstein equations. We also prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete noncompact Hermitian manifolds. (author)

Einstein's conversion from his static to an expanding universe

Science.gov (United States)

Nussbaumer, Harry

2014-02-01

In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogenous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed that Albert Einstein's fundamental equations also allow dynamical worlds, and in 1927 Georges Lemaître, backed by observational evidence, concluded that our universe was expanding. Einstein impetuously rejected Friedman's as well as Lemaître's findings. However, in 1931 he retracted his former static model in favour of a dynamic solution. This investigation follows Einstein on his hesitating path from a static to the expanding universe. Contrary to an often advocated belief the primary motive for his switch was not observational evidence, but the realisation that his static model was unstable.

Einstein's pathway to the special theory of relativity

CERN Document Server

Weinstein, Galina

2015-01-01

This book pieces together the jigsaw puzzle of Einstein's journey to discovering the special theory of relativity. Between 1902 and 1905, Einstein sat in the Patent Office and may have made calculations on old pieces of paper that were once patent drafts. One can imagine Einstein trying to hide from his boss, writing notes on small sheets of paper, and, according to reports, seeing to it that the small sheets of paper on which he was writing would vanish into his desk-drawer as soon as he heard footsteps approaching his door. He probably discarded many pieces of papers and calculations and flu

On gravitational wave energy in Einstein gravitational theory

International Nuclear Information System (INIS)

Folomeshkin, V.N.; Vlasov, A.A.

1978-01-01

By the example of precise wave solutions for the Einstein equations it is shown that a standard commonly adopted formulation of energy-momentum problem with pseudotensors provides us either with a zero or sign-variable values for the energy of gravitational waves. It is shown that if in the Einstein gravitational theory a strict transition to the limits of weak fields is realised then the theory gives us an unambiguous zero result for weak gravitational waves. The well-known non-zero result arises due to incorrect transition to weak field approximation in the Einstein gravitation theory

On the estimation variance for the specific Euler-Poincaré characteristic of random networks.

Science.gov (United States)

Tscheschel, A; Stoyan, D

2003-07-01

The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.

Restricted gravity: Abelian projection of Einstein's theory

International Nuclear Information System (INIS)

Cho, Y.M.

2013-01-01

Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection Γμ into the restricted connection made of the potential of the maximal Abelian subgroup H of Lorentz group G and the valence connection made of G/H part of the potential which transforms covariantly under Lorentz gauge transformation. With this we show that Einstein's theory can be decomposed into the restricted gravity made of the restricted connection which has the full Lorentz gauge invariance which has the valence connection as gravitational source. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory,

New Information about Albert Einstein's Brain.

Science.gov (United States)

Falk, Dean

2009-01-01

In order to glean information about hominin (or other) brains that no longer exist, details of external neuroanatomy that are reproduced on endocranial casts (endocasts) from fossilized braincases may be described and interpreted. Despite being, of necessity, speculative, such studies can be very informative when conducted in light of the literature on comparative neuroanatomy, paleontology, and functional imaging studies. Albert Einstein's brain no longer exists in an intact state, but there are photographs of it in various views. Applying techniques developed from paleoanthropology, previously unrecognized details of external neuroanatomy are identified on these photographs. This information should be of interest to paleoneurologists, comparative neuroanatomists, historians of science, and cognitive neuroscientists. The new identifications of cortical features should also be archived for future scholars who will have access to additional information from improved functional imaging technology. Meanwhile, to the extent possible, Einstein's cerebral cortex is investigated in light of available data about variation in human sulcal patterns. Although much of his cortical surface was unremarkable, regions in and near Einstein's primary somatosensory and motor cortices were unusual. It is possible that these atypical aspects of Einstein's cerebral cortex were related to the difficulty with which he acquired language, his preference for thinking in sensory impressions including visual images rather than words, and his early training on the violin.

Time-of-flight expansion of binary Bose-Einstein condensates at finite temperature

DEFF Research Database (Denmark)

Lee, K. L.; Jorgensen, N. B.; Wacker, L. J.

2018-01-01

Ultracold quantum gases provide a unique setting for studying and understanding the properties of interacting quantum systems. Here, we investigate a multi-component system of Rb-87-K-39 Bose-Einstein condensates (BECs) with tunable interactions both theoretically and experimentally. Such multi-c...

Swimming holonomy principles, exemplified with a Euler fluid in two dimensions

International Nuclear Information System (INIS)

Hannay, J H

2012-01-01

The idealized problem of swimming—the self-propulsion phenomenon whereby a cyclic change of shape of a ‘swimmer’ produces a net movement—is well studied for the case of a very viscous incompressible liquid. The opposite limit of zero viscosity, the ideal or ‘Euler’ fluid, has also received some attention. There remain to be articulated and explored some points of principle, set here in the context of the Euler fluid in two dimensions, though partly common to both limits and to both two and three dimensions. (i) Perhaps surprisingly, both limits are purely geometric effects, ‘holonomies’, not dependent on any timings or rates, but only on the sequence of shapes adopted by the swimmer. (ii) A principle fully determining swimming in a Euler fluid is simply stated: the fluid moves at every moment so as to minimize the sum of its and the swimmer's kinetic energy. (iii) Euler swimming would be solvable explicitly were it not for the standard impasse of potential theory: to find the boundary normal derivative of a function obeying Laplace's equation given its value around the boundary (or vice versa). As usual more analytical progress is possible in two dimensions (by complexifying) than three, but full tractability still requires the extreme of slight, rapid swimming strokes, and a simple example is given. In both limits, for a non-symmetrical swimming stroke, a rotation or orientation holonomy accompanies the translational one—the swimmer has turned somewhat as well as translated. The whole holonomy is non-Abelian (the order of the shape sequence matters), but (iv) for two dimensions the rotation part is Abelian. A benefit (albeit cosmetic) is that the one-stroke displacement and turning can be written down as a complex line integral. (v) Another benefit is that while Stokes's theorem (in shape space) is normally sacrificed in non-Abelian holonomies, a partial recovery of the theorem is possible in two-dimensional swimming. To illustrate this last

Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensates

Energy Technology Data Exchange (ETDEWEB)

Casati, Giulio [Center for Nonlinear and Complex Systems, Universita degli Studi dell' Insubria and Istituto Nazionale per la Fisica della Materia, Unita di Como, Via Valleggio 11, 22100 Como (Italy); Poletti, Dario [Center for Nonlinear and Complex Systems, Universita degli Studi dell' Insubria and Istituto Nazionale per la Fisica della Materia, Unita di Como, Via Valleggio 11, 22100 Como (Italy)

2007-05-15

We study cold atoms and Bose-Einstein condensates exposed to time-dependent standing waves of light. We first discuss a quantum chaotic dissipative ratchet using the method of quantum trajectories. This system is characterized by directed transport emerging from a quantum strange attractor. We then present a very simple model of directed transport with cold atoms in a pair of periodically flashed optical lattices. Finally we study the dynamics of a dilute Bose-Einstein condensate confined in a toroidal trap and exposed to a pair of periodically flashed optical lattices. We show that the many-body atom-atom interactions, treated within the mean-field approximation, can generate directed transport.

Fermilab | Science | Questions for the Universe | Einstein's Dream of

Science.gov (United States)

newsletter Einstein's Dream of Unified Forces In this Section: Einstein's Dream of Unified Forces Are there dream of an ultimate explanation for everything from the tiniest quanta of particle physics to the

Einstein's enigma or black holes in my bubble bath

CERN Document Server

Vishveshwara, C V

2006-01-01

A funny rendition of the story of gravitation theory from the early historic origins to the developments in astrophysics, focusing on Albert Einstein''s theory of general relativity and black-hole physics.

Radiating Kerr particle in Einstein universe

International Nuclear Information System (INIS)

Vaidya, P.C.; Patel, L.K.

1989-01-01

A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field. (author). 7 refs

Demonstration of Multisetting One-Way Einstein-Podolsky-Rosen Steering in Two-Qubit Systems

Science.gov (United States)

Xiao, Ya; Ye, Xiang-Jun; Sun, Kai; Xu, Jin-Shi; Li, Chuan-Feng; Guo, Guang-Can

2017-04-01

Einstein-Podolsky-Rosen (EPR) steering describes the ability of one party to remotely affect another's state through local measurements. One of the most distinguishable properties of EPR steering is its asymmetric aspect. Steering can work in one direction but fail in the opposite direction. This type of one-way steering, which is different from the symmetry concepts of entanglement and Bell nonlocality, has garnered much interest. However, an experimental demonstration of genuine one-way EPR steering in the simplest scenario, i.e., one that employs two-qubit systems, is still lacking. In this Letter, we experimentally demonstrate one-way EPR steering with multimeasurement settings for a class of two-qubit states, which are still one-way steerable even with infinite settings. The steerability is quantified by the steering radius, which represents a necessary and sufficient steering criterion. The demonstrated one-way steering in the simplest bipartite quantum system is of fundamental interest and may provide potential applications in one-way quantum information tasks.

Stationary axisymmetric four dimensional space-time endowed with Einstein metric

International Nuclear Information System (INIS)

Hasanuddin; Azwar, A.; Gunara, B. E.

2015-01-01

In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time

On Einstein's kinematics and his derivation of Lorentz transformation equations

International Nuclear Information System (INIS)

Gulati, Shobha; Gulati, S.P.

1981-01-01

Recently the present authors have claimed that Einstein's historic derivation of 1905 of Lorentz transformation equations is a 'howler' - a correct result achieved through some incorrect steps. In the present contribution, this howler is fully resolved. Incidently, Einstein's kinematical considerations are found to be void of any new definitional elements or conventionality as unjustifiably claimed by Einstein and some other scientists. (author)

Reassessing the Ritz-Einstein debate on the radiation asymmetry in classical electrodynamics

Science.gov (United States)

Frisch, Mathias; Pietsch, Wolfgang

2016-08-01

We investigate the debate between Walter Ritz and Albert Einstein on the origin and nature of the radiation asymmetry. We argue that Ritz's views on the radiation asymmetry were far richer and nuanced than the oft-cited joint letter with Einstein (Ritz & Einstein, 1909) suggests, and that Einstein's views in 1909 on the asymmetry are far more ambiguous than is commonly recognized. Indeed, there is strong evidence that Einstein ultimately came to agree with Ritz that elementary radiation processes in classical electrodynamics are non-symmetric and fully retarded.

Shear-free flows of a perfect fluid

International Nuclear Information System (INIS)

Barnes, A.

1984-01-01

Previous results on shear-free fluid flows are reviewed. Attention is then restricted to flows which satisfy the additional condition that the Weyl tensor is purely electric: Hsub(ac)=*Csub(abcd)usup(b)usup(d)=O where usup(a) is the velocity vector of the fluid. The analysis is also applied to Einstein spaces admitting a shear-free timelike vector field usup(a). If the Weyl tensor is purely electric or purely magnetic, it is shown that usup(a) is necessarily irrotational unless the spacetime has constant curvature. (author)

Einstein, Bohr, and Bell

Science.gov (United States)

Bellac, Michel Le

2014-11-01

The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a

Einstein's Gravity and Dark Energy/Matter

CERN Document Server

Sarfatti, J

2003-01-01

Should Einstein's general relativity be quantized in the usual way even though it is not renormalizable the way the spin 1/2 lepto-quark - spin 1 gauge force boson local field theories are? Condensed matter theorists using P.W. Anderson's "More is different" approach, consistent with Andrei Sakharov's idea of "metric elasticity" with gravity emergent out of quantum electrodynamic zero point vacuum fluctuations, is the approach I take in this paper. The QED vacuum in globally-flat Minkowski space-time is unstable due to exchange of virtual photons between virtual electrons and positron "holes" near the -mc2 Fermi surface well inside the 2mc2 energy gap. This results in a non-perturbative emergence of both Einstein's gravity and a unified dark energy/dark matter w = -1 exotic vacuum zero point fluctuation field controlled by the local macro-quantum vacuum coherent field. The latter is a Bose-Einstein condensate of virtual off-mass-shell bound electron-positron pairs. The dark matter exotic vacuum phase with pos...

Discrete Bose-Einstein spectra

International Nuclear Information System (INIS)

Vlad, Valentin I.; Ionescu-Pallas, Nicholas

2001-03-01

The Bose-Einstein energy spectrum of a quantum gas, confined in a rigid cubic box, is shown to become discrete and strongly dependent on the box geometry (size L), temperature, T and atomic mass number, A at , in the region of small γ=A at TV 1/3 . This behavior is the consequence of the random state degeneracy in the box. Furthermore, we demonstrate that the total energy does not obey the conventional law any longer, but a new law, which depends on γ and on the quantum gas fugacity. This energy law imposes a faster decrease to zero than it is classically expected, for γ→0. The lighter the gas atoms, the higher the temperatures or the box size, for the same effects in the discrete Bose-Einstein regime. (author)

On the motion of incompressible inhomogeneous Euler-Korteweg fluids

Czech Academy of Sciences Publication Activity Database

Bulíček, M.; Feireisl, Eduard; Málek, J.; Shvydkoy, R.

2010-01-01

Roč. 3, č. 3 (2010), s. 497-515 ISSN 1937-1632 R&D Projects: GA MŠk LC06052; GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : Korteweg fluid * inhomogeneous Euler fluid * Korteweg stress * local-in-time well-posedness * smooth solution Subject RIV: BA - General Mathematics http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5226

Albert Einstein

International Nuclear Information System (INIS)

Anon.

1979-01-01

In a single year, 1905, Albert Einstein made several dramatic contributions to physics. He deduced the true nature of Brownian motion (doing much to underline the molecular and atomic nature of matter), he demonstrated the particle nature of light in a way which was accessible to experimental investigation (the work for which he received the Nobel prize) and, most dramatically of all, he conceived the special theory of relativity

Beyond Einstein: Exploring the Extreme Universe

Science.gov (United States)

Barbier, Louis M.

2005-01-01

This paper will give an overview of the NASA Universe Division Beyond Einstein program. The Beyond Einstein program consists of a series of exploratory missions to investigate some of the most important and pressing problems in modern-day astrophysics - including searches for Dark Energy and studies of the earliest times in the universe, during the inflationary period after the Big Bang. A variety of new technologies are being developed both in the science instrumentation these missions will carry and in the spacecraft that will carry those instruments.

Partially massless graviton on beyond Einstein spacetimes

Science.gov (United States)

Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael

2017-06-01

We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.

Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method

International Nuclear Information System (INIS)

Suescun D, D.; Oviedo T, M.

2017-09-01

In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

The formative years of relativity the history and meaning of Einstein's Princeton lectures : featuring Einstein's classic text The meaning of relativity in its historical context

CERN Document Server

Gutfreund, Hanoch

2017-01-01

First published in 1922 and based on lectures delivered in May 1921, Albert Einstein's The Meaning of Relativity offered an overview and explanation of the then new and controversial theory of relativity. The work would go on to become a monumental classic, printed in numerous editions and translations worldwide. Now, The Formative Years of Relativity introduces Einstein's masterpiece to new audiences. This beautiful volume contains Einstein's insightful text, accompanied by important historical materials and commentary looking at the origins and development of general relativity. Hanoch Gutfreund and Jurgen Renn provide fresh, original perspectives, placing Einstein's achievements into a broader context for all readers. In this book, Gutfreund and Renn tell the rich story behind the early reception, spread, and consequences of Einstein's ideas during the formative years of general relativity in the late 1910s and 1920s. They show that relativity's meaning changed radically throughout the nascent years of it...

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

Science.gov (United States)

Batina, John T.

1991-01-01

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

On coordinates and coordinate transformation in Einstein's theory of gravitation

International Nuclear Information System (INIS)

Chou Peiyuan

1983-01-01

This investigation is a further exposition of the significance of coordinates and their transformation in Einstein's theory of gravitation. The author considers the static axisymmetric field as an example, starts with its metric in the cylindrical coordinates, transforms this metric and the field equations into the Weyl-Levi-Civita system of coordinates, and supplements them with the harmonic condition. Both of the field equations and the harmonic condition are then transformed back to the original Cartesian system. Solutions for the static fields of an infinite plane with uniform surface density and an infinite rod with uniform linear density of matter, and of a body with spherical symmetry, are obtained again to show the necessity of the harmonic condition in their solutions. The fact that under the harmonic condition the solutions of the field equations for these problems contain their corresponding Newtonian potentials as approximations, is a strong support to the argument that the harmonic condition should be a physical supplement to Einstein's theory of gravitation. (Auth.)

Evaluating of air flow movements and thermal comfort in a model room with Euler equation: Two dimensional study

Energy Technology Data Exchange (ETDEWEB)

Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)

2011-02-15

This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)

Einstein's Symphony: A Gravitational Wave Voyage Through Space and Time

Science.gov (United States)

Shapiro Key, Joey; Yunes, Nico; Grimberg, Irene

2015-01-01

Einstein's Symphony: A Gravitational Wave Voyage Through Space and Time is a gravitational wave astronomy planetarium show in production by a collaboration of scientists, filmmakers, and artisits from the Center for Gravitational Wave Astonomy (CGWA) at the University of Texas at Brownsville (UTB) and Montana State University (MSU). The project builds on the success of the interdisciplinary Celebrating Einstein collaboration. The artists and scientists who created the A Shout Across Time original film and the Black (W)hole immersive art installation for Celebrating Einstein are teaming with the Museum of the Rockies Taylor Planetarium staff and students to create a new full dome Digistar planetarium show that will be freely and widely distributed to planetaria in the US and abroad. The show uses images and animations filmed and collected for A Shout Across Time and for Black (W)hole as well as new images and animations and a new soundtrack composed and produced by the MSU School of Music to use the full capability of planetarium sound systems. The planetarium show will be narrated with ideas drawn from the Celebrating Einstein danced lecture on gravitational waves that the collaboration produced. The combination of products, resources, and team members assembled for this project allows us to create an original planetarium show for a fraction of the cost of a typical show. In addition, STEM education materials for G6-12 students and teachers will be provided to complement and support the show. This project is supported by the Texas Space Grant Consortium (TSGC), Montana Space Grant Consortium (MSGC), and the American Physical Society (APS).

On the stability of the Einstein universe

International Nuclear Information System (INIS)

Soares, I.D.

1983-01-01

It is shown sthat the Einstein Universe is stable by a large class of exact perturbations, which are made starting from a detailed exam of the topology of the model, and which include perturbations of the type considered by Lemaitre. The problem is reduced to the one-dimensional motion of a particle, in a potential well whose minimum corresponds to the configuration of the Einstein Universe. (Author) [pt

The second postulate of Einstein's theory of special relativity

International Nuclear Information System (INIS)

McMorris, M.N.

1979-01-01

This paper argues that Einstein in his original publication on special relativity uses two separate principles concerning the velocity of light: (i) its value, c(s), is independent of the motion of its source; (ii) its value, c(o), is independent of the motion of the observer. Where commentators have not been plainly ignorant of the existence of both principles in Einstein's work, they have been uncertain as to which one should be put forward. Uncertainty has arisen in the literature because Einstein occassionally uses constant velocity of light without any qualification. This paper sets out specifically to clear up the uncertainty as to whether c(s) or c(o) is being referred to in the early sections. It is established that c(s) is used right up to the middle of the third section, when c(o) is introduced for the first time. The paper also emphasises that there was no need to introduce c(o) before this point. It clarifies another (neglected) point also, that in so far as Einstein uses c(s), this constancy of the wave propagation is not peculiar to light; but in so far as he uses c(o) it is. The occassion is also taken to point out a contradiction and a logical infelicity occurring in Einstein's paper. The intention here is to show that Einstein's original oaper, at least up to the derivation of the Lorentz transformation equations, was not as satisfactory as it could have been. (auth.)

Analysis of A Uniform Bernoulli – Euler Beam on Winkler Foundation ...

African Journals Online (AJOL)

ADOWIE PERE

2018-03-09

Mar 9, 2018 ... method to analyze Winkler foundation subjected to a harmonic moving load on a uniform Bernoulli – Euler Beam. MATLAB software was used to implement the Newmark time integration method to ... A lot of engineering structures under moving loads .... Because numerical procedure produce stability issue,.

Herwig Schopper Einstein's Legacy

CERN Multimedia

Schneegans, Susan

2005-01-01

"Last June, the United Nations declared 2005 the International Year of Physics and invited UNESCO to take the lead in celebrating the hundreth anniversary of Albert Einstein's legandary articles on relativisty, quantum theory and Brownian motion" (3 pages)

Einstein and general relativity: historical perspectives

International Nuclear Information System (INIS)

Chandrasekhar, S.

1978-01-01

The place of Einstein in 20th-century physics is discussed. The basic ideas that led Einstein to his theory of gravitation by the sheer power of speculative thought are described in the most general terms. The prediction of the bending of starlight by the Sun and the eclipse expedition of 1919 are recounted. The author feels that ''the general theory of relativity is incredibly rich in its content;...one finds a glittering face at almost every turn.'' The prediction of black holes by general relativity is noted

Mathematical implications of Einstein-Weyl causality

International Nuclear Information System (INIS)

Borchers, H.J.; Sen, R.N.

2006-01-01

The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics. (orig.)

Bohr vs. Einstein: Fortolkning af kvantemekanikken

DEFF Research Database (Denmark)

Andersen, Christian Kraglund; Wade, Andrew Christopher James

2013-01-01

Siden 1913, da Bohr fremlagde sin kvantemekaniske model for atomet, har fysikere diskuteret, hvordan kvan- temekanikken skal fortolkes. Specielt aktive i denne diskussion var Bohr og Einstein, som havde modstridende opfattelser af, hvordan kvantemekanikken skulle forstås. Kan katte være både...... levende og døde på samme tid? Kan vi teleportere partikler mellem Månen og Jorden? Disse spørgsmål, og mange flere, forsøgte Bohr og Einstein at besvare, og det vil vi ligeledes i denne artikel....

Quantum entanglement: facts and fiction - how wrong was Einstein after all?

Science.gov (United States)

Nordén, Bengt

2016-01-01

Einstein was wrong with his 1927 Solvay Conference claim that quantum mechanics is incomplete and incapable of describing diffraction of single particles. However, the Einstein-Podolsky-Rosen paradox of entangled pairs of particles remains lurking with its 'spooky action at a distance'. In molecules quantum entanglement can be viewed as basis of both chemical bonding and excitonic states. The latter are important in many biophysical contexts and involve coupling between subsystems in which virtual excitations lead to eigenstates of the total Hamiltonian, but not for the separate subsystems. The author questions whether atomic or photonic systems may be probed to prove that particles or photons may stay entangled over large distances and display the immediate communication with each other that so concerned Einstein. A dissociating hydrogen molecule is taken as a model of a zero-spin entangled system whose angular momenta are in principle possible to probe for this purpose. In practice, however, spins randomize as a result of interactions with surrounding fields and matter. Similarly, no experiment seems yet to provide unambiguous evidence of remaining entanglement between single photons at large separations in absence of mutual interaction, or about immediate (superluminal) communication. This forces us to reflect again on what Einstein really had in mind with the paradox, viz. a probabilistic interpretation of a wave function for an ensemble of identically prepared states, rather than as a statement about single particles. Such a prepared state of many particles would lack properties of quantum entanglement that make it so special, including the uncertainty upon which safe quantum communication is assumed to rest. An example is Zewail's experiment showing visible resonance in the dissociation of a coherently vibrating ensemble of NaI molecules apparently violating the uncertainty principle. Einstein was wrong about diffracting single photons where space-like anti

Free vibration of Euler and Timoshenko nanobeams using boundary characteristic orthogonal polynomials

Science.gov (United States)

Behera, Laxmi; Chakraverty, S.

2014-03-01

Vibration analysis of nonlocal nanobeams based on Euler-Bernoulli and Timoshenko beam theories is considered. Nonlocal nanobeams are important in the bending, buckling and vibration analyses of beam-like elements in microelectromechanical or nanoelectromechanical devices. Expressions for free vibration of Euler-Bernoulli and Timoshenko nanobeams are established within the framework of Eringen's nonlocal elasticity theory. The problem has been solved previously using finite element method, Chebyshev polynomials in Rayleigh-Ritz method and using other numerical methods. In this study, numerical results for free vibration of nanobeams have been presented using simple polynomials and orthonormal polynomials in the Rayleigh-Ritz method. The advantage of the method is that one can easily handle the specified boundary conditions at the edges. To validate the present analysis, a comparison study is carried out with the results of the existing literature. The proposed method is also validated by convergence studies. Frequency parameters are found for different scaling effect parameters and boundary conditions. The study highlights that small scale effects considerably influence the free vibration of nanobeams. Nonlocal frequency parameters of nanobeams are smaller when compared to the corresponding local ones. Deflection shapes of nonlocal clamped Euler-Bernoulli nanobeams are also incorporated for different scaling effect parameters, which are affected by the small scale effect. Obtained numerical solutions provide a better representation of the vibration behavior of short and stubby micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant.

The problem of electric sources in Einstein's Hermite-symmetric field theory

International Nuclear Information System (INIS)

Kreisel, E.

1986-01-01

The possibility is investigated to introduce a geometric source without A-invariance and Hermite-symmetry breaking of Einstein's Hermitian relativity. It would be very meaningful to interpret a source of this kind as electric current. With this extension Einstein's unitary field theory contains Einstein's gravitation, electromagnetism and the gluonic vacuum of chromodynamics. (author)

A note on Einstein-Sasaki metrics in D ≥ 7

International Nuclear Information System (INIS)

Chen, W; Lue, H; Pope, C N; Vazquez-Poritz, J F

2005-01-01

In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D ≥ 7. The local construction involves taking a circle bundle over a (D - 1)-dimensional Einstein-Kaehler metric that is itself constructed as a complex line bundle over a product of Einstein-Kaehler spaces. In general, the resulting Einstein-Sasaki spaces are singular, but if parameters in the local solutions satisfy appropriate rationality conditions, the metrics extend smoothly onto complete and non-singular compact manifolds. The seven-dimensional space, whose base is a complex line bundle over S 2 x S 2 , is discussed in detail since it has relevance in terms of the AdS/CFT correspondence

The world-line. Albert Einstein and modern physics

International Nuclear Information System (INIS)

Maalampi, Jukka

2008-01-01

This book is an entertaining and formula-free presentation of modern physics from the 19th century to present. The life of Albert Einstein and his scientific works are drawn as red fathom through the text. The author explains central terms and results of modern physics in populary-scientific form from the historical perspective. To the reader in humorous form an imagination is mediated how modern physics has been developed. We learn from the exciting effects of the ether, we hear from faraday and magnetic needles, from Maxwell's prediction of the electromagnetic waves, from heinrich Hertz and from the photoelectric effect. Was the Michelson-Morley experiment a measurement success or an unsuccess? Why has Einstein abandoned the ether? How has Einstein in the miraculous year 1905 revolutionated physics and why he has begged Newton for excusement? Exist atoms? What is motion? What is light and what is to be understood under ''now'' and ''here''? Light deviation or non-deviation? How act the tidal forces? And above all: How has Einstein answered these questions. We meet Poincare, Lorentz and Hilbert, Boltzmann and Bohr, Minkowski, Planck, de Broglie, Hubble and Weyl, Gamow, Hahn and Meitner, Kapiza and Landau, Fermi and many other famous scientists. What had Eddington against Chandrasekhar and what had Einstein against black holes? Why should space tourists and dream tourists make holiday not on the Loch Ness but on the safe side of a black hole? Why inveighed Pauli against Einstein? Is the concern with the atomic-bomb formula right? Smeared matter, big bang and cosmic background radiation, gravitational waves and double pulsars, the cosmological constant and the expansion of the universe are further themes, which keep the reader in breath and let no mental vacuum arise [de

Einstein's Annalen Papers: The Complete Collection 1901 - 1922

Science.gov (United States)

Renn, Jürgen

2005-05-01

In 1905, Einstein's Annus Mirabilis, Albert Einstein made three discoveries concerning the foundations of nature which form the basis of his fame as a physicist. These revolutionary papers on the light-quantum hypothesis, Brownian motion, and special relativity, were published in the journal "Annalen der Physik". All three are now established as pillars of modern science and its applications in technology and are an indispensable part of the modern world. This volume presents some of the most significant original papers which Albert Einstein ever wrote. It includes the facsimiles of the three revolutionary papers of 1905. In addition it contains papers which show the consequences of the ground-breaking ideas of these seminal papers from E=mc² to the quantum theory of specific heats. It also features Einstein's first exposition of his new general theory of relativity. Introducing the original German papers the science historians Jürgen Renn (MPI for the History of Science, Berlin), David C. Cassidy (Hofstra University, Hempstead), Michel Janssen (University of Minnesota), and Robert Rynasiewicz (John Hopkins University) complement and comment the collection with topical articles.

Einstein and interpretation of quantum field theory

International Nuclear Information System (INIS)

Kashlyun, F.

1982-01-01

The main problems of the quantum theory, the basis of which was laid by Planck in 1900 as a result of the discovery of elementary quantum of action, are examined. The most important Einstein contributions to the quantum theory are enumerated. The Einstein work about the light quanta, proved wave-particle dualism, stated one of the most complicated problems to the physics. The work on the specific heat capacity of solids shows that the quantum theory should be beyond the limits of the narrow range of the problems on black radiation. The works on the equilibrium of radiation have convincingly demonstrates statistical character of the radiation processes and have marked the way to Heizenberg form of the quantum mechanics. Einstein generalized the idea of wave-particle dualism to the ordinary gas. It helped to prepare the Schroedinger form of quantum mechanics

Coherence, Abstraction, and Personal Involvement: Albert Einstein, Physicist and Humanist.

Science.gov (United States)

Ne'eman, Yuval

1979-01-01

Reviews Einstein's main contributions to physics, and analyzes the importance of a coherent body of theory. Einstein's involvement in nonscientific issues such as nuclear disarmament is also included. (HM)

Validity of the Einstein Relation in Disordered Organic Semiconductors

NARCIS (Netherlands)

Wetzelaer, G. A. H.; Koster, L. J. A.; Blom, P. W. M.

2011-01-01

It is controversial whether energetic disorder in semiconductors is already sufficient to violate the classical Einstein relation, even in the case of thermal equilibrium. We demonstrate that the Einstein relation is violated only under nonequilibrium conditions due to deeply trapped carriers, as in

Sasaki-Einstein Manifolds and Volume Minimisation

CERN Document Server

Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung

2006-01-01

We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...

Bose-Einstein condensation of paraxial light

Science.gov (United States)

Klaers, J.; Schmitt, J.; Damm, T.; Vewinger, F.; Weitz, M.

2011-10-01

Photons, due to the virtually vanishing photon-photon interaction, constitute to very good approximation an ideal Bose gas, but owing to the vanishing chemical potential a (free) photon gas does not show Bose-Einstein condensation. However, this is not necessarily true for a lower-dimensional photon gas. By means of a fluorescence induced thermalization process in an optical microcavity one can achieve a thermal photon gas with freely adjustable chemical potential. Experimentally, we have observed thermalization and subsequently Bose-Einstein condensation of the photon gas at room temperature. In this paper, we give a detailed description of the experiment, which is based on a dye-filled optical microcavity, acting as a white-wall box for photons. Thermalization is achieved in a photon number-conserving way by photon scattering off the dye molecules, and the cavity mirrors both provide an effective photon mass and a confining potential-key prerequisites for the Bose-Einstein condensation of photons. The experimental results are in good agreement with both a statistical and a simple rate equation model, describing the properties of the thermalized photon gas.

Franz Selety (1893-1933?). His cosmological investigations and the correspondence with Einstein (German Title: Franz Selety (1893-1933?). Seine kosmologischen Arbeiten und der Briefwechsel mit Einstein)

Science.gov (United States)

Jung, Tobias

In 1922, Franz Selety, university-bred philosopher and self-educated physicist and cosmologist, developed a molecular hierarchical, spatially infinite, Newtonian cosmological model. His considerations were based on his earlier philosophical work published in 1914 as well as on the early correspondence with Einstein in 1917. Historically, the roots of hierarchical models can be seen in 18th century investigations by Thomas Wright of Durham, Immanuel Kant and Johann Heinrich Lambert. Those investigations were taken up by Edmund Fournier d'Albe and Carl Charlier at the beginning of the 20th century. Selety's cosmological model was criticized by Einstein mainly due to its spatial infiniteness which in Einstein's opinion seemed to contradict Mach's principle. This criticism sheds light on Einstein's conviction that with his first cosmological model, namely the static, spatially infinite, though unbounded Einstein Universe of 1917, the appropriate cosmological theory already had been established.

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

International Nuclear Information System (INIS)

Szirmai, G.; Nagy, D.; Domokos, P.

2010-01-01

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

Science.gov (United States)

Szirmai, G.; Nagy, D.; Domokos, P.

2010-04-01

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

Leggett-Garg tests of macrorealism for bosonic systems including double-well Bose-Einstein condensates and atom interferometers

Science.gov (United States)

Rosales-Zárate, L.; Opanchuk, B.; He, Q. Y.; Reid, M. D.

2018-04-01

We construct quantifiable generalizations of Leggett-Garg tests for macro- and mesoscopic realism and noninvasive measurability that apply when not all outcomes of measurement can be identified as arising from one of two macroscopically distinguishable states. We show how quantum mechanics predicts a negation of the Leggett-Garg premises for strategies involving ideal negative-result, weak, and minimally invasive ("nonclumsy") projective measurements on dynamical entangled systems, as might be realized with Bose-Einstein condensates in a double-well potential, path-entangled NOON states, and atom interferometers. Potential loopholes associated with each strategy are discussed.

The Influence of Ernst Mach and Ludwig Boltzmann on Albert Einstein

International Nuclear Information System (INIS)

Broda, E.

1979-01-01

This document, written by Engelbert Broda in 1979, analyses the influence of Ernst Mach and Ludwig Boltzmann on Albert Einstein. Broda describes how Einstein and his scientific thinking benefited from Mach’s criticism on classical mechanics and its basic concepts like absolute time and absolute space. This criticism encouraged Einstein in the time he worked on his special relativity. On the other side Broda writes about the influence of Ludwig Boltzman, an atomist, whose scientific work and research prepared the ground for Einsteins work on the quantum-structure of electromagnetic radiation or the discovery of the photoelectric effect. (nowak)

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

International Nuclear Information System (INIS)

Reid, M. D.; Drummond, P. D.; Bowen, W. P.; Cavalcanti, E. G.; Lam, P. K.; Bachor, H. A.; Andersen, U. L.; Leuchs, G.

2009-01-01

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

Energy Technology Data Exchange (ETDEWEB)

Reid, M. D.; Drummond, P. D.; Bowen, W. P.; Cavalcanti, E. G.; Lam, P. K.; Bachor, H. A.; Andersen, U. L.; Leuchs, G. [ARC Centre of Excellence for Quantum-Atom Optics and Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, P.O. Box 218, Melbourne, Victoria 3122 Australia (Australia); School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072 (Australia); Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 (Australia); ARC Centre of Excellence for Quantum-Atom Optics, Building 38, The Australian National University, Canberra, Australian Capital Territory 0200 (Australia); Department of Physics, Technical University of Denmark, Building 309, 2800 Lyngby (Denmark); Max-Planck Institute for the Science of Light and Department of Physics, Universitaet Erlangen-Nuernberg, D-91058 Erlangen (Germany)

2009-10-15

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.