On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2016-05-01

On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

NASA Technical Reports Server (NTRS)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

NASA Astrophysics Data System (ADS)

Haken, Hermann

2014-12-01

After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.

A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

NASA Astrophysics Data System (ADS)

Allahverdyan, A. E.; Nieuwenhuizen, Th. M.

2002-03-01

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (“cyclic changes cost energy”), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wave function). It has been strictly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion invariance, it is applicable to situations where persistent currents occur. This clear-cut derivation allows to revive the “no perpetuum mobile in equilibrium” formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.

Learning in neural networks based on a generalized fluctuation theorem

NASA Astrophysics Data System (ADS)

Hayakawa, Takashi; Aoyagi, Toshio

2015-11-01

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces

NASA Astrophysics Data System (ADS)

Ou, Ye-Lin

2012-04-01

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4 and 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen's conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.

Cellular compartmentation follows rules: The Schnepf theorem, its consequences and exceptions: A biological membrane separates a plasmatic from a non-plasmatic phase.

PubMed

Moog, Daniel; Maier, Uwe G

2017-08-01

Is the spatial organization of membranes and compartments within cells subjected to any rules? Cellular compartmentation differs between prokaryotic and eukaryotic life, because it is present to a high degree only in eukaryotes. In 1964, Prof. Eberhard Schnepf formulated the compartmentation rule (Schnepf theorem), which posits that a biological membrane, the main physical structure responsible for cellular compartmentation, usually separates a plasmatic form a non-plasmatic phase. Here we review and re-investigate the Schnepf theorem by applying the theorem to different cellular structures, from bacterial cells to eukaryotes with their organelles and compartments. In conclusion, we can confirm the general correctness of the Schnepf theorem, noting explicit exceptions only in special cases such as endosymbiosis and parasitism. © 2017 WILEY Periodicals, Inc.

Brownian motion of graphene.

PubMed

Maragó, Onofrio M; Bonaccorso, Francesco; Saija, Rosalba; Privitera, Giulia; Gucciardi, Pietro G; Iatì, Maria Antonia; Calogero, Giuseppe; Jones, Philip H; Borghese, Ferdinando; Denti, Paolo; Nicolosi, Valeria; Ferrari, Andrea C

2010-12-28

Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.

Efficiency and formalism of quantum games

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, C.F.; Johnson, Neil F.

We show that quantum games are more efficient than classical games and provide a saturated upper bound for this efficiency. We also demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. Our analysis is based on a rigorous formulation of quantum games, from which quantum versions of the minimax theorem and the Nash equilibrium theorem can be deduced.

Comment on “On the Crooks fluctuation theorem and the Jarzynski equality” [J. Chem. Phys. 129, 091101 (2008)

PubMed Central

Adib, Artur B.

2009-01-01

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys.129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary. PMID:19566186

Comment on ``On the Crooks fluctuation theorem and the Jarzynski equality'' [J. Chem. Phys. 129, 091101 (2008)

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-06-01

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys.129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary.

The Two-Component Virial Theorem and the Physical Properties of Stellar Systems.

PubMed

Dantas; Ribeiro; Capelato; de Carvalho RR

2000-01-01

Motivated by present indirect evidence that galaxies are surrounded by dark matter halos, we investigate whether their physical properties can be described by a formulation of the virial theorem that explicitly takes into account the gravitational potential term representing the interaction of the dark halo with the baryonic or luminous component. Our analysis shows that the application of such a "two-component virial theorem" not only accounts for the scaling relations displayed by, in particular, elliptical galaxies, but also for the observed properties of all virialized stellar systems, ranging from globular clusters to galaxy clusters.

Semiclassical gravitational effects on the gravitational lensing in the spacetime of topological defects

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Rahaman, Farook; Banerjee, Ayan

2018-02-01

The theory of gravitational lensing has revealed many generic and fundamental properties of compact objects like black holes and wormholes. In this article, we utilize a recent formulation to compute the quantum effects on the deflection angle of a light ray, namely, the Gauss-Bonnet theorem (GBT) to explore the semiclassical gravitational effects in the spacetime of a point-like global monopole and a cosmic string. Previously, the Gauss-Bonnet theorem (Gibbons and Werner, 2008) was proposed as an alternative way to compute the deflection angle of light in a static, spherically symmetric and asymptotically flat spacetime. In the present article we have used the celebrated GBT that applied to the optical metric as well as the geodesic method in computing the deflection angle. Interestingly one can observe that we have found an exact result between GBT and the standard approach up to the third-order contributions terms by modifying the domain of integration for cosmic string and global monopole deflection angles. Finally we have considered the time delay in the cosmic string/global monopole spacetime and found that the delay in time is proportional to the linear mass density of the cosmic string and global monopole parameter, respectively.

A study of photon propagation in free-space based on hybrid radiosity-radiance theorem.

PubMed

Chen, Xueli; Gao, Xinbo; Qu, Xiaochao; Liang, Jimin; Wang, Lin; Yang, Da'an; Garofalakis, Anikitos; Ripoll, Jorge; Tian, Jie

2009-08-31

Noncontact optical imaging has attracted increasing attention in recent years due to its significant advantages on detection sensitivity, spatial resolution, image quality and system simplicity compared with contact measurement. However, photon transport simulation in free-space is still an extremely challenging topic for the complexity of the optical system. For this purpose, this paper proposes an analytical model for photon propagation in free-space based on hybrid radiosity-radiance theorem (HRRT). It combines Lambert's cosine law and the radiance theorem to handle the influence of the complicated lens and to simplify the photon transport process in the optical system. The performance of the proposed model is evaluated and validated with numerical simulations and physical experiments. Qualitative comparison results of flux distribution at the detector are presented. In particular, error analysis demonstrates the feasibility and potential of the proposed model for simulating photon propagation in free-space.

From the necessary to the possible: the genesis of the spin-statistics theorem

NASA Astrophysics Data System (ADS)

Blum, Alexander

2014-12-01

The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.

The B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

2018-02-01

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

Liftings and stresses for planar periodic frameworks

PubMed Central

Borcea, Ciprian; Streinu, Ileana

2015-01-01

We formulate and prove a periodic analog of Maxwell’s theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks. PMID:26973370

Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.

PubMed

Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja

2007-06-01

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

Multiplexed fluctuation-dissipation-theorem calibration of optical tweezers inside living cells

NASA Astrophysics Data System (ADS)

Yan, Hao; Johnston, Jessica F.; Cahn, Sidney B.; King, Megan C.; Mochrie, Simon G. J.

2017-11-01

In order to apply optical tweezers-based force measurements within an uncharacterized viscoelastic medium such as the cytoplasm of a living cell, a quantitative calibration method that may be applied in this complex environment is needed. We describe an improved version of the fluctuation-dissipation-theorem calibration method, which has been developed to perform in situ calibration in viscoelastic media without prior knowledge of the trapped object. Using this calibration procedure, it is possible to extract values of the medium's viscoelastic moduli as well as the force constant describing the optical trap. To demonstrate our method, we calibrate an optical trap in water, in polyethylene oxide solutions of different concentrations, and inside living fission yeast (S. pombe).

Black holes, information, and the universal coefficient theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patrascu, Andrei T.

2016-07-15

General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

NASA Astrophysics Data System (ADS)

Arnlind, Joakim; Wilson, Mitsuru

2017-01-01

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

No-go theorem for passive single-rail linear optical quantum computing.

PubMed

Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A

2013-01-01

Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miserev, D. S., E-mail: d.miserev@student.unsw.edu.au, E-mail: erazorheader@gmail.com

2016-06-15

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reducedmore » to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.« less

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

NASA Astrophysics Data System (ADS)

Badino, M.

2011-11-01

An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

Optimum testing of multiple hypotheses in quantum detection theory

NASA Technical Reports Server (NTRS)

Yuen, H. P.; Kennedy, R. S.; Lax, M.

1975-01-01

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

NASA Astrophysics Data System (ADS)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

Lung cancer diagnosis with quantitative DIC microscopy and support vector machine

NASA Astrophysics Data System (ADS)

Zheng, Longfei; Cai, Shuangshuang; Zeng, Bixin; Xu, Min

2017-01-01

We report the study of lung squamous cell carcinoma diagnosis using the TI-DIC microscopy and the scattering-phase theorem. The spatially resolved optical properties of tissue are computed from the 2D phase map via the scattering-phase theorem. The scattering coefficient, the reduced scattering coefficient, and the anisotropy factor are all found to increase with the grade of lung cancer. The retrieved optical parameters are shown to distinguish cancer cases from the normal cases with high accuracy. This label-free microscopic approach applicable to fresh tissues may be promising for in situ rapid cancer diagnosis.

Quantum stochastic thermodynamic on harmonic networks

DOE PAGES

Deffner, Sebastian

2016-01-04

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Quantum stochastic thermodynamic on harmonic networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deffner, Sebastian

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Factorization of standard model cross sections at ultrahigh energy

NASA Astrophysics Data System (ADS)

Chien, Yang-Ting; Li, Hsiang-nan

2018-03-01

The factorization theorem for organizing multiple electroweak boson emissions at future colliders with energy far above the electroweak scale is formulated. Taking the inclusive muon-pair production in electron-positron collisions as an example, we argue that the summation over isospins is demanded for constructing the universal distributions of leptons and gauge bosons in an electron. These parton distributions are shown to have the same infrared structure in the phases of broken and unbroken electroweak symmetry, an observation consistent with the Goldstone equivalence theorem. The electroweak factorization of processes involving protons is sketched, with an emphasis on the subtlety of the scalar distributions. This formalism, in which electroweak shower effects are handled from the viewpoint of factorization theorem for the first time, is an adequate framework for collider physics at ultra high energy.

Richard P. Feynman and the Feynman Diagrams

Science.gov Websites

available in full-text and on the Web. Documents: A Theorem and Its Application to Finite Tampers, DOE Fermi-Thomas Theory; DOE Technical Report, April 28, 1947 Mathematical Formulation of the Quantum Theory

The derivative-free Fourier shell identity for photoacoustics.

PubMed

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

Nongeostrophic theory of zonally averaged circulation. I - Formulation

NASA Technical Reports Server (NTRS)

Tung, Ka Kit

1986-01-01

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations (mass conservation, thermodynamics, and zonal momentum) on a sphere. The relationship between the mean meridional circulation and diabatic heating rate is studied. Differences between results of nongeostropic theory and the geostrophic formulation concerning the role of eddy forcing of the diabatic circulation and the nonlinear nearly inviscid limit versus the geostrophic limit are discussed. Consideration is given to the Eliassen-Palm flux divergence, the Eliassen-Palm pseudodivergence, the nonacceleration theorem, and the nonlinear nongeostrophic Taylor relationship.

Extended optical theorem in isotropic solids and its application to the elastic radiation force

NASA Astrophysics Data System (ADS)

Leão-Neto, J. P.; Lopes, J. H.; Silva, G. T.

2017-04-01

In this article, we derive the extended optical theorem for the elastic-wave scattering by a spherical inclusion (with and without absorption) in a solid matrix. This theorem expresses the extinction cross-section, i.e., the time-averaged power extracted from the incoming beam per its intensity, regarding the partial-wave expansion coefficients of the incident and scattered waves. We also establish the connection between the optical theorem and the elastic radiation force by a plane wave in a linear and isotropic solid. We obtain the absorption, scattering, and extinction efficiencies (the corresponding power per characteristic incident intensity per sphere cross-section area) for a plane wave and a spherically focused beam. We discuss to which extent the radiation force theory for plane waves can be used to the focused beam case. Considering an iron sphere embedded in an aluminum matrix, we numerically compute the scattering and elastic radiation force efficiencies. The radiation force on a stainless steel sphere embedded in a tissue-like medium (soft solid) is also computed. In this case, resonances are observed in the force as a function of the sphere size parameter (the wavenumber times the sphere radius). Remarkably, the relative difference between our findings and previous lossless liquid models is about 100% in the long-wavelength limit. Regarding some applications, the obtained results have a direct impact on ultrasound-based elastography techniques and ultrasonic nondestructive testing, as well as implantable devices activated by ultrasound.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johannsen, Tim; Psaltis, Dimitrios, E-mail: timj@physics.arizona.ed, E-mail: dpsaltis@email.arizona.ed

According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Kerr spacetimemore » that are critical to interpreting observations of black holes and demonstrate their dependence on the spin and quadrupole moment. In particular, we show that the location of the innermost stable circular orbit and the gravitational lensing experienced by photons are affected significantly at even modest deviations of the quadrupole moment from the value predicted by the no-hair theorem. We argue that observations of black hole images, of relativistically broadened iron lines, as well as of thermal X-ray spectra from accreting black holes will lead in the near future to an experimental test of the no-hair theorem.« less

Quantum identities for the action

NASA Astrophysics Data System (ADS)

Gozzi, E.

2018-04-01

In this paper we derive various identities involving the action functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.

Unified connected theory of few-body reaction mechanisms in N-body scattering theory

NASA Technical Reports Server (NTRS)

Polyzou, W. N.; Redish, E. F.

1978-01-01

A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nielsen, Michael A.; School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Queensland 4072; Dawson, Christopher M.

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which showmore » that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.« less

On the analogues of Szegő's theorem for ergodic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsch, W; Pastur, L A

2015-01-31

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

Estimates of green tensors for certain boundary value problems

NASA Technical Reports Server (NTRS)

Solonnikov, V.

1988-01-01

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

Differentiability of correlations in realistic quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique

2015-09-15

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumedmore » to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.« less

Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar

2007-09-01

We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

Weak ergodicity of population evolution processes.

PubMed

Inaba, H

1989-10-01

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by Garrett Birkhoff, who showed that ergodic properties generally hold for an appropriate class of multiplicative processes. First, we construct a general theory of multiplicative processes on a Banach lattice. Next, we formulate a dynamical model of a multistate population and show that its evolution operator forms a multiplicative process on the state space of the population. Subsequently, we investigate a sufficient condition that guarantees the weak ergodicity of the multiplicative process. Finally, we prove the weak and strong ergodic theorems for the multistate population and resolve the consistency problem.

Structure of rapidity divergences in multi-parton scattering soft factors

NASA Astrophysics Data System (ADS)

Vladimirov, Alexey

2018-04-01

We discuss the structure of rapidity divergences that are presented in the soft factors of transverse momentum dependent (TMD) factorization theorems. To provide the discussion on the most general level we consider soft factors for multi-parton scattering. We show that the rapidity divergences are result of the gluon exchanges with the distant transverse plane, and are structurally equivalent to the ultraviolet divergences. It allows to formulate and to prove the renormalization theorem for rapidity divergences. The proof is made with the help the conformal transformation which maps rapidity divergences to ultraviolet divergences. The theorem is the systematic form of the factorization of rapidity divergences, which is required for the definition of TMD parton distributions. In particular, the definition of multi parton distributions is presented. The equivalence of ultraviolet and rapidity divergences leads to the exact relation between soft and rapidity anomalous dimensions. Using this relation we derive the rapidity anomalous dimension at the three-loop order.

Modeling scattering enhancements at isolated resonances using energy conservation, reciprocity, symmetry, and the optical theorem

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Osterhoudt, Curtis F.

2003-04-01

Sound scattered by some objects in water exhibits isolated narrow resonances that are sufficiently large in amplitude to dominate the low-frequency scattering. Examples include the quadrupole mode of thin spherical shells and of solid plastic spheres [B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 107, 1930-1936 (2000)] and organ-pipe modes of water-filled pipes [C. F. Osterhoudt and P. L. Marston, J. Acoust. Soc. Am. 110, 2773 (2001)]. This presentation concerns simple methods for approximating the scattering. In the case of spheres, ray theory for the backscattering reduces to a simple form for high-Q modes: Eq. (58) of Marston [J. Acoust. Soc. Am. 83, 25-37 (1988)]. This result gives the backscattering form function at resonance (in the usual normalization) to have the magnitude 2(2n+1)/ka. Here n is the partial wave index associated with the mode of the sphere and ka is the product of the wave number and the sphere radius. This result may also be derived directly from energy conservation and the optical theorem. Scattering amplitudes associated with high-Q organ pipe resonances of open cylindrical pipes are also derived here by a related method using the energy conservation, reciprocity, symmetry, and the optical theorem.

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

A smooth reversible dynamical system (SRDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions (the Chew-Low equations for p- wave πN- scattering) are considered. This SRDS is splitted into 1- and 2-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous 3-point functional equation. Non-algebraic integrability of SRDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a non-resonant fixed point. The proof is based on the classical Feldman-Baker theorem on linear forms of logarithms of algebraic numbers, which, in turn, relies upon solving the 7th Hilbert problem by A.I. Gel'fond and T. Schneider and new powerful methods of A. Baker in the theory of transcendental numbers. The general theorem, following from the Feldman-Baker theorem, on applicability of the Siegel theorem to the set of the eigenvalues λ ɛ Cn of a mapping at a non-resonant fixed point which belong to the algebraic number field A is formulated and proved. The main results are presented in Theorems 1-3, 5, 7, 8 and Remarks 3, 7.

A note about Norbert Wiener and his contribution to Harmonic Analysis and Tauberian Theorems

NASA Astrophysics Data System (ADS)

Almira, J. M.; Romero, A. E.

2009-05-01

In this note we explain the main motivations Norbert Wiener had for the creation of his Generalized Harmonic Analysis [13] and his Tauberian Theorems [14]. Although these papers belong to the most pure mathematical tradition, they were deeply based on some Engineering and Physics Problems and Wiener was able to use them for such diverse areas as Optics, Brownian motion, Filter Theory, Prediction Theory and Cybernetics.

Superfield quantization

NASA Astrophysics Data System (ADS)

Batalin, I. A.; Bering, K.; Damgaard, P. H.

1998-03-01

We present a superfield formulation of the quantization program for theories with first-class constraints. An exact operator formulation is given, and we show how to set up a phase-space path integral entirely in terms of superfields. BRST transformations and canonical transformations enter on equal footing, and they allow us to establish a superspace analog of the BFV theorem. We also present a formal derivation of the Lagrangian superfield analogue of the field-antifield formalism by an integration over half of the phase-space variables.

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Rotational dynamics with geometric algebra

NASA Technical Reports Server (NTRS)

Hestenes, D.

1983-01-01

A new spinor formulation of rotational dynamics is developed. A general theorem is established reducing the theory of the symmetric top to that of the spherical top. The classical problems of Lagrange and Poinsot are treated in detail, along with a modern application to the theory of magnetic resonance.

Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-06-01

We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.

[ ] or SUCCESS is Not Enough: Current Technology and Future Directions in Proof Presentation

NASA Technical Reports Server (NTRS)

Schumann, Johann; Robinson, Peter; Clancy, Daniel (Technical Monitor)

2001-01-01

Automated theorem provers for first order logic are now around for several decades. Over the last few years, their deductive power to solve hard problems has increased tremendously. The annual CASC system competitions [Se97] give a clear picture of this situation. However, today's automated theorem provers are restricted "more by general usability than by raw deductive power." As a result of this, there are only very few serious applications of automated theorem provers. There are numerous features which a theorem prover lacks for real-world applicability. An automated theorem prover (as it is currently seen) is nothing more than a fast and elaborate search procedure. In that sense, an ATP can compared to a formulated race car, cool and fast, but virtually unusable for shopping groceries around the corner. Many important features are missing, or are optimized for speed rather than for applicability. [Schol] identifies important features which are needed for practical usability like detection of non-theorems, handling of modal/inductive proof tasks, control of the prover, and proof output. In this paper, we will focus solely on the last point, the presentation of the ATP's result to the user. In the rest of this paper, we will first discuss the general importance of providing feedback to the user, then we will describe the system ExplainIt!, a part of the deductive synthesis system AMPHION/NAV. In the conclusions we will relate proof presentation to other ways of post-processing a proof found by an ATP and stress their role in the future of automated deduction.

Battling Arrow's Paradox to Discover Robust Water Management Alternatives

NASA Astrophysics Data System (ADS)

Kasprzyk, J. R.; Reed, P. M.; Hadka, D.

2013-12-01

This study explores whether or not Arrow's Impossibility Theorem, a theory of social choice, affects the formulation of water resources systems planning problems. The theorem discusses creating an aggregation function for voters choosing from more than three alternatives for society. The Impossibility Theorem is also called Arrow's Paradox, because when trying to add more voters, a single individual's preference will dictate the optimal group decision. In the context of water resources planning, our study is motivated by recent theoretical work that has generalized the insights for Arrow's Paradox to the design of complex engineered systems. In this framing of the paradox, states of society are equivalent to water planning or design alternatives, and the voters are equivalent to multiple planning objectives (e.g. minimizing cost or maximizing performance). Seen from this point of view, multi-objective water planning problems are functionally equivalent to the social choice problem described above. Traditional solutions to such multi-objective problems aggregate multiple performance measures into a single mathematical objective. The Theorem implies that a subset of performance concerns will inadvertently dictate the overall design evaluations in unpredictable ways using such an aggregation. We suggest that instead of aggregation, an explicit many-objective approach to water planning can help overcome the challenges posed by Arrow's Paradox. Many-objective planning explicitly disaggregates measures of performance while supporting the discovery of the planning tradeoffs, employing multiobjective evolutionary algorithms (MOEAs) to find solutions. Using MOEA-based search to address Arrow's Paradox requires that the MOEAs perform robustly with increasing problem complexity, such as adding additional objectives and/or decisions. This study uses comprehensive diagnostic evaluation of MOEA search performance across multiple problem formulations (both aggregated and many-objective) to show whether or not aggregating performance measures biases decision making. In this study, we explore this hypothesis using an urban water portfolio management case study in the Lower Rio Grande Valley. The diagnostic analysis shows that modern self-adaptive MOEA search is efficient, effective, and reliable for the more complex many-objective LRGV planning formulations. Results indicate that although many classical water systems planning frameworks seek to account for multiple objectives, the common practice of reducing the problem into one or more highly aggregated performance measures can severely and negatively bias planning decisions.

Generalization of the optical theorem for an arbitrary multipole in the presence of a transparent half-space

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2017-07-01

The optical theorem is generalized to the case of excitation of a local inhomogeneity introduced in a transparent substrate by a multipole of arbitrary order. It is shown that, to calculate the generalized extinction cross section, it is sufficient to calculate the derivatives of the scattered field at a single point by adding a constant and a definite integral. Apart from general scientific interest, the proposed generalization makes it possible to calculate the absorption cross section by subtracting the scattering cross section from the extinction cross section. The latter fact is important, because the scattered field in the far zone contains no Sommerfeld integrals. In addition, the proposed generalization allows one to test computer modules for the case where a lossless inhomogeneity is considered.

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

NASA Astrophysics Data System (ADS)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

No-Hair Theorem for Black Holes in Astrophysical Environments

NASA Astrophysics Data System (ADS)

Gürlebeck, Norman

2015-04-01

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

No-hair theorem for black holes in astrophysical environments.

PubMed

Gürlebeck, Norman

2015-04-17

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

Influence of dispatching rules on average production lead time for multi-stage production systems.

PubMed

Hübl, Alexander; Jodlbauer, Herbert; Altendorfer, Klaus

2013-08-01

In this paper the influence of different dispatching rules on the average production lead time is investigated. Two theorems based on covariance between processing time and production lead time are formulated and proved theoretically. Theorem 1 links the average production lead time to the "processing time weighted production lead time" for the multi-stage production systems analytically. The influence of different dispatching rules on average lead time, which is well known from simulation and empirical studies, can be proved theoretically in Theorem 2 for a single stage production system. A simulation study is conducted to gain more insight into the influence of dispatching rules on average production lead time in a multi-stage production system. We find that the "processing time weighted average production lead time" for a multi-stage production system is not invariant of the applied dispatching rule and can be used as a dispatching rule independent indicator for single-stage production systems.

What Makes the Foucault Pendulum Move among the Stars?

ERIC Educational Resources Information Center

Phillips, Norman

2004-01-01

Foucault's pendulum exhibition in 1851 occurred in an era now known by development of the theorems of Coriolis and the formulation of dynamical meteorology by Ferrel. Yet today the behavior of the pendulum is often misunderstood. The existence of a horizontal component of Newtonian gravitation is essential for understanding the behavior with…

Spin-adapted matrix product states and operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

A Geometric Puzzle That Leads To Fibonacci Sequences.

ERIC Educational Resources Information Center

Rulf, Benjamin

1998-01-01

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Variational formulation for dissipative continua and an incremental J-integral

NASA Astrophysics Data System (ADS)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Symmetry and conservation laws in semiclassical wave packet dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohsawa, Tomoki, E-mail: tomoki@utdallas.edu

2015-03-15

We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum asmore » well as naturally corresponds to the quantum picture.« less

Modeling, simulation, and estimation of optical turbulence

NASA Astrophysics Data System (ADS)

Formwalt, Byron Paul

This dissertation documents three new contributions to simulation and modeling of optical turbulence. The first contribution is the formalization, optimization, and validation of a modeling technique called successively conditioned rendering (SCR). The SCR technique is empirically validated by comparing the statistical error of random phase screens generated with the technique. The second contribution is the derivation of the covariance delineation theorem, which provides theoretical bounds on the error associated with SCR. It is shown empirically that the theoretical bound may be used to predict relative algorithm performance. Therefore, the covariance delineation theorem is a powerful tool for optimizing SCR algorithms. For the third contribution, we introduce a new method for passively estimating optical turbulence parameters, and demonstrate the method using experimental data. The technique was demonstrated experimentally, using a 100 m horizontal path at 1.25 m above sun-heated tarmac on a clear afternoon. For this experiment, we estimated C2n ≈ 6.01 · 10-9 m-23 , l0 ≈ 17.9 mm, and L0 ≈ 15.5 m.

Normal order and extended Wick theorem for a multiconfiguration reference wave function

NASA Astrophysics Data System (ADS)

Kutzelnigg, Werner; Mukherjee, Debashis

1997-07-01

A generalization of normal ordering and of Wick's theorem with respect to an arbitrary reference function Φ as some generalized "physical vacuum" is formulated in a different (but essentially equivalent) way than that suggested previously by one of the present authors. Guiding principles are that normal order operators with respect to any reference state must be expressible as linear combinations of those with respect to the genuine vacuum, that the vacuum expectation value of a normal order operator must vanish (with respect to the vacuum to which it is in normal order), and that the well-known formalism for a single Slater determinant as physical vacuum must be contained as a special case. The derivation is largely based on the concepts of "Quantum Chemistry in Fock space," which means that particle-number-conserving operators (excitation operators) play a central role. Nevertheless, the contraction rules in the frame of a generalized Wick theorem are derived, that hold for non-particle-number-conserving operators as well. The contraction rules are formulated and illustrated in terms of diagrams. The contractions involve the "residual n-particle density matrices" λ, which are the irreducible (non-factorizable) parts of the conventional n-particle density matrices γ, in the sense of a cumulant expansion for the density. A spinfree formulation is presented as well. The expression of the Hamiltonian in normal order with respect to a multiconfiguration reference function leads to a natural definition of a generalized Fock operator. MC-SCF-theory is easily worked out in this context. The paper concludes with a discussion of the excited configurations and the first-order interacting space, that underlies a perturbative coupled cluster type correction to the MCSCF function for an arbitrary reference function, and with general implications of the new formalism, that is related to "internally contracted multireference configuration interaction." The present generalization of normal ordering is not only valid for arbitrary reference functions, but also if the reference state is an ensemble state.

Comparative study of methods to calibrate the stiffness of a single-beam gradient-force optical tweezers over various laser trapping powers

PubMed Central

Sarshar, Mohammad; Wong, Winson T.; Anvari, Bahman

2014-01-01

Abstract. Optical tweezers have become an important instrument in force measurements associated with various physical, biological, and biophysical phenomena. Quantitative use of optical tweezers relies on accurate calibration of the stiffness of the optical trap. Using the same optical tweezers platform operating at 1064 nm and beads with two different diameters, we present a comparative study of viscous drag force, equipartition theorem, Boltzmann statistics, and power spectral density (PSD) as methods in calibrating the stiffness of a single beam gradient force optical trap at trapping laser powers in the range of 0.05 to 1.38 W at the focal plane. The equipartition theorem and Boltzmann statistic methods demonstrate a linear stiffness with trapping laser powers up to 355 mW, when used in conjunction with video position sensing means. The PSD of a trapped particle’s Brownian motion or measurements of the particle displacement against known viscous drag forces can be reliably used for stiffness calibration of an optical trap over a greater range of trapping laser powers. Viscous drag stiffness calibration method produces results relevant to applications where trapped particle undergoes large displacements, and at a given position sensing resolution, can be used for stiffness calibration at higher trapping laser powers than the PSD method. PMID:25375348

Possible violation of the optical theorem in LHC experiments

NASA Astrophysics Data System (ADS)

Kupczynski, M.

2014-12-01

The optical theorem (OT), allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude, is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains an imaginary part of the forward elastic scattering amplitude that is not directly measurable. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However, if one takes seriously the idea that the hadrons are extended particles, one may define a unitary S matrix such that one cannot prove the OT. Moreover, data violating the OT do exist, but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago, but they were forgotten. In this paper we will recall these results in an understandable way, and we will give the additional arguments why the OT can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.

Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem

USGS Publications Warehouse

Snieder, R.; Van Wijk, K.; Haney, M.; Calvert, R.

2008-01-01

The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. ?? 2008 The American Physical Society.

Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe.

PubMed

Lee, Jaesun; Achenbach, Jan D; Cho, Younho

2018-03-01

Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation. Copyright © 2017 Elsevier B.V. All rights reserved.

Force, torque, linear momentum, and angular momentum in classical electr odynamics

NASA Astrophysics Data System (ADS)

Mansuripur, Masud

2017-10-01

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative force law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

An efficient formulation of Krylov's prediction model for train induced vibrations based on the dynamic reciprocity theorem.

PubMed

Degrande, G; Lombaert, G

2001-09-01

In Krylov's analytical prediction model, the free field vibration response during the passage of a train is written as the superposition of the effect of all sleeper forces, using Lamb's approximate solution for the Green's function of a halfspace. When this formulation is extended with the Green's functions of a layered soil, considerable computational effort is required if these Green's functions are needed in a wide range of source-receiver distances and frequencies. It is demonstrated in this paper how the free field response can alternatively be computed, using the dynamic reciprocity theorem, applied to moving loads. The formulation is based on the response of the soil due to the moving load distribution for a single axle load. The equations are written in the wave-number-frequency domain, accounting for the invariance of the geometry in the direction of the track. The approach allows for a very efficient calculation of the free field vibration response, distinguishing the quasistatic contribution from the effect of the sleeper passage frequency and its higher harmonics. The methodology is validated by means of in situ vibration measurements during the passage of a Thalys high-speed train on the track between Brussels and Paris. It is shown that the model has good predictive capabilities in the near field at low and high frequencies, but underestimates the response in the midfrequency band.

Advanced Topics in Space Situational Awareness

DTIC Science & Technology

2007-11-07

34super-resolution." Such optical superresolution is characteristic of many model-based image processing algorithms, and reflects the incorporation of...Sampling Theorem," J. Opt. Soc. Am. A, vol. 24, 311-325 (2007). [39] S. Prasad, "Digital and Optical Superresolution of Low-Resolution Image Sequences," Un...wavefront coding for the specific application of extension of image depth well beyond what is possible in a standard imaging system. The problem of optical

Enter the reverend: introduction to and application of Bayes' theorem in clinical ophthalmology.

PubMed

Thomas, Ravi; Mengersen, Kerrie; Parikh, Rajul S; Walland, Mark J; Muliyil, Jayprakash

2011-12-01

Ophthalmic practice utilizes numerous diagnostic tests, some of which are used to screen for disease. Interpretation of test results and many clinical management issues are actually problems in inverse probability that can be solved using Bayes' theorem. Use two-by-two tables to understand Bayes' theorem and apply it to clinical examples. Specific examples of the utility of Bayes' theorem in diagnosis and management. Two-by-two tables are used to introduce concepts and understand the theorem. The application in interpretation of diagnostic tests is explained. Clinical examples demonstrate its potential use in making management decisions. Positive predictive value and conditional probability. The theorem demonstrates the futility of testing when prior probability of disease is low. Application to untreated ocular hypertension demonstrates that the estimate of glaucomatous optic neuropathy is similar to that obtained from the Ocular Hypertension Treatment Study. Similar calculations are used to predict the risk of acute angle closure in a primary angle closure suspect, the risk of pupillary block in a diabetic undergoing cataract surgery, and the probability that an observed decrease in intraocular pressure is due to the medication that has been started. The examples demonstrate how data required for management can at times be easily obtained from available information. Knowledge of Bayes' theorem helps in interpreting test results and supports the clinical teaching that testing for conditions with a low prevalence has a poor predictive value. In some clinical situations Bayes' theorem can be used to calculate vital data required for patient management. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

About the best approximations with trigonometric polynomials on the class W0Hω¯ of the space L, part II

NASA Astrophysics Data System (ADS)

Nikolova, Yanka

2013-12-01

In this paper we obtain estimation for the best approximation En(W0Hω¯) in the L-metric, where W0Hω¯ is the conjugate of the class W0Hω, i.e. W0Hω¯ =def {f¯,f∈W0Hω}. Our results concern evaluations of the function Φ(\\overlineG\\overline;x), where Φ(G;x) is the so-called ∑-representation of the function G, as defined in [2, p.144], and \\overlineG\\overline(x) denotes the conjugate of the function G(x). After some preliminaries, we formulate three basic theorems (Theorems 2, 3, 4) from the first part of this work [9], necessary for the estimation of the functional Fω(g¯) = supf∈Hω ∫ 02πf(t)ṡg¯(t)dt. Specially, in Theorem 4 we prove an inequality for this functional and show that the estimation is exact, i.e. the inequality becomes equality for some specific conjugate functions. Next, the new results in this paper are given as Theorems 5 and 6, with detailed proofs. Furthermore, in our work we prove the following estimation: f¯n,0‖L≤En(W0Hω¯)L≤2f¯n,0‖L.

Interpersonal Persuasion I: Formulation and First Test of a Rules-Based Theory.

ERIC Educational Resources Information Center

Lulofs, Roxane Salyer

A great deal of research has been done in the area of "compliance-message" tactics and strategies, but this research has not produced a coherent framework for studying this interpersonal communication process. Based on six axioms concerning the nature of communication behavior in general and on one postulate and five theorems defining…

Quantum-field-theoretical approach to phase–space techniques: Symmetric Wick theorem and multitime Wigner representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plimak, L.I., E-mail: Lev.Plimak@mbi-berlin.de; Olsen, M.K.

2014-12-15

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. Analogs of Wick’s theorem for the Weyl ordering are verified. Using the Bose–Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed.

Generalized parametric down conversion, many particle interferometry, and Bell's theorem

NASA Technical Reports Server (NTRS)

Choi, Hyung Sup

1992-01-01

A new field of multi-particle interferometry is introduced using a nonlinear optical spontaneous parametric down conversion (SPDC) of a photon into more than two photons. The study of SPDC using a realistic Hamiltonian in a multi-mode shows that at least a low conversion rate limit is possible. The down converted field exhibits many stronger nonclassical phenomena than the usual two photon parametric down conversion. Application of the multi-particle interferometry to a recently proposed many particle Bell's theorem on the Einstein-Podolsky-Rosen problem is given.

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neupert, Titus; He, Huan; Keyserlingk, Curt von

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

Nonequilibrium study of the intrinsic free-energy profile across a liquid-vapour interface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braga, Carlos, E-mail: ccorreia@imperial.ac.uk; Muscatello, Jordan, E-mail: jordan.muscatello@imperial.ac.uk; Lau, Gabriel, E-mail: gabriel.lau07@imperial.ac.uk

2016-01-28

We calculate an atomistically detailed free-energy profile across a heterogeneous system using a nonequilibrium approach. The path-integral formulation of Crooks fluctuation theorem is used in conjunction with the intrinsic sampling method to calculate the free-energy profile for the liquid-vapour interface of the Lennard-Jones fluid. Free-energy barriers are found corresponding to the atomic layering in the liquid phase as well as a barrier associated with the presence of an adsorbed layer as revealed by the intrinsic density profile. Our findings are in agreement with profiles calculated using Widom’s potential distribution theorem applied to both the average and the intrinsic profiles asmore » well as the literature values for the excess chemical potential.« less

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE PAGES

Neupert, Titus; He, Huan; Keyserlingk, Curt von; ...

2016-12-07

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

NASA Astrophysics Data System (ADS)

Carozzi, T. D.; Woan, G.

2009-05-01

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard `Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.

An interferometric fiber optic hydrophone with large upper limit of dynamic range

NASA Astrophysics Data System (ADS)

Zhang, Lei; Kan, Baoxi; Zheng, Baichao; Wang, Xuefeng; Zhang, Haiyan; Hao, Liangbin; Wang, Hailiang; Hou, Zhenxing; Yu, Wenpeng

2017-10-01

Interferometric fiber optic hydrophone based on heterodyne detection is used to measure the missile dropping point in the sea. The signal caused by the missile dropping in the water will be too large to be detected, so it is necessary to boost the upper limit of dynamic range (ULODR) of fiber optic hydrophone. In this article we analysis the factors which influence the ULODR of fiber optic hydrophone based on heterodyne detection, the ULODR is decided by the sampling frequency fsam and the heterodyne frequency Δf. The sampling frequency and the heterodyne frequency should be satisfied with the Nyquist sampling theorem which fsam will be two times larger than Δf, in this condition the ULODR is depended on the heterodyne frequency. In order to enlarge the ULODR, the Nyquist sampling theorem was broken, and we proposed a fiber optic hydrophone which the heterodyne frequency is larger than the sampling frequency. Both the simulation and experiment were done in this paper, the consequences are similar: When the sampling frequency is 100kHz, the ULODR of large heterodyne frequency fiber optic hydrophone is 2.6 times larger than that of the small heterodyne frequency fiber optic hydrophone. As the heterodyne frequency is larger than the sampling frequency, the ULODR is depended on the sampling frequency. If the sampling frequency was set at 2MHz, the ULODR of fiber optic hydrophone based on heterodyne detection will be boosted to 1000rad at 1kHz, and this large heterodyne fiber optic hydrophone can be applied to locate the drop position of the missile in the sea.

Different Formulations of the Orthogonal Array Problem and Their Symmetries

DTIC Science & Technology

2014-06-19

t). Note that OAP(k, s, t, λ) is a polytope not an unbounded polyhedron because it can be embedded inside the hypercube [0, λ]m. Theorem 5. The OAP(k...3.1) is a facet since otherwise OAP(k, s, t, λ) would be an unbounded polyhedron . Then there exists Ny ∈ Rm satisfying all but the 28 facet defining

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems.more » Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.« less

Phase space analysis in anisotropic optical systems

NASA Technical Reports Server (NTRS)

Rivera, Ana Leonor; Chumakov, Sergey M.; Wolf, Kurt Bernardo

1995-01-01

From the minimal action principle follows the Hamilton equations of evolution for geometric optical rays in anisotropic media. As in classical mechanics of velocity-dependent potentials, the velocity and the canonical momentum are not parallel, but differ by an anisotropy vector potential, similar to that of linear electromagnetism. Descartes' well known diagram for refraction is generalized and a factorization theorem holds for interfaces between two anisotropic media.

Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2014-10-01

The so-called non-locality theorems aim to show that Quantum Mechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp's arguments of non-locality. We supplement the formalism of Quantum Mechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.

Matrix of moments of the Legendre polynomials and its application to problems of electrostatics

NASA Astrophysics Data System (ADS)

Savchenko, A. O.

2017-01-01

In this work, properties of the matrix of moments of the Legendre polynomials are presented and proven. In particular, the explicit form of the elements of the matrix inverse to the matrix of moments is found and theorems of the linear combination and orthogonality are proven. On the basis of these properties, the total charge and the dipole moment of a conducting ball in a nonuniform electric field, the charge distribution over the surface of the conducting ball, its multipole moments, and the force acting on a conducting ball situated on the axis of a nonuniform axisymmetric electric field are determined. All assertions are formulated in theorems, the proofs of which are based on the properties of the matrix of moments of the Legendre polynomials.

On the Lagrangian description of dissipative systems

NASA Astrophysics Data System (ADS)

Martínez-Pérez, N. E.; Ramírez, C.

2018-03-01

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and conserved quantities, like the Hamiltonian, that generate symmetry transformations and do not correspond to observables. We show that there are simple relations among the equations satisfied by these two types of quantities. In the case of the damped harmonic oscillator, from the quantities obtained by the Noether theorem follows the algebra of Feshbach and Tikochinsky. Furthermore, if we consider the whole dynamics, the degrees of freedom separate into a physical and an unphysical sector. We analyze several cases, with linear and nonlinear dissipative forces; the physical consistency of the solutions is ensured, observing that the unphysical sector has always the trivial solution.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

NASA Astrophysics Data System (ADS)

Sugama, H.

2017-12-01

Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are formulated based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the Lagrangian variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive formulations.

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

NASA Astrophysics Data System (ADS)

Herfray, Yannick

2017-11-01

This paper establishes the relation between traditional results from the (Euclidean) twistor theory and chiral formulations of general relativity (GR), especially the pure connection formulation. Starting from an SU(2)-connection only, we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear graviton theorem. Finally, we discuss what new strategies this "connection approach" to twistors suggests for constructing a twistor action for gravity. In Appendix A, we also review all known chiral Lagrangians for GR.

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

PubMed Central

2013-01-01

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

Significance of Strain in Formulation in Theory of Solid Mechanics

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

2003-01-01

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.

A quantum mechanics-based approach to model incident-induced dynamic driver behavior

NASA Astrophysics Data System (ADS)

Sheu, Jiuh-Biing

2008-08-01

A better understanding of the psychological factors influencing drivers, and the resulting driving behavior responding to incident-induced lane traffic phenomena while passing by an incident site is vital to the improvement of road safety. This paper presents a microscopic driver behavior model to explain the dynamics of the instantaneous driver decision process under lane-blocking incidents on adjacent lanes. The proposed conceptual framework decomposes the corresponding driver decision process into three sequential phases: (1) initial stimulus, (2) glancing-around car-following, and (3) incident-induced driving behavior. The theorem of quantum mechanics in optical flows is applied in the first phase to explain the motion-related perceptual phenomena while vehicles approach the incident site in adjacent lanes, followed by the incorporation of the effect of quantum optical flows in modeling the induced glancing-around car-following behavior in the second phase. Then, an incident-induced driving behavior model is formulated to reproduce the dynamics of driver behavior conducted in the process of passing by an incident site in the adjacent lanes. Numerical results of model tests using video-based incident data indicate the validity of the proposed traffic behavior model in analyzing the incident-induced lane traffic phenomena. It is also expected that such a proposed quantum-mechanics based methodology can throw more light if applied to driver psychology and response in anomalous traffic environments in order to improve road safety.

Fiber-optic coupling based on nonimaging expanded-beam optics.

PubMed

Moslehi, B; Ng, J; Kasimoff, I; Jannson, T

1989-12-01

We have fabricated and experimentally tested low-cost and mass-producible multimode fiber-optic couplers and connectors based on nonimaging beam-expanding optics and Liouville's theorem. Analysis indicates that a pair coupling loss of -0.25 dB can be achieved. Experimentally, we measured insertion losses as low as -0.38 dB. The beam expanders can be mass produced owing to the use of plastic injection-molding fabrication techniques and packaged in standard connector housings. This design is compatible with the fiber geometry and can yield highly stable coupling owing to its high tolerance for misalignments.

Nanoimprint-defined, large-area meta-surfaces for unidirectional optical transmission with superior extinction in the visible-to-infrared range.

PubMed

Yao, Yuhan; Liu, He; Wang, Yifei; Li, Yuanrui; Song, Boxiang; Wang, Richard P; Povinelli, Michelle L; Wu, Wei

2016-07-11

Optical devices with asymmetric transmission have important applications in optical systems, but optical isolators with the modal asymmetry can only be built using magneto-optical or nonlinear materials, as dictated by the Lorentz reciprocity theorem. However, optical devices with the power asymmetry can be achieved by linear materials such as metals and dielectrics. In this paper, we report a large-area, nanoimprint-defined meta-surface (stacked subwavelength gratings) with high-contrast asymmetric transmittance in the visible-to-infrared wavelength range for TM-polarized light. The physical origin of asymmetric transmission through the meta-surface is studied by analyzing the scattering matrix.

Generalized Bloch theorem for complex periodic potentials: A powerful application to quantum transport calculations

NASA Astrophysics Data System (ADS)

Zhang, X.-G.; Varga, Kalman; Pantelides, Sokrates T.

2007-07-01

Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations but have not so far been adapted for quantum transport problems with open boundary conditions. Here, we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method are demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data.

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

Math Attendees Find There's Life After Fermat Proof.

PubMed

Cipra, B

1994-02-04

The uncertain status of the recent proof of Fermat's Last Theorem (Science, 24 December 1993, p. 1967) was the hot topic in the hallways at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held 12-15 January in Cincinnati. But a few other topics did manage to get discussed. Among them: How gambling pays off in computing the volume of high-dimensional shapes; how a mathematical description of water dripping down a window pane might lead to the design of digital pulses that could race through the optical fibers of the future; and how one can be fooled infinitely often by another theorem of Fermat's.

Evolution in Stage-Structured Populations

PubMed Central

Barfield, Michael; Holt, Robert D.; Gomulkiewicz, Richard

2016-01-01

For many organisms, stage is a better predictor of demographic rates than age. Yet no general theoretical framework exists for understanding or predicting evolution in stage-structured populations. Here, we provide a general modeling approach that can be used to predict evolution and demography of stage-structured populations. This advances our ability to understand evolution in stage-structured populations to a level previously available only for populations structured by age. We use this framework to provide the first rigorous proof that Lande’s theorem, which relates adaptive evolution to population growth, applies to stage-classified populations, assuming only normality and that evolution is slow relative to population dynamics. We extend this theorem to allow for different means or variances among stages. Our next major result is the formulation of Price’s theorem, a fundamental law of evolution, for stage-structured populations. In addition, we use data from Trillium grandiflorum to demonstrate how our models can be applied to a real-world population and thereby show their practical potential to generate accurate projections of evolutionary and population dynamics. Finally, we use our framework to compare rates of evolution in age- versus stage-structured populations, which shows how our methods can yield biological insights about evolution in stage-structured populations. PMID:21460563

The new electromagnetic tetrads, infinite tetrad nesting and the non-trivial emergence of complex numbers in real theories of gravitation

NASA Astrophysics Data System (ADS)

Garat, Alcides

How complex numbers get into play in a non-trivial way in real theories of gravitation is relevant since in a unified structure they should be able to relate in a natural way with quantum theories. For a long time this issue has been lingering on both relativistic formulations and quantum theories. We will analyze this fundamental subject under the light of new group isomorphism theorems linking local internal groups of transformations and local groups of spacetime transformations. The bridge between these two kinds of transformations is represented by new tetrads introduced previously. It is precisely through these local tetrad structures that we will provide a non-trivial answer to this old issue. These new tetrads have two fundamental building components, the skeletons and the gauge vectors. It is these constructive elements that provide the mathematical support that allows to prove group isomorphism theorems. In addition to this, we will prove a unique new property, the infinite tetrad nesting, alternating the nesting with non-Abelian tetrads in the construction of the tetrad gauge vectors. As an application we will demonstrate an alternative proof of a new group isomorphism theorem.

Dynamic contact problem with adhesion and damage between thermo-electro-elasto-viscoplastic bodies

NASA Astrophysics Data System (ADS)

Hadj ammar, Tedjani; Saïdi, Abdelkader; Azeb Ahmed, Abdelaziz

2017-05-01

We study of a dynamic contact problem between two thermo-electro-elasto-viscoplastic bodies with damage and adhesion. The contact is frictionless and is modeled with normal compliance condition. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.

Mode Matching for Optical Antennas

NASA Astrophysics Data System (ADS)

Feichtner, Thorsten; Christiansen, Silke; Hecht, Bert

2017-11-01

The emission rate of a point dipole can be strongly increased in the presence of a well-designed optical antenna. Yet, optical antenna design is largely based on radio-frequency rules, ignoring, e.g., Ohmic losses and non-negligible field penetration in metals at optical frequencies. Here, we combine reciprocity and Poynting's theorem to derive a set of optical-frequency antenna design rules for benchmarking and optimizing the performance of optical antennas driven by single quantum emitters. Based on these findings a novel plasmonic cavity antenna design is presented exhibiting a considerably improved performance compared to a reference two-wire antenna. Our work will be useful for the design of high-performance optical antennas and nanoresonators for diverse applications ranging from quantum optics to antenna-enhanced single-emitter spectroscopy and sensing.

Using Bayes' theorem for free energy calculations

NASA Astrophysics Data System (ADS)

Rogers, David M.

Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.

Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators

NASA Astrophysics Data System (ADS)

Reis, J. A. A. S.; Schreck, M.

2017-04-01

The Standard Model extension (SME) parametrizes all possible Lorentz-violating contributions to the Standard Model and general relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory.

Pulsed Rabi oscillations in quantum two-level systems: beyond the area theorem

NASA Astrophysics Data System (ADS)

Fischer, Kevin A.; Hanschke, Lukas; Kremser, Malte; Finley, Jonathan J.; Müller, Kai; Vučković, Jelena

2018-01-01

The area theorem states that when a short optical pulse drives a quantum two-level system, it undergoes Rabi oscillations in the probability of scattering a single photon. In this work, we investigate the breakdown of the area theorem as both the pulse length becomes non-negligible and for certain pulse areas. Using simple quantum trajectories, we provide an analytic approximation to the photon emission dynamics of a two-level system. Our model provides an intuitive way to understand re-excitation, which elucidates the mechanism behind the two-photon emission events that can spoil single-photon emission. We experimentally measure the emission statistics from a semiconductor quantum dot, acting as a two-level system, and show good agreement with our simple model for short pulses. Additionally, the model clearly explains our recent results (Fischer and Hanschke 2017 et al Nat. Phys.) showing dominant two-photon emission from a two-level system for pulses with interaction areas equal to an even multiple of π.

The DTIC Review. Volume 2, Number 3: Optical and Infrared Detection and Countermeasures

DTIC Science & Technology

1996-10-01

are different from those en- countered in designing wavelets for other applications. For use in time- frequency analysis of signals, for example, it...view within the field of regard, and for high -fidelity simulation of optical blurring and temporal effects such as jitter. The real-time CLDWSG method ...integration methods or, for near spatially invariant FOV regions, by convolution methods or by way of the convolution theorem using OTF frequency -domain

Scattering amplitudes from multivariate polynomial division

NASA Astrophysics Data System (ADS)

Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

2012-11-01

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

A reconstruction theorem for Connes-Landi deformations of commutative spectral triples

NASA Astrophysics Data System (ADS)

Ćaćić, Branimir

2015-12-01

We formulate and prove an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes-Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes-Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes-Dubois-Violette splitting homomorphism to conclude that suitable Connes-Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense.

Nonequilibrium thermodynamics and a fluctuation theorem for individual reaction steps in a chemical reaction network

NASA Astrophysics Data System (ADS)

Pal, Krishnendu; Das, Biswajit; Banerjee, Kinshuk; Gangopadhyay, Gautam

2015-09-01

We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.

Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac

NASA Astrophysics Data System (ADS)

Fine, Dana S.; Sawin, Stephen

2017-01-01

Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

Acoustic reciprocity: An extension to spherical harmonics domain.

PubMed

Samarasinghe, Prasanga; Abhayapala, Thushara D; Kellermann, Walter

2017-10-01

Acoustic reciprocity is a fundamental property of acoustic wavefields that is commonly used to simplify the measurement process of many practical applications. Traditionally, the reciprocity theorem is defined between a monopole point source and a point receiver. Intuitively, it must apply to more complex transducers than monopoles. In this paper, the authors formulate the acoustic reciprocity theory in the spherical harmonics domain for directional sources and directional receivers with higher order directivity patterns.

Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

NASA Astrophysics Data System (ADS)

Bulgakov, V. K.; Strigunov, V. V.

2009-05-01

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

On making cuts for magnetic scalar potentials in multiply connected regions

NASA Astrophysics Data System (ADS)

Kotiuga, P. R.

1987-04-01

The problem of making cuts is of importance to scalar potential formulations of three-dimensional eddy current problems. Its heuristic solution has been known for a century [J. C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed. (Clarendon, Oxford, 1981), Chap. 1, Article 20] and in the last decade, with the use of finite element methods, a restricted combinatorial variant has been proposed and solved [M. L. Brown, Int. J. Numer. Methods Eng. 20, 665 (1984)]. This problem, in its full generality, has never received a rigorous mathematical formulation. This paper presents such a formulation and outlines a rigorous proof of existence. The technique used in the proof expose the incredible intricacy of the general problem and the restrictive assumptions of Brown [Int. J. Numer. Methods Eng. 20, 665 (1984)]. Finally, the results make rigorous Kotiuga's (Ph. D. Thesis, McGill University, Montreal, 1984) heuristic interpretation of cuts and duality theorems via intersection matrices.

How the Hilbert integral theorem inspired flow lines

NASA Astrophysics Data System (ADS)

Winston, Roland; Jiang, Lun

2017-09-01

Nonimaging Optics has been shown to achieve the theoretical limits constrained only by thermodynamic principles. The designing principles of nonimaging optics allow a non-conventional way of thinking about and generating new optical devices. Compared to conventional imaging optics which rarely utilizes the framework of thermodynamic arguments, nonimaging optics chooses to map etendue instead of rays. This fundamental shift of design paradigm frees the optics design from ray based designs which heavily relies on error tolerance analysis. Instead, the underlying thermodynamic principles guide the nonimaging design to be naturally constructed for extended light source for illumination, non-tracking concentrators and sensors that require sharp cut-off angles. We argue in this article that such optical devices which has enabled a multitude of applications depends on probabilities, geometric flux field and radiative heat transfer while "optics" in the conventional sense recedes into the background.

32 bit digital optical computer - A hardware update

NASA Technical Reports Server (NTRS)

Guilfoyle, Peter S.; Carter, James A., III; Stone, Richard V.; Pape, Dennis R.

1990-01-01

Such state-of-the-art devices as multielement linear laser diode arrays, multichannel acoustooptic modulators, optical relays, and avalanche photodiode arrays, are presently applied to the implementation of a 32-bit supercomputer's general-purpose optical central processing architecture. Shannon's theorem, Morozov's control operator method (in conjunction with combinatorial arithmetic), and DeMorgan's law have been used to design an architecture whose 100 MHz clock renders it fully competitive with emerging planar-semiconductor technology. Attention is given to the architecture's multichannel Bragg cells, thermal design and RF crosstalk considerations, and the first and second anamorphic relay legs.

CLASSICAL AREAS OF PHENOMENOLOGY: Study on the design and Zernike aberrations of a segmented mirror telescope

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Yu; Li, Lin; Huang, Yi-Fan

2009-07-01

The segmented mirror telescope is widely used. The aberrations of segmented mirror systems are different from single mirror systems. This paper uses the Fourier optics theory to analyse the Zernike aberrations of segmented mirror systems. It concludes that the Zernike aberrations of segmented mirror systems obey the linearity theorem. The design of a segmented space telescope and segmented schemes are discussed, and its optical model is constructed. The computer simulation experiment is performed with this optical model to verify the suppositions. The experimental results confirm the correctness of the model.

Connection of Scattering Principles: A Visual and Mathematical Tour

ERIC Educational Resources Information Center

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

Extension of the Kohn-Sham formulation of density functional theory to finite temperature

NASA Astrophysics Data System (ADS)

Gonis, A.; Däne, M.

2018-05-01

Based on Mermin's extension of the Hohenberg and Kohn theorems to non-zero temperature, the Kohn-Sham formulation of density functional theory (KS-DFT) is generalized to finite temperature. We show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the self-consistent solutions of the single-particle Schrödinger equation of T > 0. Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T = 0, we base our extension of KS-DFT on the determination of the excited states of a non-interacting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T > 0 in terms of the excited states of a non-interacting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T = 0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a non-interacting collection of replicas of a non-interacting N-particle system, whose ground state density is taken to match that of K non-interacting replicas of an interacting N-particle system at T = 0 . The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (Kohn-Sham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through self-consistency conditions at the zero of temperature. It is emphasized that, in departure from all existing formulations, no self-consistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.

Koopmans' theorem in the Hartree-Fock method. General formulation

NASA Astrophysics Data System (ADS)

Plakhutin, Boris N.

2018-03-01

This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.

Light field creating and imaging with different order intensity derivatives

NASA Astrophysics Data System (ADS)

Wang, Yu; Jiang, Huan

2014-10-01

Microscopic image restoration and reconstruction is a challenging topic in the image processing and computer vision, which can be widely applied to life science, biology and medicine etc. A microscopic light field creating and three dimensional (3D) reconstruction method is proposed for transparent or partially transparent microscopic samples, which is based on the Taylor expansion theorem and polynomial fitting. Firstly the image stack of the specimen is divided into several groups in an overlapping or non-overlapping way along the optical axis, and the first image of every group is regarded as reference image. Then different order intensity derivatives are calculated using all the images of every group and polynomial fitting method based on the assumption that the structure of the specimen contained by the image stack in a small range along the optical axis are possessed of smooth and linear property. Subsequently, new images located any position from which to reference image the distance is Δz along the optical axis can be generated by means of Taylor expansion theorem and the calculated different order intensity derivatives. Finally, the microscopic specimen can be reconstructed in 3D form using deconvolution technology and all the images including both the observed images and the generated images. The experimental results show the effectiveness and feasibility of our method.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Shift-Variant Multidimensional Systems.

DTIC Science & Technology

1985-05-29

i=0,1,** *N-1 in (3.1), one will get 0() i_0,1,* ,N-1 which is nonnegative due to the Perron - Frobenius Theorem [24]. That is, the A nonnegativity ...and the current input. The state-space model was extended in order to model 2-D discrete LSV systems with support on a causality cone . Subsequently...formulated as a special system of linear equations with nonnegative coefficients whose solution is required to satisfy con- straints like nonnegativity in

EPR and Bell's theorem: A critical review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stapp, H.P.

1991-01-01

The argument of Einstein, Podolsky, and Rosen is reviewed with attention to logical structure and character of assumptions. Bohr's reply is discussed. Bell's contribution is formulated without use of hidden variables, and efforts to equate hidden variables to realism are critically examined. An alternative derivation of nonlocality that makes no use of hidden variables, microrealism, counterfactual definiteness, or any other assumption alien to orthodox quantum thinking is described in detail, with particular attention to the quartet or broken-square question.

Nonrelativistic limits of colored gravity in three dimensions

NASA Astrophysics Data System (ADS)

Joung, Euihun; Li, Wenliang

2018-05-01

The three-dimensional nonrelativistic isometry algebras, namely Galilei and Newton-Hooke algebras, are known to admit double central extensions, which allows for nondegenerate bilinear forms hence for action principles through Chern-Simons formulation. In three-dimensional colored gravity, the same central extension helps the theory evade the multigraviton no-go theorems by enlarging the color-decorated isometry algebra. We investigate the nonrelativistic limits of three-dimensional colored gravity in terms of generalized İnönü-Wigner contractions.

Decentralized Control and Multicriterion Decision Making.

DTIC Science & Technology

1979-12-01

stabilizable and detectable? ’V L 42 Theorem 3.1: Existence of stabilizing solution. We assume that the system is jointly controllable R1 (0...a leader’s control that will make the system stabilizable for the follower and that in order for J to be finite the leader must choose F such1 1 that...a stabilizing solution will be developed. We restrict our attention to a formulation dealing with a linear continuous time system and in which

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Inelastic light and electron scattering in parabolic quantum dots in magnetic field: Implications of generalized Kohn's theorem

NASA Astrophysics Data System (ADS)

Kushwaha, Manvir S.

2016-03-01

We investigate a one-component, quasi-zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.

Application of the strongly coupled-mode theory to integrated optical devices

NASA Technical Reports Server (NTRS)

Chuang, Shun-Lien

1987-01-01

A theory for strongly coupled waveguides is discussed and applied to two- and three-waveguide couplers and optical wavelength filters. This theory makes use of an exact analytical relation governing the coupling coefficients and the overlap integrals. It removes almost all of the constraints imposed by a simpler and approximate coupled-mode theory by Marcatili (1986). It also satisfies the energy conservation and the reciprocity theorem self-consistently. Very good numerical results with the overlap integral as large as 49 percent are shown. The applications to electrooptical modulators, power dividers, power transfer devices, and optical filters are all presented with numerical results.

Diffraction of stochastic electromagnetic fields by a hole in a thin film with real optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2008-08-01

The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity.

FIBER AND INTEGRATED OPTICS: Optical anisotropy induced in a round trip through single-mode optical waveguides and methods for suppression of this anisotropy

NASA Astrophysics Data System (ADS)

Gelikonov, V. M.; Leonov, V. I.; Novikov, M. A.

1989-09-01

An analysis is made of the characteristics of the transformation of the polarization of light in the course of a round trip in a single-mode fiber waveguide. The Poincaré equivalence theorems are generalized for a round trip through such fibers. An investigation is reported of round-trip anisotropic properties which can be used to compensate for a regular and an irregular anisotropy of a fiber waveguide. A description is given of a compensation system containing a Faraday cell and an experimental check of the theoretical conclusions is reported.

Modeling thermoelastic distortion of optics using elastodynamic reciprocity

NASA Astrophysics Data System (ADS)

King, Eleanor; Levin, Yuri; Ottaway, David; Veitch, Peter

2015-07-01

Thermoelastic distortion resulting from optical absorption by transmissive and reflective optics can cause unacceptable changes in optical systems that employ high-power beams. In advanced-generation laser-interferometric gravitational wave detectors, for example, optical absorption is expected to result in wavefront distortions that would compromise the sensitivity of the detector, thus necessitating the use of adaptive thermal compensation. Unfortunately, these systems have long thermal time constants, and so predictive feed-forward control systems could be required, but the finite-element analysis is computationally expensive. We describe here the use of the Betti-Maxwell elastodynamic reciprocity theorem to calculate the response of linear elastic bodies (optics) to heating that has arbitrary spatial distribution. We demonstrate, using a simple example, that it can yield accurate results in computational times that are significantly less than those required for finite-element analyses.

Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions

NASA Astrophysics Data System (ADS)

Komori, Kentaro; Enomoto, Yutaro; Takeda, Hiroki; Michimura, Yuta; Somiya, Kentaro; Ando, Masaki; Ballmer, Stefan W.

2018-05-01

The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.

Implications of the Corotation Theorem on the MRI in Axial Symmetry

NASA Astrophysics Data System (ADS)

Montani, G.; Cianfrani, F.; Pugliese, D.

2016-08-01

We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z-dependence has a simple parametric role.

A biased filter for linear discrete dynamic systems.

NASA Technical Reports Server (NTRS)

Chang, J. W.; Hoerl, A. E.; Leathrum, J. F.

1972-01-01

A recursive estimator, the ridge filter, was developed for the linear discrete dynamic estimation problem. Theorems were established to show that the ridge filter can be, on the average, closer to the expected value of the system state than the Kalman filter. On the other hand, Kalman filter, on the average, is closer to the instantaneous system state than the ridge filter. The ridge filter has been formulated in such a way that the computational features of the Kalman filter are preserved.

Foundations for a theory of gravitation theories

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Lee, D. L.; Lightman, A. P.

1972-01-01

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

Robust Consumption-Investment Problem on Infinite Horizon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl

In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.

Optimal estimates of free energies from multistate nonequilibrium work data.

PubMed

Maragakis, Paul; Spichty, Martin; Karplus, Martin

2006-03-17

We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation theorem. The maximum likelihood formulation properly reweights all pathways contributing to a free energy difference and is directly applicable to simulations and experiments. We demonstrate dramatic gains in efficiency by combining the analysis with parallel tempering simulations for alchemical mutations of model amino acids.

(2 + 1)-dimensional dynamical black holes in Einstein-nonlinear Maxwell theory

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mazharimousavi, S. Habib; Halilsoy, M.

2018-02-01

Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born-Infeld electrodynamics.

News of Higher Educational Institutions, Ministry of Higher Education USSR, Radiophysics Series

DTIC Science & Technology

1960-12-30

formulate the following proposition: • • 2. " Theorem 2. If the elements AyA ^i (i^t j) of the ; determinant D ,, T*ose diagonal elements...34 OFFICE OF TECHNICAL SERVICES Ü. S. DEPARTMENT OF COMMERCE WASHINGTON 1% D * Ce U. S.’ JOINT PUBLICATIONS RESEARCH SERVICE 1636 CONNECTICUT AVE...N.W. WASHINGTON Z% D , C. FOREWORD "il ELIS publication vas ’.prepared under ■ contract "by the \\JKITED SPATES , JOIET’PUBLICATIONS RE- SEARCH

Gold nanostars as thermoplasmonic nanoparticles for optical heating.

PubMed

Rodríguez-Oliveros, R; Sánchez-Gil, José A

2012-01-02

Gold nanostars are theoretically studied as efficient thermal heaters at their corresponding localized surface-plasmon resonances (LSPRs). Numerical calculations are performed through the 3D Green's Theorem method to obtain the absorption and scattering cross sections for Au nanoparticles with star-like shape of varying symmetry and tip number. Their unique thermoplasmonic properties, with regard to their (red-shifted) LSPR wavelentgh, (∼ 30-fold increase) steady-state temperature, and scattering/absorption cross section ratios, make them specially suitable for optical heating and in turn for cancer thermal therapy.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Sampling theory for asynoptic satellite observations. I Space-time spectra, resolution, and aliasing. II - Fast Fourier synoptic mapping

NASA Technical Reports Server (NTRS)

Salby, M. L.

1982-01-01

An evaluation of the information content of asynoptic data taken in the form of nadir sonde and limb scan observations is presented, and a one-to-one correspondence is established between the alias-free data and twice-daily synoptic maps. Attention is given to space and time limitations of sampling and the orbital geometry is discussed. The sampling pattern is demonstrated to determine unique space-time spectra at all wavenumbers and frequencies. Spectral resolution and aliasing are explored, while restrictions on sampling and information content are defined. It is noted that irregular sampling at high latitudes produces spurious contamination effects. An Asynoptic Sampling Theorem is thereby formulated, as is a Synoptic Retrieval Theorem, in the second part of the article. In the latter, a procedure is developed for retrieving the unique correspondence between the asymptotic data and the synoptic maps. Applications examples are provided using data from the Nimbus-6 satellite.

On the mass of static metrics with positive cosmological constant: I

NASA Astrophysics Data System (ADS)

Borghini, Stefano; Mazzieri, Lorenzo

2018-06-01

In this paper we prove a new uniqueness result for the de Sitter solution. Our theorem is based on a new notion of mass, whose well-posedness is discussed and established in the realm of static spacetimes with positive cosmological constant that are bounded by Killing horizons. This new definition is formulated in terms of the surface gravities of the Killing horizons and agrees with the usual notion when the Schwarzschild–de Sitter solutions are considered. A positive mass statement is also shown to hold in this context. The corresponding rigidity statement coincides with the above mentioned characterization of the de Sitter solution as the only static vacuum metric with zero mass. Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a new uniqueness theorem for the anti-de Sitter spacetime, which holds under a very feeble assumption on the asymptotic behavior of the solution.

BCS, Nambu-Jona-Lasinio, and Han-Nambu: A sketch of Nambu's works in 1960-1965

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2016-06-01

The years 1960-1965 were a remarkable period for Yoichiro Nambu. Starting with a reformulation of BCS theory with emphasis on gauge invariance, he recognized the realization of spontaneous chiral symmetry breaking in particle physics as evidenced by the Goldberger-Treiman relation. A concrete model of Nambu and Jona-Lasinio illustrated the essence of the Nambu-Goldstone theorem and the idea of soft pions. After the proposal of the quark model by Gell-Mann, he together with Han constructed an alternative model of integrally charged quarks with possible non-Abelian gluons. All these remarkable works were performed during the years 1960-1965. Here I briefly review those works following the original papers of Nambu chronologically, together with a brief introduction to a formulation of Noether's theorem and the Ward-Takahashi identities using path integrals. This article is mostly based on a lecture given at the Nambu Memorial Symposium held at Osaka City University in September 2015, where Nambu started his professional career.

Amplitudes for multiphoton quantum processes in linear optics

NASA Astrophysics Data System (ADS)

Urías, Jesús

2011-07-01

The prominent role that linear optical networks have acquired in the engineering of photon states calls for physically intuitive and automatic methods to compute the probability amplitudes for the multiphoton quantum processes occurring in linear optics. A version of Wick's theorem for the expectation value, on any vector state, of products of linear operators, in general, is proved. We use it to extract the combinatorics of any multiphoton quantum processes in linear optics. The result is presented as a concise rule to write down directly explicit formulae for the probability amplitude of any multiphoton process in linear optics. The rule achieves a considerable simplification and provides an intuitive physical insight about quantum multiphoton processes. The methodology is applied to the generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light.

3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

NASA Astrophysics Data System (ADS)

Ma, Ning; Zhao, Juan; Hanson, Steen G.; Takeda, Mitsuo; Wang, Wei

2016-10-01

Laser speckle has received extensive studies of its basic properties and associated applications. In the majority of research on speckle phenomena, the random optical field has been treated as a scalar optical field, and the main interest has been concentrated on their statistical properties and applications of its intensity distribution. Recently, statistical properties of random electric vector fields referred to as Polarization Speckle have come to attract new interest because of their importance in a variety of areas with practical applications such as biomedical optics and optical metrology. Statistical phenomena of random electric vector fields have close relevance to the theories of speckles, polarization and coherence theory. In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.

Extension of the Kohn-Sham formulation of density functional theory to finite temperature

DOE PAGES

Gonis, A.; Dane, M.

2017-12-20

Based on Mermin's extension of the Hohenberg and Kohn theorems to non-zero temperature, the Kohn-Sham formulation of density functional theory (KS-DFT) is generalized to finite temperature. Here, we show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the self-consistent solutions of the single-particle Schrödinger equation of T>0.more » Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T>0 we base our extension of KS-DFT on the determination of the excited states of a non-interacting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a non-interacting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a non-interacting collection of replicas of a non-interacting N-particle system, whose ground state density is taken to match that of K non-interacting replicas of an interacting N-particle system at T>0. The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (Kohn-Sham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through self-consistency conditions at the zero of temperature. Lastly, it is emphasized that, in departure from all existing formulations, no self-consistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.« less

Extension of the Kohn-Sham formulation of density functional theory to finite temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gonis, A.; Dane, M.

Based on Mermin's extension of the Hohenberg and Kohn theorems to non-zero temperature, the Kohn-Sham formulation of density functional theory (KS-DFT) is generalized to finite temperature. Here, we show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the self-consistent solutions of the single-particle Schrödinger equation of T>0.more » Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T>0 we base our extension of KS-DFT on the determination of the excited states of a non-interacting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a non-interacting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a non-interacting collection of replicas of a non-interacting N-particle system, whose ground state density is taken to match that of K non-interacting replicas of an interacting N-particle system at T>0. The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (Kohn-Sham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through self-consistency conditions at the zero of temperature. Lastly, it is emphasized that, in departure from all existing formulations, no self-consistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.« less

A reciprocity formulation for the EM scattering by an obstacle within a large open cavity

NASA Technical Reports Server (NTRS)

Pathak, Prabhakar H.; Burkholder, Robert J.

1993-01-01

A formulation based on a generalized reciprocity theorem is developed for analyzing the external high frequency EM scattering by a complex obstacle inside a relatively arbitrary open-ended waveguide cavity when it is illuminated by an external source. This formulation is also extended to include EM fields whose time dependence may be nonperiodic. A significant advantage of this formulation is that it allows one to break up the analysis into two independent parts; one deals with the waveguide cavity shape alone and the other with the obstacle alone. The external scattered field produced by the obstacle (in the presence of the waveguide cavity structure) is given in terms of a generalized reciprocity integral over a surface S(T) corresponding to the interior waveguide cavity cross section located conveniently but sufficiently close to the obstacle. Furthermore, the fields coupled into the cavity from the source in the exterior region generally need to propagate only one-way via the open front end (which is directly illuminated) to the interior surface S(T) in this approach, and not back, in order to find the external field scattered by the obstacle.

Solving the Self-Interaction Problem in Kohn-Sham Density Functional Theory. Application to Atoms

DOE PAGES

Daene, M.; Gonis, A.; Nicholson, D. M.; ...

2014-10-14

Previously, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In our paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We also prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. Wemore » present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.« less

Operational formulation of time reversal in quantum theory

NASA Astrophysics Data System (ADS)

Oreshkov, Ognyan; Cerf, Nicolas J.

2015-10-01

The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born’s rule do not apply backward in time. Here, we resolve this problem within a rigorous operational probabilistic framework. We argue that reconciling time reversal with the probabilistic rules of the theory requires a notion of operation that permits realizations through both pre- and post-selection. We develop the generalized formulation of quantum theory that stems from this approach and give a precise definition of time-reversal symmetry, emphasizing a previously overlooked distinction between states and effects. We prove an analogue of Wigner’s theorem, which characterizes all allowed symmetry transformations in this operationally time-symmetric quantum theory. Remarkably, we find larger classes of symmetry transformations than previously assumed, suggesting a possible direction in the search for extensions of known physics.

Amplitude-phase characteristics of electromagnetic fields diffracted by a hole in a thin film with realistic optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2009-03-01

Characteristics of a quasi-spherical wave front of an electromagnetic field diffracted by a subwavelength hole in a thin film with real optical properties are studied. Related diffraction problem is solved in general by use of the scalar and vector Green's theorems and related Green's function of a boundary-value problem. Local phase deviations of a diffracted wave front from an ideal spherical front are calculated. Diffracted patterns are calculated for the coherent incident fields in case of holes array in a screen of perfect conductivity.

Degree of Approximation by a General Cλ -Summability Method

NASA Astrophysics Data System (ADS)

Sonker, S.; Munjal, A.

2018-03-01

In the present study, two theorems explaining the degree of approximation of signals belonging to the class Lip(α, p, w) by a more general C λ -method (Summability method) have been formulated. Improved estimations have been observed in terms of λ(n) where (λ(n))‑α ≤ n ‑α for 0 < α ≤ 1 as compared to previous studies presented in terms of n. These estimations of infinite matrices are very much applicable in solid state physics which further motivates for an investigation of perturbations of matrix valued functions.

Regenerative Simulation of Response Times in Networks of Queues.

DTIC Science & Technology

1979-11-01

i jobs at center 1. Nov consider the network of queues in Figure 2.2, formulated (Lewis and Shedler ( 1971 )) as a model of system overhead in...7.2 leading to point estimates and confidence intervals for the quantity r(f) are that the pairs of random variables {( V(fHk) : kall (9.2.3) are...189 Next we show that P’=P. Since P ’m"CIP for all i, we can use the Skorohod representation theorem (see Skorohod (1956) or Billingsley ( 1971 )) to

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

An entangled web of crime: Bell's theorem as a short story

NASA Astrophysics Data System (ADS)

Jacobs, Kurt; Wiseman, Howard M.

2005-10-01

Nonlocality of the type first elucidated by Bell in 1964 is a difficult concept to explain to nonspecialists and undergraduates. We attempt to do so by showing how nonlocality can be used to solve a problem in which someone might find themselves as the result of a series of normal, even if somewhat unlikely, events. Our story is told in the style of a Sherlock Holmes mystery, and is based on Mermin's formulation of the "paradoxical" illustration of quantum nonlocality discovered by Greenberger, Horne, and Zeilinger.

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

Dressed Hard States and Black Hole Soft Hair.

PubMed

Mirbabayi, Mehrdad; Porrati, Massimo

2016-11-18

A recent, intriguing Letter by Hawking, Perry, and Strominger suggests that soft photons and gravitons can be regarded as black hole hair and may be relevant to the black hole information paradox. In this Letter we make use of factorization theorems for infrared divergences of the S matrix to argue that by appropriately dressing in and out hard states, the soft-quanta-dependent part of the S matrix becomes essentially trivial. The information paradox can be fully formulated in terms of dressed hard states, which do not depend on soft quanta.

Performance limitations of translationally symmetric nonimaging devices

NASA Astrophysics Data System (ADS)

Bortz, John C.; Shatz, Narkis E.; Winston, Roland

2001-11-01

The component of the optical direction vector along the symmetry axis is conserved for all rays propagated through a translationally symmetric optical device. This quality, referred to herein as the translational skew invariant, is analogous to the conventional skew invariant, which is conserved in rotationally symmetric optical systems. The invariance of both of these quantities is a consequence of Noether's theorem. We show how performance limits for translationally symmetric nonimaging optical devices can be derived from the distributions of the translational skew invariant for the optical source and for the target to which flux is to be transferred. Examples of computed performance limits are provided. In addition, we show that a numerically optimized non-tracking solar concentrator utilizing symmetry-breaking surface microstructure can overcome the performance limits associated with translational symmetry. The optimized design provides a 47.4% increase in efficiency and concentration relative to an ideal translationally symmetric concentrator.

Noninvasive determination of optical lever sensitivity in atomic force microscopy

NASA Astrophysics Data System (ADS)

Higgins, M. J.; Proksch, R.; Sader, J. E.; Polcik, M.; Mc Endoo, S.; Cleveland, J. P.; Jarvis, S. P.

2006-01-01

Atomic force microscopes typically require knowledge of the cantilever spring constant and optical lever sensitivity in order to accurately determine the force from the cantilever deflection. In this study, we investigate a technique to calibrate the optical lever sensitivity of rectangular cantilevers that does not require contact to be made with a surface. This noncontact approach utilizes the method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] to calibrate the spring constant of the cantilever in combination with the equipartition theorem [J. L. Hutter and J. Bechhoefer, Rev. Sci. Instrum. 64, 1868 (1993)] to determine the optical lever sensitivity. A comparison is presented between sensitivity values obtained from conventional static mode force curves and those derived using this noncontact approach for a range of different cantilevers in air and liquid. These measurements indicate that the method offers a quick, alternative approach for the calibration of the optical lever sensitivity.

The analysis of decimation and interpolation in the linear canonical transform domain.

PubMed

Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Huang, Lei; Feng, Li

2016-01-01

Decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. As the linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to analyze the decimation and interpolation in the LCT domain. In this paper, the definition of equivalent filter in the LCT domain have been given at first. Then, by applying the definition, the direct implementation structure and polyphase networks for decimator and interpolator in the LCT domain have been proposed. Finally, the perfect reconstruction expressions for differential filters in the LCT domain have been presented as an application. The proposed theorems in this study are the bases for generalizations of the multirate signal processing in the LCT domain, which can advance the filter banks theorems in the LCT domain.

Geometric optics for a coupling model of electromagnetic and gravitational fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jing, Jiliang, E-mail: jljing@hunnu.edu.cn; Chen, Songbai; Pan, Qiyuan

2016-04-15

The coupling between the electromagnetic and gravitational fields results in “faster than light” photons, and then the first and third laws of geometric optics are invalid in usual spacetime. By introducing an effective spacetime, we find that the wave vector can be casted into null and then it obeys the geodesic equation, the polarization vector is perpendicular to the rays, and the number of photons is conserved. That is to say, the laws of geometric optics are valid for the modified theory in the effective spacetime. We also show that the focusing theorem of light rays for the modified theorymore » in the effective spacetime can be cast into the usual form.« less

Research on the Calculation Method of Optical Path Difference of the Shanghai Tian Ma Telescope

NASA Astrophysics Data System (ADS)

Dong, J.; Fu, L.; Jiang, Y. B.; Liu, Q. H.; Gou, W.; Yan, F.

2016-03-01

Based on the Shanghai Tian Ma Telescope (TM), an optical path difference calculation method of the shaped Cassegrain antenna is presented in the paper. Firstly, the mathematical model of the TM optics is established based on the antenna reciprocity theorem. Secondly, the TM sub-reflector and main reflector are fitted by the Non-Uniform Rational B-Splines (NURBS). Finally, the method of optical path difference calculation is implemented, and the expanding application of the Ruze optical path difference formulas in the TM is researched. The method can be used to calculate the optical path difference distributions across the aperture field of the TM due to misalignment like the axial and lateral displacements of the feed and sub-reflector, or the tilt of the sub-reflector. When the misalignment quantity is small, the expanding Ruze optical path difference formulas can be used to calculate the optical path difference quickly. The paper supports the real-time measurement and adjustment of the TM structure. The research has universality, and can provide reference for the optical path difference calculation of other radio telescopes with shaped surfaces.

On physical optics for calculating scattering from coated bodies

NASA Technical Reports Server (NTRS)

Baldauf, J.; Lee, S. W.; Ling, H.; Chou, R.

1989-01-01

The familiar physical optics (PO) approximation is no longer valid when the perfectly conducting scatterer is coated with dielectric material. This paper reviews several possible PO formulations. By comparing the PO formulation with the moment method solution based on the impedance boundary condition for the case of the coated cone-sphere, a PO formulation using both electric and magnetic currents consistently gives the best numerical results. Comparisons of the exact moment method with the PO formulations using the impedance boundary condition and the PO formulation using the Fresnel reflection coefficient for the case of scattering from the cone-ellipsoid demonstrate that the Fresnel reflection coefficient gives the best numerical results in general.

Wave-Based Algorithms and Bounds for Target Support Estimation

DTIC Science & Technology

2015-05-15

vector electromagnetic formalism in [5]. This theory leads to three main variants of the optical theorem detector, in particular, three alternative...further expands the applicability for transient pulse change detection of ar- bitrary nonlinear-media and time-varying targets [9]. This report... electromagnetic methods a new methodology to estimate the minimum convex source region and the (possibly nonconvex) support of a scattering target from knowledge of

On the far-field computation of acoustic radiation forces.

PubMed

Martin, P A

2017-10-01

It is known that the steady acoustic radiation force on a scatterer due to incident time-harmonic waves can be calculated by evaluating certain integrals of velocity potentials over a sphere surrounding the scatterer. The goal is to evaluate these integrals using far-field approximations and appropriate limits. Previous derivations are corrected, clarified, and generalized. Similar corrections are made to textbook derivations of optical theorems.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

NASA Astrophysics Data System (ADS)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Design and analysis of coherent OCDM en/decoder based on photonic crystal

NASA Astrophysics Data System (ADS)

Zhang, Chongfu; Qiu, Kun

2008-08-01

The design and performance analysis of a new coherent optical en/decoder based on photonic crystal (PhC) for optical code -division -multiple (OCDM) are presented in this paper. In this scheme, the optical pulse phase and time delay can be flexibly controlled by photonic crystal phase shifter and time delayer by using the appropriate design of fabrication. According to the PhC transmission matrix theorem, combination calculation of the impurity and normal period layers is applied, and performances of the PhC-based optical en/decoder are also analyzed. The reflection, transmission, time delay characteristic and optical spectrum of pulse en/decoded are studied for the waves tuned in the photonic band-gap by numerical calculation. Theoretical analysis and numerical results indicate that the optical pulse is achieved to properly phase modulation and time delay, and an auto-correlation of about 8 dB ration and cross-correlation is gained, which demonstrates the applicability of true pulse phase modulation in a number of applications.

Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

NASA Astrophysics Data System (ADS)

Nickelsen, Daniel

2017-07-01

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

Radiation and scattering from bodies of translation, volume 1

NASA Astrophysics Data System (ADS)

Medgyesi-Mitschang, L. N.

1980-04-01

An analytical formulation, based on the method of moments (MM) is described for solving electromagnetic problems associated with finite-length cylinders of arbitrary cross section, denoted in this report as bodies of translation (BOT). This class of bodies can be used to model structures with noncircular cross sections such as wings, fins, and aircraft fuselages. The theoretical development parallels in part the MM formulation developed earlier by Mautz and Harrington for bodies of revolution (BOR). Like the latter approach, a modal expansion is used to describe the unknown surface currents on the BOT. The present analysis has been developed to treat the far-field radiation and scattering from a BOT excited by active antennas or illuminated by a plane wave of arbitrary polarization and angle of incidence. In addition, the electric and magnetic near-field components are determined in the vicinity of active and passive apertures (slots). Using the Schelkunoff equivalence theorem, the aperture-coupled fields within a BOT are also obtained. The formulation has been implemented by a computer algorithm and validated using accepted data in the literature.

Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

NASA Astrophysics Data System (ADS)

Chen, Zhenhua; Chen, Xun; Wu, Wei

2013-04-01

In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.

A model of freezing foods with liquid nitrogen using special functions

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-05-01

A food freezing model is analyzed analytically. The model is based on the heat diffusion equation in the case of cylindrical shaped food frozen by liquid nitrogen; and assuming that the thermal conductivity of the cylindrical food is radially modulated. The model is solved using the Laplace transform method, the Bromwich theorem, and the residue theorem. The temperature profile in the cylindrical food is presented as an infinite series of special functions. All the required computations are performed with computer algebra software, specifically Maple. Using the numeric values of the thermal and geometric parameters for the cylindrical food, as well as the thermal parameters of the liquid nitrogen freezing system, the temporal evolution of the temperature in different regions in the interior of the cylindrical food is presented both analytically and graphically. The duration of the liquid nitrogen freezing process to achieve the specified effect on the cylindrical food is computed. The analytical results are expected to be of importance in food engineering and cooking engineering. As a future research line, the formulation and solution of freezing models with thermal memory is proposed.

Dynamic inversion enables external magnets to concentrate ferromagnetic rods to a central target.

PubMed

Nacev, A; Weinberg, I N; Stepanov, P Y; Kupfer, S; Mair, L O; Urdaneta, M G; Shimoji, M; Fricke, S T; Shapiro, B

2015-01-14

The ability to use magnets external to the body to focus therapy to deep tissue targets has remained an elusive goal in magnetic drug targeting. Researchers have hitherto been able to manipulate magnetic nanotherapeutics in vivo with nearby magnets but have remained unable to focus these therapies to targets deep within the body using magnets external to the body. One of the factors that has made focusing of therapy to central targets between magnets challenging is Samuel Earnshaw's theorem as applied to Maxwell's equations. These mathematical formulations imply that external static magnets cannot create a stable potential energy well between them. We posited that fast magnetic pulses could act on ferromagnetic rods before they could realign with the magnetic field. Mathematically, this is equivalent to reversing the sign of the potential energy term in Earnshaw's theorem, thus enabling a quasi-static stable trap between magnets. With in vitro experiments, we demonstrated that quick, shaped magnetic pulses can be successfully used to create inward pointing magnetic forces that, on average, enable external magnets to concentrate ferromagnetic rods to a central location.

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

Li, Hui-Ran; Luo, Ming-Xing; Lai, Hong

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Grassmannians for scattering amplitudes in 4d $$\\mathcal{N}=4 $$ SYM and 3d ABJM

DOE PAGES

Elvang, Henriette; Huang, Yu-tin; Keeler, Cynthia; ...

2014-12-31

Scattering amplitudes in 4d N=4 super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space. Here, after a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations. A similar strategy allows us to derive a new Grassmannian integral for 3d N = 6 ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data. Themore » result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for N = 4 SYM.« less

Combinatorial optimization games

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, X.; Ibaraki, Toshihide; Nagamochi, Hiroshi

1997-06-01

We introduce a general integer programming formulation for a class of combinatorial optimization games, which immediately allows us to improve the algorithmic result for finding amputations in the core (an important solution concept in cooperative game theory) of the network flow game on simple networks by Kalai and Zemel. An interesting result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several interesting problems, and apply them to resolve algorithmic andmore » complexity issues for their cores along the line as put forward in: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation x, test whether x is in the core. We also explore the properties of totally balanced games in this succinct formulation of cooperative games.« less

Symmetry for the duration of entropy-consuming intervals.

PubMed

García-García, Reinaldo; Domínguez, Daniel

2014-05-01

We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function Φ, which can be interpreted as an entropy associated with the fluctuations of the violation fraction. The function Φ, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of Φ. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possible applications of our results for the estimation of free-energy differences from single-molecule experiments.

Deflection of light by rotating regular black holes using the Gauss-Bonnet theorem

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Övgün, Ali; Saavedra, Joel; Vásquez, Yerko; González, P. A.

2018-06-01

In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-García (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the Gauss-Bonnet theorem (GBT) and show that the deflection of light can be viewed as a partially topological effect in which the deflection angle can be calculated by considering a domain outside of the light ray applied to the black hole optical geometries. Then, we demonstrate also the deflection angle via the geodesics formalism for these black holes to verify our results and explore the differences with the Kerr solution. These black holes have, in addition to the total mass and rotation parameter, different parameters of electric charge, magnetic charge, and deviation parameter. We find that the deflection of light has correction terms coming from these parameters, which generalizes the Kerr deflection angle.

Analytic solution for quasi-Lambertian radiation transfer.

PubMed

Braun, Avi; Gordon, Jeffrey M

2010-02-10

An analytic solution is derived for radiation transfer between flat quasi-Lambertian surfaces of arbitrary orientation, i.e., surfaces that radiate in a Lambertian fashion but within a numerical aperture smaller than unity. These formulas obviate the need for ray trace simulations and provide exact, physically transparent results. Illustrative examples that capture the salient features of the flux maps and the efficiency of flux transfer are presented for a few configurations of practical interest. There is also a fundamental reciprocity relation for quasi-Lambertian exchange, akin to the reciprocity theorem for fully Lambertian surfaces. Applications include optical fiber coupling, fiber-optic biomedical procedures, and solar concentrators.

Unidirectional invisibility and non-reciprocal transmission in two and three dimensions.

PubMed

Loran, Farhang; Mostafazadeh, Ali

2016-07-01

We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations and discuss its three-dimensional generalization. In particular, we construct an infinite class of unidirectionally invisible optical potentials that describe the scattering of normally incident transverse electric waves by an infinite planar slab with refractive-index modulations along both the normal directions to the electric field. A by-product of this investigation is a demonstration of non-reciprocal transmission in two dimensions. To elucidate this phenomenon, we state and prove a general reciprocity theorem that applies to quantum scattering theory of real and complex potentials in two and three dimensions.

Exploration of Data Fusion between Polarimetric Radar and Multispectral Image Data

DTIC Science & Technology

2012-09-01

target decomposition theorems in radar polarimetry . Transactions on Geoscience and Remote Sensing, 34(2), 498–518. Cloude, S. R. (1985). Target...Proceedings of the Journees Internationales De La Polarimetrie Radar (JIPR ‘90), Nantes, France. Huynen, J. R. (1965). Measurement of theTarget scattering...J. A. (2006). Review of passive imaging polarimetry for remote sensing applications. Applied Optics, 45(22), 5453–5469. Vanzyl, J., Zebker, H

Diffractive centrosymmetric 3D-transmission phase gratings positioned at the image plane of optical systems transform lightlike 4D-WORLD as tunable resonators into spectral metrics...

NASA Astrophysics Data System (ADS)

Lauinger, Norbert

1999-08-01

Diffractive 3D phase gratings of spherical scatterers dense in hexagonal packing geometry represent adaptively tunable 4D-spatiotemporal filters with trichromatic resonance in visible spectrum. They are described in the (lambda) - chromatic and the reciprocal (nu) -aspects by reciprocal geometric translations of the lightlike Pythagoras theorem, and by the direction cosine for double cones. The most elementary resonance condition in the lightlike Pythagoras theorem is given by the transformation of the grating constants gx, gy, gz of the hexagonal 3D grating to (lambda) h1h2h3 equals (lambda) 111 with cos (alpha) equals 0.5. Through normalization of the chromaticity in the von Laue-interferences to (lambda) 111, the (nu) (lambda) equals (lambda) h1h2h3/(lambda) 111-factor of phase velocity becomes the crucial resonance factor, the 'regulating device' of the spatiotemporal interaction between 3D grating and light, space and time. In the reciprocal space equal/unequal weights and times in spectral metrics result at positions of interference maxima defined by hyperbolas and circles. A database becomes built up by optical interference for trichromatic image preprocessing, motion detection in vector space, multiple range data analysis, patchwide multiple correlations in the spatial frequency spectrum, etc.

Polarizability and the optical theorem for a two-level atom with radiative broadening

NASA Astrophysics Data System (ADS)

Berman, Paul R.; Boyd, Robert W.; Milonni, Peter W.

2006-11-01

The effect of spontaneous decay on the linear polarizability of an atom is typically included by adding imaginary parts to the frequency denominators that appear in the Kramers-Heisenberg formula. It has been shown for a two-level atom with radiative broadening that these (frequency-dependent) imaginary parts must be included in both the resonant and antiresonant frequency denominators [P. W. Milonni and R. W. Boyd, Phys. Rev. A 69, 023814 (2004)]; however, the expression obtained by Milonni and Boyd for the polarizability does not satisfy the optical theorem, if contributions from non-rotating-wave terms are included. In this paper, we derive a more accurate expression for the polarizability. The calculations are rather complicated and require that we go beyond the standard Weisskopf-Wigner approximation. We present calculations carried out in both the Heisenberg and Schrödinger pictures, since they offer complementary methods for understanding the dynamics of the Rayleigh scattering associated with the atomic polarizability. Moreover, it is shown that the shifts associated with the excited state are not the Lamb shifts of an isolated atom, but depend on the dynamics of the atom-field interaction. Our results for the polarizability are consistent with those obtained recently by Loudon and Barnett using a Green’s-function approach.

Are reconstruction filters necessary?

NASA Astrophysics Data System (ADS)

Holst, Gerald C.

2006-05-01

Shannon's sampling theorem (also called the Shannon-Whittaker-Kotel'nikov theorem) was developed for the digitization and reconstruction of sinusoids. Strict adherence is required when frequency preservation is important. Three conditions must be met to satisfy the sampling theorem: (1) The signal must be band-limited, (2) the digitizer must sample the signal at an adequate rate, and (3) a low-pass reconstruction filter must be present. In an imaging system, the signal is band-limited by the optics. For most imaging systems, the signal is not adequately sampled resulting in aliasing. While the aliasing seems excessive mathematically, it does not significantly affect the perceived image. The human visual system detects intensity differences, spatial differences (shapes), and color differences. The eye is less sensitive to frequency effects and therefore sampling artifacts have become quite acceptable. Indeed, we love our television even though it is significantly undersampled. The reconstruction filter, although absolutely essential, is rarely discussed. It converts digital data (which we cannot see) into a viewable analog signal. There are several reconstruction filters: electronic low-pass filters, the display media (monitor, laser printer), and your eye. These are often used in combination to create a perceived continuous image. Each filter modifies the MTF in a unique manner. Therefore image quality and system performance depends upon the reconstruction filter(s) used. The selection depends upon the application.

Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field

NASA Astrophysics Data System (ADS)

Cheng, J. L.; Guo, C.

2018-05-01

Graphene exhibits extremely strong optical nonlinearity in a perpendicular magnetic field, the optical conductivities show complicated field dependence at a moderate light intensity, and the perturbation theory fails. The full optical currents induced by a periodic field are nonperturbatively investigated in an equation-of-motion framework based on the Floquet theorem, with the scattering described phenomenologically. The nonlinear responses are understood in terms of the dressed electronic states, or Floquet states, which could be characterized by a weak probe light field. The method is illustrated for a magnetic field at 5 T and a driving field with photon energy 0.05 eV. Our results show that the perturbation theory works for weak fields <3 kV/cm, confirming the unusual strong light-matter interaction for Landau levels of graphene. Our approach can be easily extended to other systems.

Mathematical model of blasting schemes management in mining operations in presence of random disturbances

NASA Astrophysics Data System (ADS)

Kazakova, E. I.; Medvedev, A. N.; Kolomytseva, A. O.; Demina, M. I.

2017-11-01

The paper presents a mathematical model of blasting schemes management in presence of random disturbances. Based on the lemmas and theorems proved, a control functional is formulated, which is stable. A universal classification of blasting schemes is developed. The main classification attributes are suggested: the orientation in plan the charging wells rows relatively the block of rocks; the presence of cuts in the blasting schemes; the separation of the wells series onto elements; the sequence of the blasting. The periodic regularity of transition from one Short-delayed scheme of blasting to another is proved.

What Makes the Foucault Pendulum Move among the Stars?

NASA Astrophysics Data System (ADS)

Phillips, Norman

2004-11-01

Foucault's pendulum exhibition in 1851 occurred in an era now known by development of the theorems of Coriolis and the formulation of dynamical meteorology by Ferrel. Yet today the behavior of the pendulum is often misunderstood. The existence of a horizontal component of Newtonian gravitation is essential for understanding the behavior with respect to the stars. Two simple mechanical principles describe why the path of oscillation is fixed only at the poles; the principle of centripetal acceleration and the principle of conservation of angular momentum. A sky map is used to describe the elegant path among the stars produced by these principles.

Covariant information-density cutoff in curved space-time.

PubMed

Kempf, Achim

2004-06-04

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.

Log-Concavity and Strong Log-Concavity: a review

PubMed Central

Saumard, Adrien; Wellner, Jon A.

2016-01-01

We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on ℝ under convolution follows from a fundamental monotonicity result of Efron (1969). We provide a new proof of Efron's theorem using the recent asymmetric Brascamp-Lieb inequality due to Otto and Menz (2013). Along the way we review connections between log-concavity and other areas of mathematics and statistics, including concentration of measure, log-Sobolev inequalities, convex geometry, MCMC algorithms, Laplace approximations, and machine learning. PMID:27134693

On the sensitivity of complex, internally coupled systems

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw

1988-01-01

A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.

Lectures on the scattering of light. [by dielectric sphere

NASA Technical Reports Server (NTRS)

Saxon, D. S.

1974-01-01

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Orbit of the OJ287 black hole binary as determined from the General Relativity centenary flare

NASA Astrophysics Data System (ADS)

Valtonen, Mauri; Gopakumar, Achamveedu; Mikkola, Seppo; Zola, Staszek; Ciprini, Stefano; Matsumoto, Katsura; Sadakane, Kozo; Kidger, Mark; Gazeas, Kosmas; Nilsson, Kari; Berdyugin, Andrei; Piirola, Vilppu; Jermak, Helen; Baliyan, Kiran; Hudec, Rene; Reichart, Daniel

2016-05-01

OJ287 goes through large optical flares twice each 12 years. The times of these flares have been predicted successfully now 5 times using a black hole binary model. In this model a secondary black hole goes around a primary black hole, impacting the accretion disk of the latter twice per orbital period, creating a thermal flare. Together with 6 flares from the historical data base, the set of flare timings determines uniquely the 7 parameters of the model: the two masses, the primary spin, the major axis, eccentricity and the phase of the orbit, plus a time delay parameter that gives the extent of time between accretion disk impacts and the related optical flares. Based on observations by the OJ287-15/16 Collaboration, OJ287 went into the phase of rapid flux rise on November 25, on the centenary of Einstein’s General Relativity, and peaked on December 5. At that time OJ287 was the brightest in over 30 years in optical wavelengths. The flare was of low polarization, and did not extend beyond the optical/UV region of the spectrum. On top of the main flare there were a number of small flares; their excess brightness correlates well with the simultaneous X-ray data. With these properties the main flare qualifies as the marker of the orbit of the secondary going around the primary black hole. Since the orbit solution is strongly over-determined, its parameters are known very accurately, at better than one percent level for the masses and the spin. The next flare is predicted to peak on July 28, 2019.Detailed monitoring of this event should allow us to test, for the first time, the celebrated black hole no-hair theorem for a massive black hole at the 10% level. The present data is consistent with the theorem only at a 30% level. The main difficulty in observing OJ287 from Earth at our predicted epoch is its closeness to the sun. Therefore, it is desirable to monitor OJ287 from a space-based telescope not in the vicinity of Earth. Unfortunately, this unique opportunity for testing the above celebrated theorem of General Relativity using OJ287 will not be available again until after several orbital cycles.The full list of participants in the OJ287-15/16 Collaboration is found in ApJL 819, L37, 2016.

Study on photon transport problem based on the platform of molecular optical simulation environment.

PubMed

Peng, Kuan; Gao, Xinbo; Liang, Jimin; Qu, Xiaochao; Ren, Nunu; Chen, Xueli; Ma, Bin; Tian, Jie

2010-01-01

As an important molecular imaging modality, optical imaging has attracted increasing attention in the recent years. Since the physical experiment is usually complicated and expensive, research methods based on simulation platforms have obtained extensive attention. We developed a simulation platform named Molecular Optical Simulation Environment (MOSE) to simulate photon transport in both biological tissues and free space for optical imaging based on noncontact measurement. In this platform, Monte Carlo (MC) method and the hybrid radiosity-radiance theorem are used to simulate photon transport in biological tissues and free space, respectively, so both contact and noncontact measurement modes of optical imaging can be simulated properly. In addition, a parallelization strategy for MC method is employed to improve the computational efficiency. In this paper, we study the photon transport problems in both biological tissues and free space using MOSE. The results are compared with Tracepro, simplified spherical harmonics method (SP(n)), and physical measurement to verify the performance of our study method on both accuracy and efficiency.

Study on Photon Transport Problem Based on the Platform of Molecular Optical Simulation Environment

PubMed Central

Peng, Kuan; Gao, Xinbo; Liang, Jimin; Qu, Xiaochao; Ren, Nunu; Chen, Xueli; Ma, Bin; Tian, Jie

2010-01-01

As an important molecular imaging modality, optical imaging has attracted increasing attention in the recent years. Since the physical experiment is usually complicated and expensive, research methods based on simulation platforms have obtained extensive attention. We developed a simulation platform named Molecular Optical Simulation Environment (MOSE) to simulate photon transport in both biological tissues and free space for optical imaging based on noncontact measurement. In this platform, Monte Carlo (MC) method and the hybrid radiosity-radiance theorem are used to simulate photon transport in biological tissues and free space, respectively, so both contact and noncontact measurement modes of optical imaging can be simulated properly. In addition, a parallelization strategy for MC method is employed to improve the computational efficiency. In this paper, we study the photon transport problems in both biological tissues and free space using MOSE. The results are compared with Tracepro, simplified spherical harmonics method (S P n), and physical measurement to verify the performance of our study method on both accuracy and efficiency. PMID:20445737

Energy conservation - A test for scattering approximations

NASA Technical Reports Server (NTRS)

Acquista, C.; Holland, A. C.

1980-01-01

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Multidimensional optical spectroscopy of a single molecule in a current-carrying state

NASA Astrophysics Data System (ADS)

Rahav, S.; Mukamel, S.

2010-12-01

The nonlinear optical signals from an open system consisting of a molecule connected to metallic leads, in response to a sequence of impulsive pulses, are calculated using a superoperator formalism. Two detection schemes are considered: coherent stimulated emission and incoherent fluorescence. The two provide similar but not identical information. The necessary superoperator correlation functions are evaluated either by converting them to ordinary (Hilbert space) operators which are then expanded in many-body states, or by using Wick's theorem for superoperators to factorize them into nonequilibrium two point Green's functions. As an example we discuss a stimulated Raman process that shows resonances involving two different charge states of the molecule in the same signal.

Optical Gaps in Pristine and Heavily Doped Silicon Nanocrystals: DFT versus Quantum Monte Carlo Benchmarks.

PubMed

Derian, R; Tokár, K; Somogyi, B; Gali, Á; Štich, I

2017-12-12

We present a time-dependent density functional theory (TDDFT) study of the optical gaps of light-emitting nanomaterials, namely, pristine and heavily B- and P-codoped silicon crystalline nanoparticles. Twenty DFT exchange-correlation functionals sampled from the best currently available inventory such as hybrids and range-separated hybrids are benchmarked against ultra-accurate quantum Monte Carlo results on small model Si nanocrystals. Overall, the range-separated hybrids are found to perform best. The quality of the DFT gaps is correlated with the deviation from Koopmans' theorem as a possible quality guide. In addition to providing a generic test of the ability of TDDFT to describe optical properties of silicon crystalline nanoparticles, the results also open up a route to benchmark-quality DFT studies of nanoparticle sizes approaching those studied experimentally.

Reciprocity theory of homogeneous reactions

NASA Astrophysics Data System (ADS)

Agbormbai, Adolf A.

1990-03-01

The reciprocity formalism is applied to the homogeneous gaseous reactions in which the structure of the participating molecules changes upon collision with one another, resulting in a change in the composition of the gas. The approach is applied to various classes of dissociation, recombination, rearrangement, ionizing, and photochemical reactions. It is shown that for the principle of reciprocity to be satisfied it is necessary that all chemical reactions exist in complementary pairs which consist of the forward and backward reactions. The backward reaction may be described by either the reverse or inverse process. The forward and backward processes must satisfy the same reciprocity equation. Because the number of dynamical variables is usually unbalanced on both sides of a chemical equation, it is necessary that this balance be established by including as many of the dynamical variables as needed before the reciprocity equation can be formulated. Statistical transformation models of the reactions are formulated. The models are classified under the titles free exchange, restricted exchange and simplified restricted exchange. The special equations for the forward and backward processes are obtained. The models are consistent with the H theorem and Le Chatelier's principle. The models are also formulated in the context of the direct simulation Monte Carlo method.

An adhesive contact mechanics formulation based on atomistically induced surface traction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fan, Houfu; Ren, Bo; Li, Shaofan, E-mail: shaofan@berkeley.edu

2015-12-01

In this work, we have developed a novel multiscale computational contact formulation based on the generalized Derjuguin approximation for continua that are characterized by atomistically enriched constitutive relations in order to study macroscopic interaction between arbitrarily shaped deformable continua. The proposed adhesive contact formulation makes use of the microscopic interaction forces between individual particles in the interacting bodies. In particular, the double-layer volume integral describing the contact interaction (energy, force vector, matrix) is converted into a double-layer surface integral through a mathematically consistent approach that employs the divergence theorem and a special partitioning technique. The proposed contact model is formulatedmore » in the nonlinear continuum mechanics framework and implemented using the standard finite element method. With no large penalty constant, the stiffness matrix of the system will in general be well-conditioned, which is of great significance for quasi-static analysis. Three numerical examples are presented to illustrate the capability of the proposed method. Results indicate that with the same mesh configuration, the finite element computation based on the surface integral approach is faster and more accurate than the volume integral based approach. In addition, the proposed approach is energy preserving even in a very long dynamic simulation.« less

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

NASA Astrophysics Data System (ADS)

Prószyński, W.; Kwaśniak, M.

2018-03-01

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.

Physical scales in the Wigner-Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nedjalkov, M., E-mail: mixi@iue.tuwien.ac.at; Selberherr, S.; Ferry, D.K.

2013-01-15

The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner-Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. Itmore » is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner-Boltzmann evolution is demonstrated. - Highlights: Black-Right-Pointing-Pointer Dimensionless parameters determine the ratio of quantum or classical WB evolution. Black-Right-Pointing-Pointer The scaling theorem evaluates the decoherence effect due to scattering. Black-Right-Pointing-Pointer Evolution processes are grouped into classes of equivalence.« less

The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem

NASA Astrophysics Data System (ADS)

Avksentyev, E. A.

2015-11-01

The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.

Radiation and scattering by thin-wire structures in the complex frequency domain. [electromagnetic theory for thin-wire antennas

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1974-01-01

Piecewise-sinusoidal expansion functions and Galerkin's method are employed to formulate a solution for an arbitrary thin-wire configuration in a homogeneous conducting medium. The analysis is performed in the real or complex frequency domain. In antenna problems, the solution determines the current distribution, impedance, radiation efficiency, gain and far-field patterns. In scattering problems, the solution determines the absorption cross section, scattering cross section and the polarization scattering matrix. The electromagnetic theory is presented for thin wires and the forward-scattering theorem is developed for an arbitrary target in a homogeneous conducting medium.

State space approach to mixed boundary value problems.

NASA Technical Reports Server (NTRS)

Chen, C. F.; Chen, M. M.

1973-01-01

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kharroubi, Idris, E-mail: kharroubi@ceremade.dauphine.fr; Lim, Thomas, E-mail: lim@ensiie.fr; Ngoupeyou, Armand, E-mail: armand.ngoupeyou@univ-paris-diderot.fr

2013-12-15

In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.

Stability of a diffuse linear pinch with axial boundaries

NASA Technical Reports Server (NTRS)

Einaudi, G.; Van Hoven, G.

1981-01-01

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

H-theorem and Maxwell demon in quantum physics

NASA Astrophysics Data System (ADS)

Kirsanov, N. S.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.; Blatter, G.; Lesovik, G. B.

2018-02-01

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

A Class of time-fractional hemivariational inequalities with application to frictional contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Migórski, Stanisław

2018-03-01

In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin-Voigt law. The friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals. The variational formulation of this problem leads to a fractional hemivariational inequality.

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local Couplings

NASA Astrophysics Data System (ADS)

Große, Johannes

2007-11-01

This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, in a second part the conformal anomaly of four dimensional supersymmetric quantum field theories coupled to classical N=1 supergravity is explored in a superfield formulation. The complete basis for the anomaly and consistency conditions, which arise from cohomological considerations, are given. Possible implications for an extension of Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field theories are discussed.

Thermodynamics and statistical mechanics. [thermodynamic properties of gases

NASA Technical Reports Server (NTRS)

1976-01-01

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

NASA Astrophysics Data System (ADS)

de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.

2016-11-01

In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.

A novel coherent optical en/decoder for optical label processing of OCDM-based optical packets switching networks

NASA Astrophysics Data System (ADS)

Zhang, Chongfu; Qiu, Kun

2007-11-01

A coherent optical en/decoder based on photonic crystal (PhC) for optical code-division-multiple (OCDM)-based optical label (OCDM-OL) optical packets switching (OPS) networks is proposed in this paper. In this scheme, the optical pulse phase and time delay can be flexibly controlled by the photonic crystal phase shifter and delayer using the appropriate design of fabrication. In this design, the combination calculation of the impurity and normal period layers is applied, according to the PhC transmission matrix theorem. The design and theoretical analysis of the PhC-based optical coherent en/decoder is mainly focused. In addition, the performances of the PhC-based optical en/decoders are analyzed in detail. The reflection, the transmission, delay characteristic and the optical spectrum of pulse en/decoded are studied for the waves tuned in the photonic band-gap by the numerical calculation, taking into account 1-Dimension (1D) PhC. Theoretical analysis and numerical results show that optical pulse is achieved to properly phase modulation and time delay by the proposed scheme, optical label based on OCDM is rewrote successfully by new code for OCDM-based OPS (OCDM-OPS), and an over 8.5 dB ration of auto- and cross-correlation is gained, which demonstrates the applicability of true pulse phase modulation in a number of applications.

Generalized free-space diffuse photon transport model based on the influence analysis of a camera lens diaphragm.

PubMed

Chen, Xueli; Gao, Xinbo; Qu, Xiaochao; Chen, Duofang; Ma, Xiaopeng; Liang, Jimin; Tian, Jie

2010-10-10

The camera lens diaphragm is an important component in a noncontact optical imaging system and has a crucial influence on the images registered on the CCD camera. However, this influence has not been taken into account in the existing free-space photon transport models. To model the photon transport process more accurately, a generalized free-space photon transport model is proposed. It combines Lambertian source theory with analysis of the influence of the camera lens diaphragm to simulate photon transport process in free space. In addition, the radiance theorem is also adopted to establish the energy relationship between the virtual detector and the CCD camera. The accuracy and feasibility of the proposed model is validated with a Monte-Carlo-based free-space photon transport model and physical phantom experiment. A comparison study with our previous hybrid radiosity-radiance theorem based model demonstrates the improvement performance and potential of the proposed model for simulating photon transport process in free space.

A Multi-scale Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear Stresses

NASA Technical Reports Server (NTRS)

Iurlaro, Luigi; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander

2013-01-01

The Refined Zigzag Theory (RZT) enables accurate predictions of the in-plane displacements, strains, and stresses. The transverse shear stresses obtained from constitutive equations are layer-wise constant. Although these transverse shear stresses are generally accurate in the average, layer-wise sense, they are nevertheless discontinuous at layer interfaces, and thus they violate the requisite interlaminar continuity of transverse stresses. Recently, Tessler applied Reissner's mixed variational theorem and RZT kinematic assumptions to derive an accurate and efficient shear-deformation theory for homogeneous, laminated composite, and sandwich beams, called RZT(m), where "m" stands for "mixed". Herein, the RZT(m) for beams is extended to plate analysis, where two alternative assumptions for the transverse shear stresses field are examined: the first follows Tessler's formulation, whereas the second is based on Murakami's polynomial approach. Results for elasto-static simply supported and cantilever plates demonstrate that Tessler's formulation results in a powerful and efficient structural theory that is well-suited for the analysis of multilayered composite and sandwich panels.

Point vortex interactions on a toroidal surface.

PubMed

Sakajo, Takashi; Shimizu, Yuuki

2016-07-01

Owing to non-constant curvature and a handle structure, it is not easy to imagine intuitively how flows with vortex structures evolve on a toroidal surface compared with those in a plane, on a sphere and a flat torus. In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N -point vortices from Green's function associated with the Laplace-Beltrami operator there, and we then formulate it as a Hamiltonian dynamical system with the help of the symplectic geometry and the uniformization theorem. Based on this Hamiltonian formulation, we show that the 2-vortex problem is integrable. We also investigate the point vortex equilibria and the motion of two-point vortices with the strengths of the same magnitude as one of the fundamental vortex interactions. As a result, we find some characteristic interactions between point vortices on the torus. In particular, two identical point vortices can be locally repulsive under a certain circumstance.

Point vortex interactions on a toroidal surface

PubMed Central

Shimizu, Yuuki

2016-01-01

Owing to non-constant curvature and a handle structure, it is not easy to imagine intuitively how flows with vortex structures evolve on a toroidal surface compared with those in a plane, on a sphere and a flat torus. In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N-point vortices from Green's function associated with the Laplace–Beltrami operator there, and we then formulate it as a Hamiltonian dynamical system with the help of the symplectic geometry and the uniformization theorem. Based on this Hamiltonian formulation, we show that the 2-vortex problem is integrable. We also investigate the point vortex equilibria and the motion of two-point vortices with the strengths of the same magnitude as one of the fundamental vortex interactions. As a result, we find some characteristic interactions between point vortices on the torus. In particular, two identical point vortices can be locally repulsive under a certain circumstance. PMID:27493577

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugama, H.; Nunami, M.; Department of Fusion Science, SOKENDAI

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novelmore » gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.« less

RADCAT Radar Measurement Program

DTIC Science & Technology

1971-11-24

gigahertz and noncoherent at 2.4 gigahertz, were also obtained on RADCAT Vehicle 002 and are presented. Comparisons are made between the long-pulse...pulse response of Vehicles 001, 002, and the computed response based on a physical optics formulation. iv q T TABLE OF CONTENTS Section Title Page... OPTICS FORMULATION OF RAOCAT VEHICLE RESPONSE E- F HALF-SCALE MODEL MEASUREMENTS F-i REFERENCES vi LIST OF FIGURES Number Title Page 2-1 TARGET

Tensor network states in time-bin quantum optics

NASA Astrophysics Data System (ADS)

Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

2018-06-01

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

Linked-cluster formulation of electron-hole interaction kernel in real-space representation without using unoccupied states.

PubMed

Bayne, Michael G; Scher, Jeremy A; Ellis, Benjamin H; Chakraborty, Arindam

2018-05-21

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems and results were found to be in good agreement with the EOM-CCSD and GW+BSE methods. The numerical results highlight the effectiveness of the developed method for overcoming the computational barrier of accurately determining the electron-hole interaction kernel to applications of large finite systems such as quantum dots and nanorods.

Physical models of polarization mode dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Menyuk, C.R.; Wai, P.K.A.

The effect of randomly varying birefringence on light propagation in optical fibers is studied theoretically in the parameter regime that will be used for long-distance communications. In this regime, the birefringence is large and varies very rapidly in comparison to the nonlinear and dispersive scale lengths. We determine the polarization mode dispersion, and we show that physically realistic models yield the same result for polarization mode dispersion as earlier heuristic models that were introduced by Poole. We also prove an ergodic theorem.

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-05-01

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

Probing the Fluctuations of Optical Properties in Time-Resolved Spectroscopy

NASA Astrophysics Data System (ADS)

Randi, Francesco; Esposito, Martina; Giusti, Francesca; Misochko, Oleg; Parmigiani, Fulvio; Fausti, Daniele; Eckstein, Martin

2017-11-01

We show that, in optical pump-probe experiments on bulk samples, the statistical distribution of the intensity of ultrashort light pulses after interaction with a nonequilibrium complex material can be used to measure the time-dependent noise of the current in the system. We illustrate the general arguments for a photoexcited Peierls material. The transient noise spectroscopy allows us to measure to what extent electronic degrees of freedom dynamically obey the fluctuation-dissipation theorem, and how well they thermalize during the coherent lattice vibrations. The proposed statistical measurement developed here provides a new general framework to retrieve dynamical information on the excited distributions in nonequilibrium experiments, which could be extended to other degrees of freedom of magnetic or vibrational origin.

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

ERIC Educational Resources Information Center

Moen, David H.; Powell, John E.

2005-01-01

Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

NONLINEAR OPTICAL EFFECTS AND FIBER OPTICS: Multiple stimulated optical echo in three-level media

NASA Astrophysics Data System (ADS)

Akhmediev, N. N.; Mel'nikov, I. V.

1988-12-01

It is shown that multiple stimulated optical echo may be generated in media with three closely spaced levels. The conditions for suppression of the stimulated echo signal are formulated and a proposal is described for apparatus which can be used to observe this effect.

Nonreciprocal Transverse Photonic Spin and Magnetization-Induced Electromagnetic Spin-Orbit Coupling

PubMed Central

Levy, Miguel; Karki, Dolendra

2017-01-01

We present a formulation of electromagnetic spin-orbit coupling in magneto-optic media, and propose an alternative source of spin-orbit coupling to non-paraxial optics vortices. Our treatment puts forth a formulation of nonreciprocal transverse-spin angular-momentum-density shifts for evanescent waves in magneto-optic waveguide media. It shows that magnetization-induced electromagnetic spin-orbit coupling is possible, and that it leads to unequal spin to orbital angular momentum conversion in magneto-optic media evanescent waves in opposite propagation-directions. Generation of free-space helicoidal beams based on this conversion is shown to be spin-helicity- and magnetization-dependent. We show that transverse-spin to orbital angular momentum coupling into magneto-optic waveguide media engenders spin-helicity-dependent unidirectional propagation. This unidirectional effect produces different orbital angular momenta in opposite directions upon excitation-spin-helicity reversals. PMID:28059120

Supersymmetric Transformations in Optical Fibers

NASA Astrophysics Data System (ADS)

Macho, Andrés; Llorente, Roberto; García-Meca, Carlos

2018-01-01

Supersymmetry (SUSY) has recently emerged as a tool to design unique optical structures with degenerate spectra. Here, we study several fundamental aspects and variants of one-dimensional SUSY in axially symmetric optical media, including their basic spectral features and the conditions for degeneracy breaking. Surprisingly, we find that the SUSY degeneracy theorem is partially (totally) violated in optical systems connected by isospectral (broken) SUSY transformations due to a degradation of the paraxial approximation. In addition, we show that isospectral constructions provide a dimension-independent design control over the group delay in SUSY fibers. Moreover, we find that the studied unbroken and isospectral SUSY transformations allow us to generate refractive-index superpartners with an extremely large phase-matching bandwidth spanning the S +C +L optical bands. These singular features define a class of optical fibers with a number of potential applications. To illustrate this, we numerically demonstrate the possibility of building photonic lanterns supporting broadband heterogeneous supermodes with large effective area, a broadband all-fiber true-mode (de)multiplexer requiring no mode conversion, and different mode-filtering, mode-conversion, and pulse-shaping devices. Finally, we discuss the possibility of extrapolating our results to acoustics and quantum mechanics.

Image gathering and processing - Information and fidelity

NASA Technical Reports Server (NTRS)

Huck, F. O.; Fales, C. L.; Halyo, N.; Samms, R. W.; Stacy, K.

1985-01-01

In this paper we formulate and use information and fidelity criteria to assess image gathering and processing, combining optical design with image-forming and edge-detection algorithms. The optical design of the image-gathering system revolves around the relationship among sampling passband, spatial response, and signal-to-noise ratio (SNR). Our formulations of information, fidelity, and optimal (Wiener) restoration account for the insufficient sampling (i.e., aliasing) common in image gathering as well as for the blurring and noise that conventional formulations account for. Performance analyses and simulations for ordinary optical-design constraints and random scences indicate that (1) different image-forming algorithms prefer different optical designs; (2) informationally optimized designs maximize the robustness of optimal image restorations and lead to the highest-spatial-frequency channel (relative to the sampling passband) for which edge detection is reliable (if the SNR is sufficiently high); and (3) combining the informationally optimized design with a 3 by 3 lateral-inhibitory image-plane-processing algorithm leads to a spatial-response shape that approximates the optimal edge-detection response of (Marr's model of) human vision and thus reduces the data preprocessing and transmission required for machine vision.

Coupled-oscillator theory of dispersion and Casimir-Polder interactions.

PubMed

Berman, P R; Ford, G W; Milonni, P W

2014-10-28

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r(-4), a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called "remarkable formula" for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.

A Decomposition Theorem for Finite Automata.

ERIC Educational Resources Information Center

Santa Coloma, Teresa L.; Tucci, Ralph P.

1990-01-01

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

Metriplectic Gyrokinetics and Discretization Methods for the Landau Collision Integral

NASA Astrophysics Data System (ADS)

Hirvijoki, Eero; Burby, Joshua W.; Kraus, Michael

2017-10-01

We present two important results for the kinetic theory and numerical simulation of warm plasmas: 1) We provide a metriplectic formulation of collisional electrostatic gyrokinetics that is fully consistent with the First and Second Laws of Thermodynamics. 2) We provide a metriplectic temporal and velocity-space discretization for the particle phase-space Landau collision integral that satisfies the conservation of energy, momentum, and particle densities to machine precision, as well as guarantees the existence of numerical H-theorem. The properties are demonstrated algebraically. These two result have important implications: 1) Numerical methods addressing the Vlasov-Maxwell-Landau system of equations, or its reduced gyrokinetic versions, should start from a metriplectic formulation to preserve the fundamental physical principles also at the discrete level. 2) The plasma physics community should search for a metriplectic reduction theory that would serve a similar purpose as the existing Lagrangian and Hamiltonian reduction theories do in gyrokinetics. The discovery of metriplectic formulation of collisional electrostatic gyrokinetics is strong evidence in favor of such theory and, if uncovered, the theory would be invaluable in constructing reduced plasma models. Supported by U.S. DOE Contract Nos. DE-AC02-09-CH11466 (EH) and DE-AC05-06OR23100 (JWB) and by European Union's Horizon 2020 research and innovation Grant No. 708124 (MK).

Rotation and anisotropy of galaxies revisited

NASA Astrophysics Data System (ADS)

Binney, James

2005-11-01

The use of the tensor virial theorem (TVT) as a diagnostic of anisotropic velocity distributions in galaxies is revisited. The TVT provides a rigorous global link between velocity anisotropy, rotation and shape, but the quantities appearing in it are not easily estimated observationally. Traditionally, use has been made of a centrally averaged velocity dispersion and the peak rotation velocity. Although this procedure cannot be rigorously justified, tests on model galaxies show that it works surprisingly well. With the advent of integral-field spectroscopy it is now possible to establish a rigorous connection between the TVT and observations. The TVT is reformulated in terms of sky-averages, and the new formulation is tested on model galaxies.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2005-03-01

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

Einstein’s gravity from a polynomial affine model

NASA Astrophysics Data System (ADS)

Castillo-Felisola, Oscar; Skirzewski, Aureliano

2018-03-01

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds—with or without cosmological constant—as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang–Mills theory known as Stephenson–Kilmister–Yang theory. Additionally, we find a generalization of a minimally coupled massless scalar field in General Relativity within a ‘minimally’ coupled scalar field in this affine model. Finally, we present a brief (perturbative) analysis of the propagators of the gravitational theory, and count the degrees of freedom. For completeness, we prove that a Birkhoff-like theorem is valid for the analyzed sector.

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

Natural games

NASA Astrophysics Data System (ADS)

Anttila, Jani; Annila, Arto

2011-10-01

A course of a game is formulated as a physical process that will consume free energy in the least time. Accordingly, the rate of entropy increase is the payoff function that will subsume all forms of free energy that motivate diverse decisions. Also other concepts of game theory are related to their profound physical counterparts. When the physical portrayal of behavior is mathematically analyzed, the course of a game is found to be inherently unpredictable because each move affects motives in the future. Despite the non-holonomic character of the natural process, the objective of consuming free energy in the least time will direct an extensive-form game toward a Lyapunov-stable point that satisfies the minimax theorem.

Machine-Checkable Timed CSP

NASA Technical Reports Server (NTRS)

Goethel, Thomas; Glesner, Sabine

2009-01-01

The correctness of safety-critical embedded software is crucial, whereas non-functional properties like deadlock-freedom and real-time constraints are particularly important. The real-time calculus Timed Communicating Sequential Processes (CSP) is capable of expressing such properties and can therefore be used to verify embedded software. In this paper, we present our formalization of Timed CSP in the Isabelle/HOL theorem prover, which we have formulated as an operational coalgebraic semantics together with bisimulation equivalences and coalgebraic invariants. Furthermore, we apply these techniques in an abstract specification with real-time constraints, which is the basis for current work in which we verify the components of a simple real-time operating system deployed on a satellite.

Stochastic control and the second law of thermodynamics

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Willems, J. C.

1979-01-01

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

A Free Wake Numerical Simulation for Darrieus Vertical Axis Wind Turbine Performance Prediction

NASA Astrophysics Data System (ADS)

Belu, Radian

2010-11-01

In the last four decades, several aerodynamic prediction models have been formulated for the Darrieus wind turbine performances and characteristics. We can identified two families: stream-tube and vortex. The paper presents a simplified numerical techniques for simulating vertical axis wind turbine flow, based on the lifting line theory and a free vortex wake model, including dynamic stall effects for predicting the performances of a 3-D vertical axis wind turbine. A vortex model is used in which the wake is composed of trailing stream-wise and shedding span-wise vortices, whose strengths are equal to the change in the bound vortex strength as required by the Helmholz and Kelvin theorems. Performance parameters are computed by application of the Biot-Savart law along with the Kutta-Jukowski theorem and a semi-empirical stall model. We tested the developed model with an adaptation of the earlier multiple stream-tube performance prediction model for the Darrieus turbines. Predictions by using our method are shown to compare favorably with existing experimental data and the outputs of other numerical models. The method can predict accurately the local and global performances of a vertical axis wind turbine, and can be used in the design and optimization of wind turbines for built environment applications.

Formulation of the linear model from the nonlinear simulation for the F18 HARV

NASA Technical Reports Server (NTRS)

Hall, Charles E., Jr.

1991-01-01

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

The Non-Signalling theorem in generalizations of Bell's theorem

NASA Astrophysics Data System (ADS)

Walleczek, J.; Grössing, G.

2014-04-01

Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents to signal information. In other words, as a proper principle, the non-signalling theorem may only be employed as an epistemic, phenomenological, or operational principle. Critically, our argument emphasizes that the non-signalling principle must not be used as an ontic principle about physical reality as such, i.e. as a theorem about the nature of physical reality independently of epistemic agents e.g. human observers. One major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report. Otherwise, the non-signalling theorem would equal a general "no-influence" theorem. In conclusion, under the assumption that the non-signalling theorem is epistemic (i.e. "epistemic non-signalling"), the search for deterministic approaches to quantum mechanics, including NHVTs and an emergent quantum mechanics, continues to be a viable research program towards disclosing the foundations of physical reality at its smallest dimensions.

Consistency of the adiabatic theorem.

PubMed

Amin, M H S

2009-06-05

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation are discussed.

Optimal no-go theorem on hidden-variable predictions of effect expectations

NASA Astrophysics Data System (ADS)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

Synthetic Unruh effect in cold atoms

NASA Astrophysics Data System (ADS)

Rodríguez-Laguna, Javier; Tarruell, Leticia; Lewenstein, Maciej; Celi, Alessio

2017-01-01

We propose to simulate a Dirac field near an event horizon using ultracold atoms in an optical lattice. Such a quantum simulator allows for the observation of the celebrated Unruh effect. Our proposal involves three stages: (1) preparation of the ground state of a massless two-dimensional Dirac field in Minkowski space-time; (2) quench of the optical lattice setup to simulate how an accelerated observer would view that state; (3) measurement of the local quantum fluctuation spectra by one-particle excitation spectroscopy in order to simulate a De Witt detector. According to Unruh's prediction, fluctuations measured in such a way must be thermal. Moreover, following Takagi's inversion theorem, they will obey the Bose-Einstein distribution, which will smoothly transform into the Fermi-Dirac as one of the dimensions of the lattice is reduced.

Acousto-Optic Beam Sampler, Part 2. Green’s Function Solution to Acousto-Optic Interaction Problem.

DTIC Science & Technology

This part of the ’ Acousto - Optic Beam Sampler,’ series lays down the formalism behind the Green’s function integral approach to solving the acousto ... optic scattering problem. The advantage of this formulation which is applicable to gases is shown through developing the solution to the scattering

Using Pictures to Enhance Students' Understanding of Bayes' Theorem

ERIC Educational Resources Information Center

Trafimow, David

2011-01-01

Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

PubMed

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

Axial field shaping under high-numerical-aperture focusing

NASA Astrophysics Data System (ADS)

Jabbour, Toufic G.; Kuebler, Stephen M.

2007-03-01

Kant reported [J. Mod. Optics47, 905 (2000)] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kant's formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.

Vector analogues of the Maggi-Rubinowicz theory of edge diffraction

NASA Astrophysics Data System (ADS)

Meneghini, R.; Shu, P.; Bay, J.

1980-10-01

The Maggi-Rubinowicz technique for scalar and electromagnetic fields is interpreted as a transformation of an integral over an open surface to a line integral around its rim. Maggi-Rubinowicz analogues are found for several vector physical optics representations. For diffraction from a circular aperture, a numerical comparison between these formulations shows the two methods are in agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz integrals that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields an 8 to 10 fold decrease in computation time relative to the physical optics formulation.

Vector analogues of the Maggi-Rubinowicz theory of edge diffraction

NASA Technical Reports Server (NTRS)

Meneghini, R.; Shu, P.; Bay, J.

1980-01-01

The Maggi-Rubinowicz technique for scalar and electromagnetic fields is interpreted as a transformation of an integral over an open surface to a line integral around its rim. Maggi-Rubinowicz analogues are found for several vector physical optics representations. For diffraction from a circular aperture, a numerical comparison between these formulations shows the two methods are in agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz integrals that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields an 8 to 10 fold decrease in computation time relative to the physical optics formulation.

Progress in linear optics, non-linear optics and surface alignment of liquid crystals

NASA Astrophysics Data System (ADS)

Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.

We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.

Rigorous coupled wave analysis of acousto-optics with relativistic considerations.

PubMed

Xia, Guoqiang; Zheng, Weijian; Lei, Zhenggang; Zhang, Ruolan

2015-09-01

A relativistic analysis of acousto-optics is presented, and a rigorous coupled wave analysis is generalized for the diffraction of the acousto-optical effect. An acoustic wave generates a grating with temporally and spatially modulated permittivity, hindering direct applications of the rigorous coupled wave analysis for the acousto-optical effect. In a reference frame which moves with the acoustic wave, the grating is static, the medium moves, and the coupled wave equations for the static grating may be derived. Floquet's theorem is then applied to cast these equations into an eigenproblem. Using a Lorentz transformation, the electromagnetic fields in the grating region are transformed to the lab frame where the medium is at rest, and relativistic Doppler frequency shifts are introduced into various diffraction orders. In the lab frame, the boundary conditions are considered and the diffraction efficiencies of various orders are determined. This method is rigorous and general, and the plane waves in the resulting expansion satisfy the dispersion relation of the medium and are propagation modes. Properties of various Bragg diffractions are results, rather than preconditions, of this method. Simulations of an acousto-optical tunable filter made by paratellurite, TeO(2), are given as examples.

Radiative transfer in spherical shell atmospheres. 2: Asymmetric phase functions

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Adams, C. N.

1977-01-01

The effects are investigated of sphericity on the radiation reflected from a planet with a homogeneous, conservative scattering atmosphere of optical thicknesses of 0.25 and 1.0. A Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7 is considered. Significant differences were found when these results were compared with the plane-parallel calculations. Also large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle.

On the symmetry foundation of double soft theorems

NASA Astrophysics Data System (ADS)

Li, Zhi-Zhong; Lin, Hung-Hwa; Zhang, Shun-Qing

2017-12-01

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

Feynman-like rules for calculating n-point correlators of the primordial curvature perturbation

NASA Astrophysics Data System (ADS)

Valenzuela-Toledo, César A.; Rodríguez, Yeinzon; Beltrán Almeida, Juan P.

2011-10-01

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation ζ was developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of ζ, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of ζ for those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formulating such correlators, using the Wick's theorem, may become very clutter and time-consuming.

Three-dimensional relativistic field-electron interaction in a multicavity high-power klystron. 1: Basic theory

NASA Technical Reports Server (NTRS)

Kosmahl, H. G.

1982-01-01

A theoretical investigation of three dimensional relativistic klystron action is described. The relativistic axisymmetric equations of motion are derived from the time-dependent Lagrangian function for a charged particle in electromagnetic fields. An analytical expression of the fringing RF electric and magnetic fields within and in the vicinity of the interaction gap and the space-charge forces between axially and radially elastic deformable rings of charges are both included in the formulation. This makes an accurate computation of electron motion through the tunnel of the cavities and the drift tube spaces possible. Method of analysis is based on Lagrangian formulation. Bunching is computed using a disk model of electron stream in which the electron stream is divided into axisymmetric disks of equal charge and each disk is assumed to consist of a number of concentric rings of equal charges. The Individual representative groups of electrons are followed through the interaction gaps and drift tube spaces. Induced currents and voltages in interacting cavities are calculated by invoking the Shockley-Ramo theorem.

The causal meaning of Fisher’s average effect

PubMed Central

LEE, JAMES J.; CHOW, CARSON C.

2013-01-01

Summary In order to formulate the Fundamental Theorem of Natural Selection, Fisher defined the average excess and average effect of a gene substitution. Finding these notions to be somewhat opaque, some authors have recommended reformulating Fisher’s ideas in terms of covariance and regression, which are classical concepts of statistics. We argue that Fisher intended his two averages to express a distinction between correlation and causation. On this view, the average effect is a specific weighted average of the actual phenotypic changes that result from physically changing the allelic states of homologous genes. We show that the statistical and causal conceptions of the average effect, perceived as inconsistent by Falconer, can be reconciled if certain relationships between the genotype frequencies and non-additive residuals are conserved. There are certain theory-internal considerations favouring Fisher’s original formulation in terms of causality; for example, the frequency-weighted mean of the average effects equaling zero at each locus becomes a derivable consequence rather than an arbitrary constraint. More broadly, Fisher’s distinction between correlation and causation is of critical importance to gene-trait mapping studies and the foundations of evolutionary biology. PMID:23938113

Chemical Equilibrium and Polynomial Equations: Beware of Roots.

ERIC Educational Resources Information Center

Smith, William R.; Missen, Ronald W.

1989-01-01

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…

Approaching Cauchy's Theorem

ERIC Educational Resources Information Center

Garcia, Stephan Ramon; Ross, William T.

2017-01-01

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

Collagen solubility correlates with skin optical clearing.

PubMed

Hirshburg, Jason; Choi, Bernard; Nelson, J Stuart; Yeh, Alvin T

2006-01-01

Biomedical optics and photomedicine applications are challenged by the turbidity of most biological tissue systems. Nonreactive, biocompatible chemical agents can induce a reversible reduction in optical scattering of collagenous tissues such as human skin. Herein we show that a chemical agent's tissue optical clearing potential is directly related to its collagen solubility, providing a rational design basis for effective, percutaneous formulations.

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Pick's Theorem: What a Lemon!

ERIC Educational Resources Information Center

Russell, Alan R.

2004-01-01

Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.

Coupled-oscillator theory of dispersion and Casimir-Polder interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berman, P. R.; Ford, G. W.; Milonni, P. W.

2014-10-28

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength.more » However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.« less

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

The geometric Mean Value Theorem

NASA Astrophysics Data System (ADS)

de Camargo, André Pierro

2018-05-01

In a previous article published in the American Mathematical Monthly, Tucker (Amer Math Monthly. 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying Rolle's theorem to a function like Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as a technical existence theorem used to prove intuitively obvious statements. Moreover, he argued that there is nothing obvious about the Mean Value Theorem without the continuity of the derivative. Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

NASA Astrophysics Data System (ADS)

Shu, Wei-Xing; Fu, Na; Lü, Xiao-Fang; Luo, Hai-Lu; Wen, Shuang-Chun; Fan, Dian-Yuan

2010-11-01

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics, which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Discontinuous gradient differential equations and trajectories in the calculus of variations

NASA Astrophysics Data System (ADS)

Bogaevskii, I. A.

2006-12-01

The concept of gradient of smooth functions is generalized for their sums with concave functions. An existence, uniqueness, and continuous dependence theorem for increasing time is formulated and proved for solutions of an ordinary differential equation the right-hand side of which is the gradient of the sum of a concave and a smooth function. With the use of this result a physically natural motion of particles, well defined even at discontinuities of the velocity field, is constructed in the variational problem of the minimal mechanical action in a space of arbitrary dimension. For such a motion of particles in the plane all typical cases of the birth and the interaction of point clusters of positive mass are described.

Voxelwise Spectral Diffusional Connectivity and its Applications to Alzheimer’s Disease and Intelligence Prediction

PubMed Central

Li, Junning; Jin, Yan; Shi, Yonggang; Dinov, Ivo D.; Wang, Danny J.; Toga, Arthur W.; Thompson, Paul M.

2014-01-01

Human brain connectivity can be studied using graph theory. Many connectivity studies parcellate the brain into regions and count fibres extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. Here we investigate whole brain connectivity from a different perspective. We propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but we derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. We use these novel measures to accurately estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer’s disease and intelligence prediction. PMID:24505723

Nonadiabatic effects in periodically driven dissipative open quantum systems

NASA Astrophysics Data System (ADS)

Reimer, Viktor; Pedersen, Kim G. L.; Tanger, Niklas; Pletyukhov, Mikhail; Gritsev, Vladimir

2018-04-01

We present a general method to calculate the periodic steady state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems—two- and three-level models as well as the driven nonlinear cavity—we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising nonadiabatic features in the response of these systems.

Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.

2013-08-01

In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S2 is constructed.

The Theory of Thermodynamic Systems with Internal Variables of State: Necessary and Sufficient Conditions for Compliance with the Second Law of Thermodynamics

NASA Astrophysics Data System (ADS)

Shnip, A. I.

2018-01-01

Based on the entropy-free thermodynamic approach, a generalized theory of thermodynamic systems with internal variables of state is being developed. For the case of nonlinear thermodynamic systems with internal variables of state and linear relaxation, the necessary and sufficient conditions have been proved for fulfillment of the second law of thermodynamics in entropy-free formulation which, according to the basic theorem of the theory, are also necessary and sufficient for the existence of a thermodynamic potential. Moreover, relations of correspondence between thermodynamic systems with memory and systems with internal variables of state have been established, as well as some useful relations in the spaces of states of both types of systems.

Long-distance Lienard-Wiechert potentials and qq-bar spin dependence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childers, R.W.

1987-12-15

The long-range spin dependence of the qq interaction is considered in a model in which the confining potential is required to be the static limit of retarded scalar and vector potentials analogous to the Lienard-Wiechert potentials of classical electrodynamics. A generalization of Darwin's method is used to obtain the corresponding Hamiltonian. The long-distance spin-dependent interaction is found to be determined completely by only two potentials: namely, the static scalar and vector potentials. This is to be compared with the four potentials required in Eichten and Feinberg's general formulation. Two different solutions are allowed by Gromes's theorem. In one, the scalarmore » potential can be linear; in the other, it must be logarithmic.« less

The study of nonlinear almost periodic differential equations without recourse to the H-classes of these equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slyusarchuk, V. E., E-mail: V.E.Slyusarchuk@gmail.com, E-mail: V.Ye.Slyusarchuk@NUWM.rv.ua

2014-06-01

The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24more » titles. (paper)« less

Optimal designs for copula models

PubMed Central

Perrone, E.; Müller, W.G.

2016-01-01

Copula modelling has in the past decade become a standard tool in many areas of applied statistics. However, a largely neglected aspect concerns the design of related experiments. Particularly the issue of whether the estimation of copula parameters can be enhanced by optimizing experimental conditions and how robust all the parameter estimates for the model are with respect to the type of copula employed. In this paper an equivalence theorem for (bivariate) copula models is provided that allows formulation of efficient design algorithms and quick checks of whether designs are optimal or at least efficient. Some examples illustrate that in practical situations considerable gains in design efficiency can be achieved. A natural comparison between different copula models with respect to design efficiency is provided as well. PMID:27453616

A note on generalized Weyl's theorem

NASA Astrophysics Data System (ADS)

Zguitti, H.

2006-04-01

We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

Review of the Usefulness of Various Rotational Seismometers with Laboratory Results of Fibre-Optic Ones Tested for Engineering Applications

PubMed Central

Jaroszewicz, Leszek R.; Kurzych, Anna; Krajewski, Zbigniew; Marć, Paweł; Kowalski, Jerzy K.; Bobra, Piotr; Zembaty, Zbigniew; Sakowicz, Bartosz; Jankowski, Robert

2016-01-01

Starting with descriptions of rotational seismology, areas of interest and historical field measurements, the fundamental requirements for rotational seismometers for seismological and engineering application are formulated. On the above basis, a review of all existing rotational seismometers is presented with a description of the principles of their operation as well as possibilities to fulfill formulated requirements. This review includes mechanical, acoustical, electrochemical and optical devices and shows that the last of these types are the most promising. It is shown that optical rotational seismometer based on the ring-laser gyroscope concept is the best for seismological applications, whereas systems based on fiber-optic gyroscopes demonstrate parameters which are also required for engineering applications. Laboratory results of the Fibre-Optic System for Rotational Events & Phenomena Monitoring using a small 1-D shaking table modified to generate rotational excitations are presented. The harmonic and time-history tests demonstrate its usefulness for recording rotational motions with rates up to 0.25 rad/s. PMID:27999299

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

DOE PAGES

Dodin, I. Y.; Zhmoginov, A. I.; Ruiz, D. E.

2017-02-24

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. We propose a different approach. Here, we show that for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. Particularly, we present a variational formulation for linear geometrical optics inmore » a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.« less

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Pressure distribution under flexible polishing tools. I - Conventional aspheric optics

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.; Hufnagel, Robert E.

1990-10-01

The paper presents a mathematical model, based on Kirchoff's thin flat plate theory, developed to determine polishing pressure distribution for a flexible polishing tool. A two-layered tool in which bending and compressive stiffnesses are equal is developed, which is formulated as a plate on a linearly elastic foundation. An equivalent eigenvalue problem and solution for a free-free plate are created from the plate formulation. For aspheric, anamorphic optical surfaces, the tool misfit is derived; it is defined as the result of movement from the initial perfect fit on the optic to any other position. The Polisher Design (POD) software for circular tools on aspheric optics is introduced. NASTRAN-based finite element analysis results are compared with the POD software, showing high correlation. By employing existing free-free eigenvalues and eigenfunctions, the work may be extended to rectangular polishing tools as well.

Eigenpolarization theory of monolithic nonplanar ring oscillators

NASA Technical Reports Server (NTRS)

Nilsson, Alan C.; Gustafson, Eric K.; Byer, Robert L.

1989-01-01

Diode-laser-pumped monolithic nonplanar ring oscillators (NPROs) in an applied magnetic field can operate as unidirectional traveling-wave lasers. The diode laser pumping, monolithic construction, and unidirectional oscillation lead to narrow linewidth radiation. Here, a comprehensive theory of the eigenpolarizations of a monolithic NPRO is presented. It is shown how the properties of the integral optical diode that forces unidirectional operation depend on the choice of the gain medium, the applied magnetic field, the output coupler, and the geometry of the nonplanar ring light path. Using optical equivalence theorems to gain insight into the polarization characteristics of the NPRO, a strategy for designing NPROs with low thresholds and large loss nonreciprocities is given. An analysis of the eigenpolarizations for one such NPRO is presented, alternative optimization approaches are considered, and the prospects for further reducing the linewidths of these lasers are briefly discussed.

Quantum technology past, present, future: quantum energetics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Choi, Sang H.

2017-04-01

Since the development of quantum physics in the early part of the 1900s, this field of study has made remarkable contributions to our civilization. Some of these advances include lasers, light-emitting diodes (LED), sensors, spectroscopy, quantum dots, quantum gravity and quantum entanglements. In 1998, the NASA Langley Research Center established a quantum technology committee to monitor the progress in this area and initiated research to determine the potential of quantum technology for future NASA missions. The areas of interest in quantum technology at NASA included fundamental quantum-optics materials associated with quantum dots and quantum wells, device-oriented photonic crystals, smart optics, quantum conductors, quantum information and computing, teleportation theorem, and quantum energetics. A brief review of the work performed, the progress made in advancing these technologies, and the potential NASA applications of quantum technology will be presented.

Universal properties of the near-horizon optical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbons, G. W.; Warnick, C. M.

2009-03-15

Making use of the fact that the optical geometry near a static nondegenerate Killing horizon is asymptotically hyperbolic, we investigate some universal features of black-hole horizons. Applying the Gauss-Bonnet theorem allows us to establish some general properties of gravitational lensing, valid for all black holes. Hyperbolic geometry allows us to find rates for the loss of scalar, vector, and fermionic ''hair'' as objects fall quasistatically towards the horizon, extending previous results for Schwarzschild to all static Killing horizons. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending themore » flat space result of Feinberg and Sucher. We further demonstrate how these techniques allow us to derive the exact Copson-Linet potential due to a point charge in a Schwarzschild background in a simple fashion.« less

Discovering the Theorem of Pythagoras

NASA Technical Reports Server (NTRS)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Guided Discovery of the Nine-Point Circle Theorem and Its Proof

ERIC Educational Resources Information Center

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Finite element model for MOI applications using A-V formulation

NASA Astrophysics Data System (ADS)

Xuan, L.; Shanker, B.; Udpa, L.; Shih, W.; Fitzpatrick, G.

2001-04-01

Magneto-optic imaging (MOI) is a relatively new sensor application of an extension of bubble memory technology to NDT and produce easy-to-interpret, real time analog images. MOI systems use a magneto-optic (MO) sensor to produce analog images of magnetic flux leakage from surface and subsurface defects. The instrument's capability in detecting the relatively weak magnetic fields associated with subsurface defects depends on the sensitivity of the magneto-optic sensor. The availability of a theoretical model that can simulate the MOI system performance is extremely important for optimization of the MOI sensor and hardware system. A nodal finite element model based on magnetic vector potential formulation has been developed for simulating MOI phenomenon. This model has been used for predicting the magnetic fields in simple test geometry with corrosion dome defects. In the case of test samples with multiple discontinuities, a more robust model using the magnetic vector potential Ā and electrical scalar potential V is required. In this paper, a finite element model based on A-V formulation is developed to model complex circumferential crack under aluminum rivets in dimpled countersink.

The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors.

PubMed

Nolte, Guido

2003-11-21

The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.

Geometry and symmetry in non-equilibrium thermodynamic systems

NASA Astrophysics Data System (ADS)

Sonnino, Giorgio

2017-06-01

The ultimate aim of this series of works is to establish the closure equations, valid for thermodynamic systems out from the Onsager region, and to describe the geometry and symmetry in thermodynamic systems far from equilibrium. Geometry of a non-equilibrium thermodynamic system is constructed by taking into account the second law of thermodynamics and by imposing the validity of the Glansdorff-Prigogine Universal Criterion of Evolution. These two constraints allow introducing the metrics and the affine connection of the Space of the Thermodynamic Forces, respectively. The Lie group associated to the nonlinear Thermodynamic Coordinate Transformations (TCT) leaving invariant both the entropy production σ and the Glansdorff-Prigogine dissipative quantity P, is also described. The invariance under TCT leads to the formulation of the Thermodynamic Covariance Principle (TCP): The nonlinear closure equations, i.e. the flux-force relations, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces (i.e. under TCT). The symmetry properties of a physical system are intimately related to the conservation laws characterizing the thermodynamic system. Noether's theorem gives a precise description of this relation. The macroscopic theory for closure relations, based on this geometrical description and subject to the TCP, is referred to as the Thermodynamic Field Theory (TFT). This theory ensures the validity of the fundamental theorems for systems far from equilibrium.

Enhancement of linear/nonlinear optical responses of molecular vibrations using metal nanoantennas

NASA Astrophysics Data System (ADS)

Morichika, Ikki; Kusa, Fumiya; Takegami, Akinobu; Ashihara, Satoshi

2017-04-01

Plasmonic enhancements of optical near-fields with metal nanostructures offer extensive potential for amplifying lightmatter interactions. We analytically formulate the enhancement of linear and nonlinear optical responses of molecular vibrations through resonant nanoantennas, based on a coupled-dipole model. We apply the formulae to evaluation of signal enhancement factors in the antenna-enhanced vibrational spectroscopy.

Characterization of Generalized Young Measures Generated by Symmetric Gradients

NASA Astrophysics Data System (ADS)

De Philippis, Guido; Rindler, Filip

2017-06-01

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The "local" proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti's rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.

The Poincaré-Hopf Theorem for line fields revisited

NASA Astrophysics Data System (ADS)

Crowley, Diarmuid; Grant, Mark

2017-07-01

A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.

Common fixed point theorems for maps under a contractive condition of integral type

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

Seeing the order in a mess: optical signature of periodicity in a cloud of plasmonic nanowires.

PubMed

Natarov, Denys M; Marciniak, Marian; Sauleau, Ronan; Nosich, Alexander I

2014-11-17

We consider the two-dimensional (2-D) problem of the H-polarized plane wave scattering by a linear chain of silver nanowires in a cloud of similar pseudo-randomly located wires, in the visible range. Numerical solution uses the field expansions in local coordinates and addition theorems for cylindrical functions and has a guaranteed convergence. The total scattering cross-sections and near- and far-zone field patterns are presented. The observed resonance effects are studied and compared with their counterparts in the scattering by the same linear chain of wires in free space.

Hadronic vacuum polarization and e+e- → μ+μ- cross section: Reanalysis with new precise data for σh with 4π final states included

NASA Astrophysics Data System (ADS)

Sauli, Vladimir

2018-05-01

The interference effect between leptonic radiative corrections and hadronic polarization functions is calculated via optical theorem for μ-pair production in vicinity of narrow resonances. Within seven most dominant exclusive channels of the production cross section σh(e+e- → hadrons) one achieves high acuracy which is necessary for the comparison with experiments. The result is compared with KLOE and KLOE2 experiments for μ-μ+ and μ-μ+γ productions at φ and ω/ρ meson energy.

Rayleigh, the unit for light radiance.

PubMed

Baker, D J

1974-09-01

A 0.7% accurate formula is derived for the easy conversion of power spectral radiance L(lambda) in W cm(-2) sr(-1) microm(-1)to rayleigh spectral radiance R(lambda) in rayleigh/microm, R(lambda) = 2pilambdaL(lambda) x 10(13), where the wavelength lambda is in microm. The rationale for the rayleigh unit is discussed in terms of a photon rate factor and a solid angle factor. The latter is developed in terms of an equivalence theorem about optical receivers and extended sources, and the concept is extended to the computation of photon volume emission rates from altitude profiles of zenith radiance.

A Markov Chain-based quantitative study of angular distribution of photons through turbid slabs via isotropic light scattering

NASA Astrophysics Data System (ADS)

Li, Xuesong; Northrop, William F.

2016-04-01

This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.

Ab initio method for calculating total cross sections

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Schneider, B. I.; Temkin, A.

1993-01-01

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary. Elastic scattering is calculated from T-parallel-squared, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for sigma(el) and sigma(total) are in excellent agreement with calculations of Callaway and Oza (1984). The method has wide potential applicability.

Remote detection of single emitters via optical waveguides

NASA Astrophysics Data System (ADS)

Then, Patrick; Razinskas, Gary; Feichtner, Thorsten; Haas, Philippe; Wild, Andreas; Bellini, Nicola; Osellame, Roberto; Cerullo, Giulio; Hecht, Bert

2014-05-01

The integration of lab-on-a-chip technologies with single-molecule detection techniques may enable new applications in analytical chemistry, biotechnology, and medicine. We describe a method based on the reciprocity theorem of electromagnetic theory to determine and optimize the detection efficiency of photons emitted by single quantum emitters through truncated dielectric waveguides of arbitrary shape positioned in their proximity. We demonstrate experimentally that detection of single quantum emitters via such waveguides is possible, confirming the predicted behavior of the detection efficiency. Our findings blaze the trail towards efficient lensless single-emitter detection compatible with large-scale optofluidic integration.

Experimental Study of Short-Time Brownian Motion

NASA Astrophysics Data System (ADS)

Mo, Jianyong; Simha, Akarsh; Riegler, David; Raizen, Mark

2015-03-01

We report our progress on the study of short-time Brownian motion of optically-trapped microspheres. In earlier work, we observed the instantaneous velocity of microspheres in gas and in liquid, verifying a prediction by Albert Einstein from 1907. We now report a more accurate test of the energy equipartition theorem for a particle in liquid. We also observe boundary effects on Brownian motion in liquid by setting a wall near the trapped particle, which changes the dynamics of the motion. We find that the velocity autocorrelation of the particle decreases faster as the particle gets closer to the wall.

A Converse of the Mean Value Theorem Made Easy

ERIC Educational Resources Information Center

Mortici, Cristinel

2011-01-01

The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…

Recurrence theorems: A unified account

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

A variational theorem for creep with applications to plates and columns

NASA Technical Reports Server (NTRS)

Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R

1958-01-01

A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.

Zero-Bounded Limits as a Special Case of the Squeeze Theorem for Evaluating Single-Variable and Multivariable Limits

ERIC Educational Resources Information Center

Gkioulekas, Eleftherios

2013-01-01

Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…

Correcting Duporcq's theorem☆

PubMed Central

Nawratil, Georg

2014-01-01

In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem. PMID:25540467

Optical Asymmetry and Nonlinear Light Scattering from Colloidal Gold Nanorods.

PubMed

Lien, Miao-Bin; Kim, Ji-Young; Han, Myung-Geun; Chang, You-Chia; Chang, Yu-Chung; Ferguson, Heather J; Zhu, Yimei; Herzing, Andrew A; Schotland, John C; Kotov, Nicholas A; Norris, Theodore B

2017-06-27

A systematic study is presented of the intensity-dependent nonlinear light scattering spectra of gold nanorods under resonant excitation of the longitudinal surface plasmon resonance (SPR). The spectra exhibit features due to coherent second and third harmonic generation as well as a broadband feature that has been previously attributed to multiphoton photoluminescence arising primarily from interband optical transitions in the gold. A detailed study of the spectral dependence of the scaling of the scattered light with excitation intensity shows unexpected scaling behavior of the coherent signals, which is quantitatively accounted for by optically induced damping of the SPR mode through a Fermi liquid model of the electronic scattering. The broadband feature is shown to arise not from luminescence, but from scattering of the second-order longitudinal SPR mode with the electron gas, where efficient excitation of the second order mode arises from an optical asymmetry of the nanorod. The electronic-temperature-dependent plasmon damping and the Fermi-Dirac distribution together determine the intensity dependence of the broadband emission, and the structure-dependent absorption spectrum determines the spectral shape through the fluctuation-dissipation theorem. Hence a complete self-consistent picture of both coherent and incoherent light scattering is obtained with a single set of physical parameters.

Voronovskaja's theorem revisited

NASA Astrophysics Data System (ADS)

Tachev, Gancho T.

2008-07-01

We represent a new quantitative variant of Voronovskaja's theorem for Bernstein operator. This estimate improves the recent quantitative versions of Voronovskaja's theorem for certain Bernstein-type operators, obtained by H. Gonska, P. Pitul and I. Rasa in 2006.

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Ray-optical theory of broadband partially coherent emission

NASA Astrophysics Data System (ADS)

Epstein, Ariel; Tessler, Nir; Einziger, Pinchas D.

2013-04-01

We present a rigorous formulation of the effects of spectral broadening on emission of partially coherent source ensembles embedded in multilayered formations with arbitrarily shaped interfaces, provided geometrical optics is valid. The resulting ray-optical theory, applicable to a variety of optical systems from terahertz lenses to photovoltaic cells, quantifies the fundamental interplay between bandwidth and layer dimensions, and sheds light on common practices in optical analysis of statistical fields, e.g., disregarding multiple reflections or neglecting interference cross terms.

Quantum capacity of quantum black holes

NASA Astrophysics Data System (ADS)

Adami, Chris; Bradler, Kamil

2014-03-01

The fate of quantum entanglement interacting with a black hole has been an enduring mystery, not the least because standard curved space field theory does not address the interaction of black holes with matter. We discuss an effective Hamiltonian of matter interacting with a black hole that has a precise analogue in quantum optics and correctly reproduces both spontaneous and stimulated Hawking radiation with grey-body factors. We calculate the quantum capacity of this channel in the limit of perfect absorption, as well as in the limit of a perfectly reflecting black hole (a white hole). We find that the white hole is an optimal quantum cloner, and is isomorphic to the Unruh channel with positive quantum capacity. The complementary channel (across the horizon) is entanglement-breaking with zero capacity, avoiding a violation of the quantum no-cloning theorem. The black hole channel on the contrary has vanishing capacity, while its complement has positive capacity instead. Thus, quantum states can be reconstructed faithfully behind the black hole horizon, but not outside. This work sheds new light on black hole complementarity because it shows that black holes can both reflect and absorb quantum states without violating the no-cloning theorem, and makes quantum firewalls obsolete.

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

NASA Astrophysics Data System (ADS)

Anupam, A. H.; Kundu, Arpan; Ray, Krishnendu

2018-05-01

It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

Self-consistent continuum solvation for optical absorption of complex molecular systems in solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Timrov, Iurii; Biancardi, Alessandro; Andreussi, Oliviero

2015-01-21

We introduce a new method to compute the optical absorption spectra of complex molecular systems in solution, based on the Liouville approach to time-dependent density-functional perturbation theory and the revised self-consistent continuum solvation model. The former allows one to obtain the absorption spectrum over a whole wide frequency range, using a recently proposed Lanczos-based technique, or selected excitation energies, using the Casida equation, without having to ever compute any unoccupied molecular orbitals. The latter is conceptually similar to the polarizable continuum model and offers the further advantages of allowing an easy computation of atomic forces via the Hellmann-Feynman theorem andmore » a ready implementation in periodic-boundary conditions. The new method has been implemented using pseudopotentials and plane-wave basis sets, benchmarked against polarizable continuum model calculations on 4-aminophthalimide, alizarin, and cyanin and made available through the QUANTUM ESPRESSO distribution of open-source codes.« less

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Zhang, Likun

2014-11-01

The scattering of optical and acoustical beams is relevant to the levitation and manipulation of drops. Here we examine theoretical developments in the acoustical case. We previously showed how the optical theorem for extinction can be extended to invariant beams. The example of a sphere in a Bessel beam facilitates the direct comparison with a circular disc computed using Babinet's principle and the Kirchhoff approximation. In related work, by considering traveling or standing wave first-order vortex beams we previously showed that the radiation torque is the ratio of the absorbed power and the radian acoustic frequency. By modifying the scattering to account for the viscosity of the surrounding fluid in the analysis of the absorbed power, approximations for radiation torque and force are obtained at long wavelengths in special cases and these can be compared with results published elsewhere.

PARTICLE DISPLACEMENTS ON THE WALL OF A BOREHOLE FROM INCIDENT PLANE WAVES.

USGS Publications Warehouse

Lee, M.W.

1987-01-01

Particle displacements from incident plane waves at the wall of a fluid-filled borehole are formulated by applying the seismic reciprocity theorem to far-field displacement fields. Such displacement fields are due to point forces acting on a fluid-filled borehole under the assumption of long wavelengths. The displacement fields are analyzed to examine the effect of the borehole on seismic wave propagation, particularly for vertical seismic profiling (VSP) measurements. When the shortest wavelength of interest is approximately 25 times longer than the borehole's diameter, the scattered displacements are proportional to the first power of incident frequency and borehole diameter. When the shortest wavelength of interest is about 40 times longer than the borehole's diameter, borehole effects on VSP measurements using a wall-locking geophone are negligible.

Effects of active links on epidemic transmission over social networks

NASA Astrophysics Data System (ADS)

Zhu, Guanghu; Chen, Guanrong; Fu, Xinchu

2017-02-01

A new epidemic model with two infection periods is developed to account for the human behavior in social network, where newly infected individuals gradually restrict most of future contacts or are quarantined, causing infectivity change from a degree-dependent form to a constant. The corresponding dynamics are formulated by a set of ordinary differential equations (ODEs) via mean-field approximation. The effects of diverse infectivity on the epidemic dynamics ​are examined, with a behavioral interpretation of the basic reproduction number. Results show that such simple adaptive reactions largely determine the impact of network structure on epidemics. Particularly, a theorem proposed by Lajmanovich and Yorke in 1976 is generalized, so that it can be applied for the analysis of the epidemic models with multi-compartments especially network-coupled ODE systems.

Conservation laws for waves on a string from isometries and conformal isometries of the Minkowski metric

NASA Astrophysics Data System (ADS)

Miller, Brandon; Menon, Balraj

Noether's theorems describe the interplay between variational symmetries (symmetries of the action functional) and local conservation laws admitted by a physical system. In Lagrangian field theories defined on a differentiable manifold  endowed with a metric g, the variational symmetries are intimately tied to the isometries of the metric g. We highlight this connection by relating the variational symmetries of waves on a string to the isometries and conformal isometries of the Minkowski metric. The associated local conservation laws and conserved quantities for this physical system are determined and their physical significance discussed. The geometric nature of these conservation laws are further elucidated by discussing their Poisson bracket formulation in the Hamiltonian framework. This work was partially supported by the UCA Robert Noyce Scholars Program.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

NASA Astrophysics Data System (ADS)

Halkos, George E.; Tsilika, Kyriaki D.

2011-09-01

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

Conservation laws shape dissipation

NASA Astrophysics Data System (ADS)

Rao, Riccardo; Esposito, Massimiliano

2018-02-01

Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—we define a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux-force contributions controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.

Visual Theorems.

ERIC Educational Resources Information Center

Davis, Philip J.

1993-01-01

Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

Note on the theorems of Bjerknes and Crocco

NASA Technical Reports Server (NTRS)

Theodorsen, Theodore

1946-01-01

The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.

Analysis of non locality proofs in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2012-02-01

Two kinds of non-locality theorems in Quantum Mechanics are taken into account: the theorems based on the criterion of reality and the quite different theorem proposed by Stapp. In the present work the analyses of the theorem due to Greenberger, Horne, Shimony and Zeilinger, based on the criterion of reality, and of Stapp's argument are shown. The results of these analyses show that the alleged violations of locality cannot be considered definitive.

PYGMALION: A Creative Programming Environment

DTIC Science & Technology

1975-06-01

iiiiiimimmmimm wm^m^mmm’ wi-i ,»■»’■’.■- v* 26 Examples of Purely Iconic Reasoning 1-H Pythagoras ’ original proof of the Pythagorean Theorem ... Theorem Proving Machine񓟋. His program employed properties of the representation to guide the proof of theorems . His simple heruristic "Reject...one theorem the square of the hypotenuse. "Every proposition is presented as a self-contained fact relying on its own intrinsic evidence. Instead

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

Electrically conductive, black thermal control coatings for space craft application. II - Silicone matrix formulation

NASA Technical Reports Server (NTRS)

Hribar, V. F.; Bauer, J. L.; O'Donnell, T. P.

1986-01-01

Five black electrically conductive thermal-control coatings have been formulated and tested for application on the Galileo spacecraft. The coatings consisted of organic and inorganic systems applied on titanium and aluminum surfaces. The coatings were tested under simulated space environment conditions. Coated specimens were subjected to thermal radiation and convective and conductive heating from -196 to 538 C. Mechanical, physical, thermal, electrical, and optical characteristics, formulation, mixing, application, surface preparation of substrates, and a method of determining electrical resistance are presented for the silicone matrix formulation designated as GF-580.

How nonlinear optics can merge interferometry for high resolution imaging

NASA Astrophysics Data System (ADS)

Ceus, D.; Reynaud, F.; Tonello, A.; Delage, L.; Grossard, L.

2017-11-01

High resolution stellar interferometers are very powerful efficient instruments to get a better knowledge of our Universe through the spatial coherence analysis of the light. For this purpose, the optical fields collected by each telescope Ti are mixed together. From the interferometric pattern, two expected information called the contrast Cij and the phase information φij are extracted. These information lead to the Vij, called the complex visibility, with Vij=Cijexp(jφij). For each telescope doublet TiTj, it is possible to get a complex visibility Vij. The Zernike Van Cittert theorem gives a relationship between the intensity distribution of the object observed and the complex visibility. The combination of the acquired complex visibilities and a reconstruction algorithm allows imaging reconstruction. To avoid lots of technical difficulties related to infrared optics (components transmission, thermal noises, thermal cooling…), our team proposes to explore the possibility of using nonlinear optical techniques. This is a promising alternative detection technique for detecting infrared optical signals. This way, we experimentally demonstrate that frequency conversion does not result in additional bias on the interferometric data supplied by a stellar interferometer. In this presentation, we report on wavelength conversion of the light collected by each telescope from the infrared domain to the visible. The interferometric pattern is observed in the visible domain with our, so called, upconversion interferometer. Thereby, one can benefit from mature optical components mainly used in optical telecommunications (waveguide, coupler, multiplexer…) and efficient low-noise detection schemes up to the single-photon counting level.

Zonal-flow dynamics from a phase-space perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruiz, D. E.; Parker, J. B.; Shi, E. L.

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional termsmore » missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.« less

Zonal-flow dynamics from a phase-space perspective

DOE PAGES

Ruiz, D. E.; Parker, J. B.; Shi, E. L.; ...

2016-12-16

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. But, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. Furthermore, we derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional termsmore » missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. We present numerical simulations to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.« less

Analytical instrumentation infrastructure for combinatorial and high-throughput development of formulated discrete and gradient polymeric sensor materials arrays

NASA Astrophysics Data System (ADS)

Potyrailo, Radislav A.; Hassib, Lamyaa

2005-06-01

Multicomponent polymer-based formulations of optical sensor materials are difficult and time consuming to optimize using conventional approaches. To address these challenges, our long-term goal is to determine relationships between sensor formulation and sensor response parameters using new scientific methodologies. As the first step, we have designed and implemented an automated analytical instrumentation infrastructure for combinatorial and high-throughput development of polymeric sensor materials for optical sensors. Our approach is based on the fabrication and performance screening of discrete and gradient sensor arrays. Simultaneous formation of multiple sensor coatings into discrete 4×6, 6×8, and 8×12 element arrays (3-15μL volume per element) and their screening provides not only a well-recognized acceleration in the screening rate, but also considerably reduces or even eliminates sources of variability, which are randomly affecting sensors response during a conventional one-at-a-time sensor coating evaluation. The application of gradient sensor arrays provides additional capabilities for rapid finding of the optimal formulation parameters.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core

NASA Astrophysics Data System (ADS)

Fazzolari, Fiorenzo A.; Carrera, Erasmo

2014-02-01

In this paper, the Ritz minimum energy method, based on the use of the Principle of Virtual Displacements (PVD), is combined with refined Equivalent Single Layer (ESL) and Zig Zag (ZZ) shell models hierarchically generated by exploiting the use of Carrera's Unified Formulation (CUF), in order to engender the Hierarchical Trigonometric Ritz Formulation (HTRF). The HTRF is then employed to carry out the free vibration analysis of doubly curved shallow and deep functionally graded material (FGM) shells. The PVD is further used in conjunction with the Gauss theorem to derive the governing differential equations and related natural boundary conditions. Donnell-Mushtari's shallow shell-type equations are given as a particular case. Doubly curved FGM shells and doubly curved sandwich shells made up of isotropic face sheets and FGM core are investigated. The proposed shell models are widely assessed by comparison with the literature results. Two benchmarks are provided and the effects of significant parameters such as stacking sequence, boundary conditions, length-to-thickness ratio, radius-to-length ratio and volume fraction index on the circular frequency parameters and modal displacements are discussed.

A gauge-theoretic approach to gravity.

PubMed

Krasnov, Kirill

2012-08-08

Einstein's general relativity (GR) is a dynamical theory of the space-time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less

Mitigation of epidemics in contact networks through optimal contact adaptation *

PubMed Central

Youssef, Mina; Scoglio, Caterina

2013-01-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights. PMID:23906209

Mitigation of epidemics in contact networks through optimal contact adaptation.

PubMed

Youssef, Mina; Scoglio, Caterina

2013-08-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.

Space Imagery Enhancement Investigations; Software for Processing Middle Atmosphere Data

DTIC Science & Technology

2011-12-19

SUPPLEMENTARY NOTES 14. ABSTRACT This report summarizes work related to optical superresolution for the ideal incoherent 1D spread function...optical superresolution , incoherent image eigensystem, image registration, multi-frame image reconstruction, deconvolution 16. SECURITY... Superresolution -Related Investigations ............................................................................. 1 2.2.1 Eigensystem Formulations

Band-gap tuning and optical response of two-dimensional Si x C 1 - x : A first-principles real-space study of disordered two-dimensional materials

DOE PAGES

Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda; ...

2017-08-09

We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen–Baerends corrected exchange potential. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene Si xC 1–x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussedmore » in the light of the available experimental and other theoretical data. As a result, our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.« less

Band-gap tuning and optical response of two-dimensional Si x C 1 - x : A first-principles real-space study of disordered two-dimensional materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda

We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen–Baerends corrected exchange potential. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene Si xC 1–x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussedmore » in the light of the available experimental and other theoretical data. As a result, our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.« less

General Theorems about Homogeneous Ellipsoidal Inclusions

ERIC Educational Resources Information Center

Korringa, J.; And Others

1978-01-01

Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

Localized magnetoplasmons in quantum dots: Magneto-optical absorption, Raman scattering, and inelastic electron scattering

NASA Astrophysics Data System (ADS)

Kushwaha, M. S.

We investigate a one-component, quasi-zero dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de-Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron-energy-loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron-energy-loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in such diverse fields as quantum computing and medical imaging.

A no-hair theorem for black holes in f(R) gravity

NASA Astrophysics Data System (ADS)

Cañate, Pedro

2018-01-01

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

Generalized Browder's and Weyl's theorems for Banach space operators

NASA Astrophysics Data System (ADS)

Curto, Raúl E.; Han, Young Min

2007-12-01

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).

A dual potential formulation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Gegg, S. G.; Pletcher, R. H.; Steger, J. L.

1989-01-01

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Lanchester-Type Models of Warfare. Volume II

DTIC Science & Technology

1980-10-01

the so-called PERRON - FROBENIUS theorem50 for nonnegative matrices that one can guarantee that (without any further assumptions about A and B) there...always exists a vector of nonnegative values such that, for example, (7.18.6) holds. Before we state the PERRON - FROBENIUS theorem for nonnegative...a proof of this important theorem). THEOREM .5.-1.1 ( PERRON [121] and FROBENIUS [60]): Let C z 0 be an n x n matrix. Then, 1. C has a nonnegative real

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Statistics of optical vortex wander on propagation through atmospheric turbulence.

PubMed

Gu, Yalong

2013-04-01

The transverse position of an optical vortex on propagation through atmospheric turbulence is studied. The probability density of the optical vortex position on a transverse plane in the atmosphere is formulated in weak turbulence by using the Born approximation. With these formulas, the effect of aperture averaging on topological charge detection is investigated. These results provide quantitative guidelines for the design of an optimal detector of topological charge, which has potential application in optical vortex communication systems.

Architecture studies and system demonstrations for optical parallel processor for AI and NI

NASA Astrophysics Data System (ADS)

Lee, Sing H.

1988-03-01

In solving deterministic AI problems the data search for matching the arguments of a PROLOG expression causes serious bottleneck when implemented sequentially by electronic systems. To overcome this bottleneck we have developed the concepts for an optical expert system based on matrix-algebraic formulation, which will be suitable for parallel optical implementation. The optical AI system based on matrix-algebraic formation will offer distinct advantages for parallel search, adult learning, etc.

A Note on a Sampling Theorem for Functions over GF(q)n Domain

NASA Astrophysics Data System (ADS)

Ukita, Yoshifumi; Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi

In digital signal processing, the sampling theorem states that any real valued function ƒ can be reconstructed from a sequence of values of ƒ that are discretely sampled with a frequency at least twice as high as the maximum frequency of the spectrum of ƒ. This theorem can also be applied to functions over finite domain. Then, the range of frequencies of ƒ can be expressed in more detail by using a bounded set instead of the maximum frequency. A function whose range of frequencies is confined to a bounded set is referred to as bandlimited function. And a sampling theorem for bandlimited functions over Boolean domain has been obtained. Here, it is important to obtain a sampling theorem for bandlimited functions not only over Boolean domain (GF(q)n domain) but also over GF(q)n domain, where q is a prime power and GF(q) is Galois field of order q. For example, in experimental designs, although the model can be expressed as a linear combination of the Fourier basis functions and the levels of each factor can be represented by GF(q)n, the number of levels often take a value greater than two. However, the sampling theorem for bandlimited functions over GF(q)n domain has not been obtained. On the other hand, the sampling points are closely related to the codewords of a linear code. However, the relation between the parity check matrix of a linear code and any distinct error vectors has not been obtained, although it is necessary for understanding the meaning of the sampling theorem for bandlimited functions. In this paper, we generalize the sampling theorem for bandlimited functions over Boolean domain to a sampling theorem for bandlimited functions over GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over GF(q)n domain and linear codes.

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

Generalized Dandelin’s Theorem

NASA Astrophysics Data System (ADS)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2011-08-01

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant-Friedrichs-Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier "energy-conserving" explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.

Exact charge and energy conservation in implicit PIC with mapped computational meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guangye; Barnes, D. C.

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov Poisson formulation), ours is based on a nonlinearly converged Vlasov Amp re (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant Friedrichs Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicitmore » time steps (unlike the earlier energy-conserving explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.« less

Characterization of green synthesized nano-formulation (ZnO-A. vera) and their antibacterial activity against pathogens.

PubMed

Qian, Yiguang; Yao, Jun; Russel, Mohammad; Chen, Ke; Wang, Xiaoyu

2015-03-01

The application of nanotechnology in medicine has recently been a breakthrough in therapeutic drugs formulation. This paper presents the structural and optical characterization of a new green nano-formulation (ZnO-Aloe vera) with considerable antibacterial activity against pathogenic bacteria. Its particle structure, size and morphology were characterized by XRD, TEM and SEM. And optical absorption spectra and photoluminescence were measured synchronously. Their antibacterial activity against Escherichia coli and Staphylococcus aureus was also investigated using thermokinetic profiling and agar well diffusion method. The nano-formulation is spherical shape and hexagonal with a particle size ranging from 25 to 65 nm as well as an increased crystallite size of 49 nm. For antibacterial activity, the maximum inhibition zones of ZnO and ZnO+A. vera are 18.33 and 26.45 mm for E. coli, 22.11 and 28.12 mm for S. aureus (p<0.05). Considering Pmax, Qt and k, ZnO+A. vera nano-formulation has a significant (p < 0.05) antibacterial effect against S. aureus almost at all concentration and against E. coli at 15 and 25mg/L. ZnO+A. vera nano-formulation is much more toxic against S. aureus than E. coli, with an IC50 of 13.12 mg/L and 21.31 mg/L, respectively. The overall results reveal that the ZnO-A. vera nano-formulation has good surface energy, crystallinity, transmission, and enriched antibacterial activities. Their antibacterial properties are possibly relevant to particle size, microstructural ionization, the crystal formation and the Gram property of pathogens. This ZnO-A. vera nano-formulation could be utilized effectively as a spectral and significant antibacterial agent for pathogens in future medical and environmental concerns. Copyright © 2015 Elsevier B.V. All rights reserved.

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.

Impossible colorings and Bell's theorem

NASA Astrophysics Data System (ADS)

Aravind, P. K.

1999-11-01

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell-Kochen-Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.

Understanding Rolle's Theorem

ERIC Educational Resources Information Center

Parameswaran, Revathy

2009-01-01

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…

An Application of the Perron-Frobenius Theorem to a Damage Model Problem.

DTIC Science & Technology

1985-04-01

RO-RI6I 20B AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A ill I DAMAGOE MODEL PR BLEM.. (U) PITTSBURGH UNIV PA CENTER FOR I MULTIYARIATE...any copyright notation herein. * . .r * j * :h ~ ** . . .~. ~ % *~’ :. ~ ~ v 4 .% % %~ AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A DAMAGE...University of Sheffield, U.K. S ~ Summry Using the Perron - Frobenius theorem, it is established that if’ (X,Y) is a random vector of non-negative

International Conference on Fixed Point Theory and Applications (Colloque International Theorie Du Point Fixe et Applications)

DTIC Science & Technology

1989-06-09

Theorem and the Perron - Frobenius Theorem in matrix theory. We use the Hahn-Banach theorem and do not use any fixed-point related concepts. 179 A...games defined b’, tions 87 Isac G. Fixed point theorems on convex cones , generalized pseudo-contractive mappings and the omplementarity problem 89...and (II), af(x) ° denotes the negative polar cone ot of(x). This condition are respectively called "inward" and "outward". Indeed, when X is convex

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Markov Property of the Conformal Field Theory Vacuum and the a Theorem.

PubMed

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-06-30

We use strong subadditivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give new proof of the irreversibility of the renormalization group in d=4 space-time dimensions-the a theorem. This extends the proofs of the c and F theorems in dimensions d=2 and d=3 based on vacuum entanglement entropy, and gives a unified picture of all known irreversibility theorems in relativistic quantum field theory.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Nonlocal Quantum Information Transfer Without Superluminal Signalling and Communication

NASA Astrophysics Data System (ADS)

Walleczek, Jan; Grössing, Gerhard

2016-09-01

It is a frequent assumption that—via superluminal information transfers—superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a `no-go' theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell's theorem, we argue that Bell employed both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie-Bohm theory. This position we refer to as "effective non-signalling". By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as "axiomatic non-signalling". In search of a decisive communication-theoretic criterion for differentiating between "axiomatic" and "effective" non-signalling, we employ the operational framework offered by Shannon's mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. We find that an effective non-signalling theorem represents two sub-theorems: (1) Non-transfer-control (NTC) theorem, and (2) Non-signification-control (NSC) theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. Effective non-signalling prevents the instantaneous, i.e., superluminal, transfer of message-encoded information through the controlled use—by a sender-receiver pair —of informationally-correlated detection events, e.g., in EPR-type experiments. An effective non-signalling theorem allows for nonlocal quantum information transfer yet—at the same time—effectively denies superluminal signalling and communication.

On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

Ergodic theorem, ergodic theory, and statistical mechanics

PubMed Central

Moore, Calvin C.

2015-01-01

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697

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

NASA Astrophysics Data System (ADS)

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.

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

A Polarization Responsive System for Microwaves

DTIC Science & Technology

1980-12-01

radioastronomy employs much longer wave- lengths than optics, but the electromagnetic wave formulation of polari- zation is the same for optics as it is for... Radioastronomy . New York: McGraw-Hill, 1966. 8. Kuck, D. J., D. Lawrie and A. H. Samek. High Speed Computer and Algorithm Organization. New York: Academic

Complementary Huygens Principle for Geometrical and Nongeometrical Optics

ERIC Educational Resources Information Center

Luis, Alfredo

2007-01-01

We develop a fundamental principle depicting the generalized ray formulation of optics provided by the Wigner function. This principle is formally identical to the Huygens-Fresnel principle but in terms of opposite concepts, rays instead of waves, and incoherent superpositions instead of coherent ones. This ray picture naturally includes…

Proof of the Spin Statistics Connection 2: Relativistic Theory

NASA Astrophysics Data System (ADS)

Santamato, Enrico; De Martini, Francesco

2017-12-01

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

Quantum fluctuation theorems and generalized measurements during the force protocol.

PubMed

Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter; Campisi, Michele; Hänggi, Peter

2014-03-01

Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed fluctuation theorems with an arbitrary number of intervening measurements are obtained.

Testing First-Order Logic Axioms in AutoCert

NASA Technical Reports Server (NTRS)

Ahn, Ki Yung; Denney, Ewen

2009-01-01

AutoCert [2] is a formal verification tool for machine generated code in safety critical domains, such as aerospace control code generated from MathWorks Real-Time Workshop. AutoCert uses Automated Theorem Provers (ATPs) [5] based on First-Order Logic (FOL) to formally verify safety and functional correctness properties of the code. These ATPs try to build proofs based on user provided domain-specific axioms, which can be arbitrary First-Order Formulas (FOFs). These axioms are the most crucial part of the trusted base, since proofs can be submitted to a proof checker removing the need to trust the prover and AutoCert itself plays the part of checking the code generator. However, formulating axioms correctly (i.e. precisely as the user had really intended) is non-trivial in practice. The challenge of axiomatization arise from several dimensions. First, the domain knowledge has its own complexity. AutoCert has been used to verify mathematical requirements on navigation software that carries out various geometric coordinate transformations involving matrices and quaternions. Axiomatic theories for such constructs are complex enough that mistakes are not uncommon. Second, adjusting axioms for ATPs can add even more complexity. The axioms frequently need to be modified in order to have them in a form suitable for use with ATPs. Such modifications tend to obscure the axioms further. Thirdly, speculating validity of the axioms from the output of existing ATPs is very hard since theorem provers typically do not give any examples or counterexamples.

Radiative transfer in spherical shell atmospheres. II - Asymmetric phase functions

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Adams, C. N.

1978-01-01

This paper investigates the effects of sphericity on the radiation reflected from a planet with a homogeneous conservative-scattering atmosphere of optical thicknesses of 0.25 and 1.0. A Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7 was considered. Significant differences were found when these results were compared with the plane-parallel calculations. Also, large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle. These results will be useful to researchers in the field of remote sensing and planetary spectroscopy.

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leblond, Herve; Kremer, David; Mihalache, Dumitru

2010-03-15

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Interface extinction and subsurface peaking of the radiation pattern of a line source

NASA Technical Reports Server (NTRS)

Engheta, N.; Papas, C. H.; Elachi, C.

1981-01-01

The radiation pattern of a line source lying along the plane interface of two dielectric half-spaces is calculated. It is found that the pattern at the interface has a null (interface extinction); that the pattern in the upper half-space, whose index of refraction is taken to be less than that of the lower half-space, has a single lobe with a maximum normal to the interface; and that the pattern in the lower half-space (subsurface region) has two maxima (peaks) straddling symmetrically a minimum. Interpretation of these results in terms of ray optics, Oseen's extinction theorem, and the Cerenkov effect are given.

The Pythagorean Roots of Introductory Physics

NASA Astrophysics Data System (ADS)

Clarage, James B.

2013-03-01

Much of the mathematical reasoning employed in the typical introductory physics course can be traced to Pythagorean roots planted over two thousand years ago. Besides obvious examples involving the Pythagorean theorem, I draw attention to standard physics problems and derivations which often unknowingly rely upon the Pythagoreans' work on proportion, music, geometry, harmony, the golden ratio, and cosmology. Examples are drawn from mechanics, electricity, sound, optics, energy conservation and relativity. An awareness of the primary sources of the mathematical techniques employed in the physics classroom could especially benefit students and educators at schools which encourage integration of their various courses in history, science, philosophy, and the arts.

Continuous variable quantum cryptography using coherent states.

PubMed

Grosshans, Frédéric; Grangier, Philippe

2002-02-04

We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with Gaussian statistics.

Restoration of longitudinal images.

PubMed

Hu, Y; Frieden, B R

1988-01-15

In this paper, a method of restoring longitudinal images is developed. By using the transfer function for longitudinal objects, and inverse filtering, a longitudinal image may be restored. The Fourier theory and sampling theorems for transverse images cannot be used directly in the longitudinal case. A modification and reasonable approximation are introduced. We have numerically established a necessary relationship between just-resolved longitudinal separation (after inverse filtering), noise level, and the taking conditions of object distance and lens diameter. An empirical formula is also found to well-fit the computed results. This formula may be of use for designing optical systems which are to image longitudinal details, such as in robotics or microscopy.

Competing order parameters in Fermi systems with engineered band dispersion

NASA Astrophysics Data System (ADS)

Wu, Chien-Te; Boyack, Rufus; Anderson, Brandon; Levin, K.

We explore a variety of competing phases in 2D and 3D Fermi gases in the presence of novel dispersion relations resulting from a shaken optical lattice. We incorporate spin imbalance along with attractive interactions. In 3D, at the mean field level we present phase diagrams reflecting the stability of alternative order parameters in the pairing (including LOFF) and charge density wave channels. We perform analogous studies in 2D, where we focus on the competition between different paired phases. Important in this regard is that our 2D studies are consistent with the Mermin Wagner theorem, so that, while there is competition, conventional superfluidity cannot occur

Bring the Pythagorean Theorem "Full Circle"

ERIC Educational Resources Information Center

Benson, Christine C.; Malm, Cheryl G.

2011-01-01

Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…

The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project

ERIC Educational Resources Information Center

Robiette, Alan G.

1975-01-01

Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)

Using Discovery in the Calculus Class

ERIC Educational Resources Information Center

Shilgalis, Thomas W.

1975-01-01

This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)

Three Lectures on Theorem-proving and Program Verification

NASA Technical Reports Server (NTRS)

Moore, J. S.

1983-01-01

Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.

Measurement of the Retention Time of Different Ophthalmic Formulations with Ultrahigh-Resolution Optical Coherence Tomography.

PubMed

Gagliano, Caterina; Papa, Vincenzo; Amato, Roberta; Malaguarnera, Giulia; Avitabile, Teresio

2018-04-01

Purpose/aim of the study: The purpose of this study was to measure the pre-corneal retention time of two marketed formulations (eye drops and eye gel) of a steroid-antibiotic fixed combination (FC) containing 0.1% dexamethasone and 0.3% netilmicin. Pre-corneal retention time was evaluated in 16 healthy subjects using an ultrahigh-resolution anterior segment spectral domain optical coherence tomography (OCT). All subjects randomly received both formulations of the FC (Netildex, SIFI, Italy). Central tear film thickness (CTFT) was measured before instillation (time 0) and then after 1, 10, 20, 30, 40 50, 60 and 120 min. The pre-corneal retention time was calculated by plotting CTFT as a function of time. Differences between time points and groups were analyzed by Student's t-test. CTFT increased significantly after the instillation of the eye gel formulation (p < 0.001). CTFT reached its maximum value 1 min after instillation and returned to baseline after 60 min. No effect on CTFT was observed after the instillation of eye drops. The difference between the two formulations was statistically significant at time 1 min (p < 0.0001), 10 min (p < 0.001) and 20 min (p < 0.01). The FC formulated as eye gel was retained on the ocular surface longer than the corresponding eye drop solution. Consequently, the use of the eye gel might extend the interval between instillations and decrease the frequency of administration.

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

Lipid nanoparticle vectorization of indocyanine green improves fluorescence imaging for tumor diagnosis and lymph node resection.

PubMed

Navarro, Fabrice P; Berger, Michel; Guillermet, Stéphanie; Josserand, Véronique; Guyon, Laurent; Neumann, Emmanuelle; Vinet, Françoise; Texier, Isabelle

2012-10-01

Fluorescence imaging is opening a new era in image-guided surgery and other medical applications. The only FDA approved contrast agent in the near infrared is IndoCyanine Green (ICG), which despites its low toxicity, displays poor chemical and optical properties for long-term and sensitive imaging applications in human. Lipid nanoparticles are investigated for improving ICG optical properties and in vivo fluorescence imaging sensitivity. 30 nm diameter lipid nanoparticles (LNP) are loaded with ICG. Their characterization and use for tumor and lymph node imaging are described. Nano-formulation benefits dye optical properties (6 times improved brightness) and chemical stability (>6 months at 4 degrees C in aqueous buffer). More importantly, LNP vectorization allows never reported sensitive and prolonged (>1 day) labeling of tumors and lymph nodes. Composed of human-use approved ingredients, this novel ICG nanometric formulation is foreseen to expand rapidly the field of clinical fluorescence imaging applications.

Selective optical contacting for solar spectrum management

NASA Astrophysics Data System (ADS)

Yang, Jianfeng; Chen, Weijian; Wang, Bo; Zhang, Zhilong; Huang, Shujuan; Shrestha, Santosh; Wen, Xiaoming; Patterson, Robert; Conibeer, Gavin

2017-02-01

Solar spectrum management using up/down conversion is an important method to improve the photovoltaic energy conversion efficiency. It asks for a monochromatic luminescence absorption at the band edge of the photovoltaic device to reduce both the sub-band-gap and over-band-gap energy losses. Here, we demonstrate an energy selective optical contacting concept to improve the luminescence transfer efficiency for spectrum management. By increasing both the luminescence emission and re-absorption ability through photonic resonance, an efficient photon transfer channel could be established between the luminescence emitter and the photovoltaic component in a near-field region. This concept is not only able to compensate the insufficient band edge absorption ability of the photovoltaic device, but also to break the far-field limitation of luminescence radiation. The energy selection on the optical spectrum naturally imposed by the mode resonance is also helpful to improve the monochromaticity of the luminescence yield. In this paper, a photonic crystal cavity is used to realize the optical contacting concept between a thin silicon film and spectrum converter. The optical power and photon flux transferred between different components are calculated analytically using the electromagnetic Green's function. The corresponding radiative dipole moment is estimated by the fluctuation-dissipation theorem. The example shows an over 80 times enhancement in the luminescence absorbance by the silicon layer, illustrating the great potential of this concept to be applied on nano-structured photovoltaic devices.

Three-dimensional refractive index and fluorescence tomography using structured illumination (Conference Presentation)

NASA Astrophysics Data System (ADS)

Park, GwangSik; Shin, SeungWoo; Kim, Kyoohyun; Park, YongKeun

2017-02-01

Optical diffraction tomography (ODT) has been an emerging optical technique for label-free imaging of three-dimensional (3-D) refractive index (RI) distribution of biological samples. ODT employs interferometric microscopy for measuring multiple holograms of samples with various incident angles, from which the Fourier diffraction theorem reconstructs the 3-D RI distribution of samples from retrieved complex optical fields. Since the RI value is linearly proportional to the protein concentration of biological samples where the proportional coefficient is called as refractive index increment (RII), reconstructed 3-D RI tomograms provide precise structural and biochemical information of individual biological samples. Because most proteins have similar RII value, however, ODT has limited molecular specificity, especially for imaging eukaryotic cells having various types of proteins and subcellular organelles. Here, we present an ODT system combined with structured illumination microscopy which can measure the 3-D RI distribution of biological samples as well as 3-D super-resolution fluorescent images in the same optical setup. A digital micromirror device (DMD) controls the incident angle of the illumination beam for tomogram reconstruction, and the same DMD modulates the structured illumination pattern of the excitation beam for super-resolution fluorescent imaging. We first validate the proposed method for simultaneous optical diffraction tomographic imaging and super-resolution fluorescent imaging of fluorescent beads. The proposed method is also exploited for various biological samples.

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

The Law of Cosines for an "n"-Dimensional Simplex

ERIC Educational Resources Information Center

Ding, Yiren

2008-01-01

Using the divergence theorem technique of L. Eifler and N.H. Rhee, "The n-dimensional Pythagorean Theorem via the Divergence Theorem" (to appear: Amer. Math. Monthly), we extend the law of cosines for a triangle in a plane to an "n"-dimensional simplex in an "n"-dimensional space.

When 95% Accurate Isn't: Exploring Bayes's Theorem

ERIC Educational Resources Information Center

CadwalladerOlsker, Todd D.

2011-01-01

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

Optimal Keno Strategies and the Central Limit Theorem

ERIC Educational Resources Information Center

Johnson, Roger W.

2006-01-01

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

Computer Algebra Systems and Theorems on Real Roots of Polynomials

ERIC Educational Resources Information Center

Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

2010-01-01

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Counting Heron Triangles with Constraints

DTIC Science & Technology

2013-01-25

Heron triangle is an integer, then b is even, say b = 2b1. By Pythagoras ’ theorem , a4 = h2 +4b21, and since in a Heron triangle, the heights are always...our first result, which follows an idea of [10, Theorem 2.3]. Theorem 4. Let a, b be two fixed integers, and let ab be factored as in (1). Then H(a, b...which we derive the result. Theorem 4 immediately offers us an interesting observation regarding a special class of fixed sides (a, b). Corollary 5. If

Which symmetry? Noether, Weyl, and conservation of electric charge

NASA Astrophysics Data System (ADS)

Brading, Katherine A.

In 1918, Emmy Noether published a (now famous) theorem establishing a general connection between continuous 'global' symmetries and conserved quantities. In fact, Noether's paper contains two theorems, and the second of these deals with 'local' symmetries; prima facie, this second theorem has nothing to do with conserved quantities. In the same year, Hermann Weyl independently made the first attempt to derive conservation of electric charge from a postulated gauge symmetry. In the light of Noether's work, it is puzzling that Weyl's argument uses local gauge symmetry. This paper explores the relationships between Weyl's work, Noether's two theorems, and the modern connection between gauge symmetry and conservation of electric charge. This includes showing that Weyl's connection is essentially an application of Noether's second theorem, with a novel twist.

Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells

NASA Astrophysics Data System (ADS)

Itoh, Kazuyoshi

2015-12-01

Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.

Optical Asymmetry and Nonlinear Light Scattering from Colloidal Gold Nanorods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lien, Miao-Bin; Kim, Ji-Young; Han, Myung-Geun

A systematic study is presented of the intensity-dependent nonlinear light scattering spectra of gold nanorods under resonant excitation of the longitudinal surface plasmon resonance (SPR). The spectra exhibit features due to coherent second and third harmonic generation as well as a broadband feature that has been previously attributed to multiphoton photoluminescence arising primarily from interband optical transitions in the gold. A detailed study of the spectral dependence of the scaling of the scattered light with excitation intensity shows unexpected scaling behavior of the coherent signals, which is quantitatively accounted for by optically induced damping of the SPR mode through amore » Fermi liquid model of the electronic scattering. The broadband feature is shown to arise not from luminescence, but from scattering of the secondorder longitudinal SPR mode with the electron gas, where efficient excitation of the 2nd order mode arises from an optical asymmetry of the nanorod. The electronic-temperature-dependent plasmon damping and the Fermi-Dirac distribution together determine the intensity dependence of the broadband emission, and the structure-dependent absorption spectrum determines the spectral shape through the fluctuation-dissipation theorem. Hence a complete self-consistent picture of both coherent and incoherent light scattering is obtained with a single set of physical parameters.« less

Optical Asymmetry and Nonlinear Light Scattering from Colloidal Gold Nanorods

DOE PAGES

Lien, Miao-Bin; Kim, Ji-Young; Han, Myung-Geun; ...

2017-05-16

A systematic study is presented of the intensity-dependent nonlinear light scattering spectra of gold nanorods under resonant excitation of the longitudinal surface plasmon resonance (SPR). The spectra exhibit features due to coherent second and third harmonic generation as well as a broadband feature that has been previously attributed to multiphoton photoluminescence arising primarily from interband optical transitions in the gold. A detailed study of the spectral dependence of the scaling of the scattered light with excitation intensity shows unexpected scaling behavior of the coherent signals, which is quantitatively accounted for by optically induced damping of the SPR mode through amore » Fermi liquid model of the electronic scattering. The broadband feature is shown to arise not from luminescence, but from scattering of the secondorder longitudinal SPR mode with the electron gas, where efficient excitation of the 2nd order mode arises from an optical asymmetry of the nanorod. The electronic-temperature-dependent plasmon damping and the Fermi-Dirac distribution together determine the intensity dependence of the broadband emission, and the structure-dependent absorption spectrum determines the spectral shape through the fluctuation-dissipation theorem. Hence a complete self-consistent picture of both coherent and incoherent light scattering is obtained with a single set of physical parameters.« less

Formal verification of an oral messages algorithm for interactive consistency

NASA Technical Reports Server (NTRS)

Rushby, John

1992-01-01

The formal specification and verification of an algorithm for Interactive Consistency based on the Oral Messages algorithm for Byzantine Agreement is described. We compare our treatment with that of Bevier and Young, who presented a formal specification and verification for a very similar algorithm. Unlike Bevier and Young, who observed that 'the invariant maintained in the recursive subcases of the algorithm is significantly more complicated than is suggested by the published proof' and who found its formal verification 'a fairly difficult exercise in mechanical theorem proving,' our treatment is very close to the previously published analysis of the algorithm, and our formal specification and verification are straightforward. This example illustrates how delicate choices in the formulation of the problem can have significant impact on the readability of its formal specification and on the tractability of its formal verification.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys. 53, 033505 (2012)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.

In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final resultsmore » are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)].« less

Effective spin physics in two-dimensional cavity QED arrays

NASA Astrophysics Data System (ADS)

Minář, Jiří; Güneş Söyler, Şebnem; Rotondo, Pietro; Lesanovsky, Igor

2017-06-01

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis-Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.

Effect of Entropy Generation on Wear Mechanics and System Reliability

NASA Astrophysics Data System (ADS)

Gidwani, Akshay; James, Siddanth; Jagtap, Sagar; Karthikeyan, Ram; Vincent, S.

2018-04-01

Wear is an irreversible phenomenon. Processes such as mutual sliding and rolling between materials involve entropy generation. These processes are monotonic with respect to time. The concept of entropy generation is further quantified using Degradation Entropy Generation theorem formulated by Michael D. Bryant. The sliding-wear model can be extrapolated to different instances in order to further provide a potential analysis of machine prognostics as well as system and process reliability for various processes besides even mere mechanical processes. In other words, using the concept of ‘entropy generation’ and wear, one can quantify the reliability of a system with respect to time using a thermodynamic variable, which is the basis of this paper. Thus in the present investigation, a unique attempt has been made to establish correlation between entropy-wear-reliability which can be useful technique in preventive maintenance.

Forward Compton scattering with weak neutral current: Constraints from sum rules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorchtein, Mikhail; Zhang, Xilin

2015-06-09

We generalize forward real Compton amplitude to the case of the interference of the electromagnetic and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference structure functions and obtain a new set of sum rules. Furthermore, we address a possible new sum rule that relates the product of the axial charge and magnetic moment of the nucleon to the 0th moment of the structure function g5(ν, 0). For the dispersive γ Z-box correction to the proton’s weak charge, the application of the GDH sum rule allows us to reduce the uncertainty due to resonance contributionsmore » by a factor of two. Finally, the finite energy sum rule helps addressing the uncertainty in that calculation due to possible duality violations.« less

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

2002-01-01

We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.

A rapid boundary integral equation technique for protein electrostatics

NASA Astrophysics Data System (ADS)

Grandison, Scott; Penfold, Robert; Vanden-Broeck, Jean-Marc

2007-06-01

A new boundary integral formulation is proposed for the solution of electrostatic field problems involving piecewise uniform dielectric continua. Direct Coulomb contributions to the total potential are treated exactly and Green's theorem is applied only to the residual reaction field generated by surface polarisation charge induced at dielectric boundaries. The implementation shows significantly improved numerical stability over alternative schemes involving the total field or its surface normal derivatives. Although strictly respecting the electrostatic boundary conditions, the partitioned scheme does introduce a jump artefact at the interface. Comparison against analytic results in canonical geometries, however, demonstrates that simple interpolation near the boundary is a cheap and effective way to circumvent this characteristic in typical applications. The new scheme is tested in a naive model to successfully predict the ground state orientation of biomolecular aggregates comprising the soybean storage protein, glycinin.

The Theory of Quantized Fields. III

DOE R&D Accomplishments Database

Schwinger, J.

1953-05-01

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Low temperature and UV curable sol-gel coatings for long lasting optical fiber biosensors

NASA Astrophysics Data System (ADS)

Otaduy, D.; Villar, A.; Gomez-Herrero, E.; Goitandia, A. M.; Gorritxategi, E.; Quintana, I.

2010-04-01

The use of optical fibers as sensing element is increasing in clinical, pharmaceutical and industrial applications. Excellent light delivery, long interaction length, low cost and ability not only to excite the target molecules but also to capture the emitted light from the targets are the hallmarks of optical fiber as biosensors. In biosensors based on fiber optics the interaction with the analyte can occur within an element of the optical fiber. One of the techniques for this kind of biosensors is to remove the fiber optic cladding and substitute it for biological coatings that will interact with the parameter to sensorize. The deposition of these layers can be made by sol-gel technology. The sol-gel technology is being increasingly used mainly due to the high versatility to tailor their optical features. Incorporation of suitable chemical and biochemical sensing agents have allowed determining pH, gases, and biochemical species, among others. Nonetheless, the relatively high processing temperatures and short lifetime values mean severe drawbacks for a successful exploitation of sol-gel based coated optical fibres. With regard to the latter, herein we present the design, preparation and characterization of novel sol-gel coated optical fibres. Low temperature and UV curable coating formulations were optimized to achieve a good adhesion and optical performance. The UV photopolymerizable formulation was comprised by glycidoxypropyltrimethoxysilane (GLYMO), Tetraethylorthosilicate (TEOS) and an initiator. While the thermoset coating was prepared by using 3-aminopropyltrimethoxysilane, GLYMO, and TEOS as main reagents. Both curable sol-gel coated fibres were analysed by FTIR, SEM and optical characterization. Furthermore, in the present work a new technique for silica cladding removal has been developed by ultra-short pulses laser processing, getting good dimensional accuracy and surface integrity.

Time Evolution of the Dynamical Variables of a Stochastic System.

ERIC Educational Resources Information Center

de la Pena, L.

1980-01-01

By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)

A Generalization of the Prime Number Theorem

ERIC Educational Resources Information Center

Bruckman, Paul S.

2008-01-01

In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…

A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone

ERIC Educational Resources Information Center

Stupel, Moshe; Ben-Chaim, David

2013-01-01

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

Leaning on Socrates to Derive the Pythagorean Theorem

ERIC Educational Resources Information Center

Percy, Andrew; Carr, Alistair

2010-01-01

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

Unpacking Rouché's Theorem

ERIC Educational Resources Information Center

Howell, Russell W.; Schrohe, Elmar

2017-01-01

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

The Classical Version of Stokes' Theorem Revisited

ERIC Educational Resources Information Center

Markvorsen, Steen

2008-01-01

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

The Parity Theorem Shuffle

ERIC Educational Resources Information Center

Smith, Michael D.

2016-01-01

The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…

Visualizing the Central Limit Theorem through Simulation

ERIC Educational Resources Information Center

Ruggieri, Eric

2016-01-01

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

Virtual continuity of measurable functions and its applications

NASA Astrophysics Data System (ADS)

Vershik, A. M.; Zatitskii, P. B.; Petrov, F. V.

2014-12-01

A classical theorem of Luzin states that a measurable function of one real variable is `almost' continuous. For measurable functions of several variables the analogous statement (continuity on a product of sets having almost full measure) does not hold in general. The search for a correct analogue of Luzin's theorem leads to a notion of virtually continuous functions of several variables. This apparently new notion implicitly appears in the statements of embedding theorems and trace theorems for Sobolev spaces. In fact it reveals the nature of such theorems as statements about virtual continuity. The authors' results imply that under the conditions of Sobolev theorems there is a well-defined integration of a function with respect to a wide class of singular measures, including measures concentrated on submanifolds. The notion of virtual continuity is also used for the classification of measurable functions of several variables and in some questions on dynamical systems, the theory of polymorphisms, and bistochastic measures. In this paper the necessary definitions and properties of admissible metrics are recalled, several definitions of virtual continuity are given, and some applications are discussed. Bibliography: 24 titles.

Use of equivalent spheres to model the relation between radar reflectivity and optical extinction of ice cloud particles.

PubMed

Donovan, David Patrick; Quante, Markus; Schlimme, Ingo; Macke, Andreas

2004-09-01

The effect of ice crystal size and shape on the relation between radar reflectivity and optical extinction is examined. Discrete-dipole approximation calculations of 95-GHz radar reflectivity and ray-tracing calculations are applied to ice crystals of various habits and sizes. Ray tracing was used primarily to calculate optical extinction and to provide approximate information on the lidar backscatter cross section. The results of the combined calculations are compared with Mie calculations applied to collections of different types of equivalent spheres. Various equivalent sphere formulations are considered, including equivalent radar-lidar spheres; equivalent maximum dimension spheres; equivalent area spheres, and equivalent volume and equivalent effective radius spheres. Marked differences are found with respect to the accuracy of different formulations, and certain types of equivalent spheres can be used for useful prediction of both the radar reflectivity at 95 GHz and the optical extinction (but not lidar backscatter cross section) over a wide range of particle sizes. The implications of these results on combined lidar-radar ice cloud remote sensing are discussed.

Band-gap tuning and optical response of two-dimensional SixC1 -x : A first-principles real-space study of disordered two-dimensional materials

NASA Astrophysics Data System (ADS)

Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda; Datta, Sujoy; Johnson, Duane D.; Mookerjee, Abhijit

2017-08-01

We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique [Mookerjee, J. Phys. C 6, 1340 (1973), 10.1088/0022-3719/6/8/003] formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen-Baerends corrected exchange potential [Singh, Harbola, Hemanadhan, Mookerjee, and Johnson, Phys. Rev. B 93, 085204 (2016), 10.1103/PhysRevB.93.085204]. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene SixC1 -x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussed in the light of the available experimental and other theoretical data. Our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.

Automated analysis in generic groups

NASA Astrophysics Data System (ADS)

Fagerholm, Edvard

This thesis studies automated methods for analyzing hardness assumptions in generic group models, following ideas of symbolic cryptography. We define a broad class of generic and symbolic group models for different settings---symmetric or asymmetric (leveled) k-linear groups --- and prove ''computational soundness'' theorems for the symbolic models. Based on this result, we formulate a master theorem that relates the hardness of an assumption to solving problems in polynomial algebra. We systematically analyze these problems identifying different classes of assumptions and obtain decidability and undecidability results. Then, we develop automated procedures for verifying the conditions of our master theorems, and thus the validity of hardness assumptions in generic group models. The concrete outcome is an automated tool, the Generic Group Analyzer, which takes as input the statement of an assumption, and outputs either a proof of its generic hardness or shows an algebraic attack against the assumption. Structure-preserving signatures are signature schemes defined over bilinear groups in which messages, public keys and signatures are group elements, and the verification algorithm consists of evaluating ''pairing-product equations''. Recent work on structure-preserving signatures studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While the size of keys and signatures is crucial for many applications, another aspect of performance is the time it takes to verify a signature. The most expensive operation during verification is the computation of pairings. However, the concrete number of pairings is not captured by the number of pairing-product equations considered in earlier work. We consider the question of what is the minimal number of pairing computations needed to verify structure-preserving signatures. We build an automated tool to search for structure-preserving signatures matching a template. Through exhaustive search we conjecture lower bounds for the number of pairings required in the Type~II setting and prove our conjecture to be true. Finally, our tool exhibits examples of structure-preserving signatures matching the lower bounds, which proves tightness of our bounds, as well as improves on previously known structure-preserving signature schemes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

The Levy sections theorem revisited

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2007-06-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

Design and Fabrication of NxN Optical Couplers Based on Organic Polymer Opti al WaveGuides

DTIC Science & Technology

1994-08-01

lOxlO optical coupler utilizing photopolymerizable organic polymers. Background information on the theory of operation of the coupler culminating in a...Channel Waveguides Based on Photopolymerizable Di/Tri Acrylates," in Optoelecwonic Interconnects Ii, Ray T. Chen, John A. Neff, Editors, Proc. SPIE 2153, pp...demonstrated that acrylic polymers can be used to fabricate single-mode optical wavguides. The resins that we have formulated are photopolymerizable

Guided discovery of the nine-point circle theorem and its proof

NASA Astrophysics Data System (ADS)

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through investigation in a dynamic geometry environment, and consequently prove it using a method of guided discovery. The paper concludes with a variety of suggestions for the ways in which the whole set of activities can be implemented in geometry classrooms.

Kato type operators and Weyl's theorem

NASA Astrophysics Data System (ADS)

Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos

2005-09-01

A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).

Cooperation Among Theorem Provers

NASA Technical Reports Server (NTRS)

Waldinger, Richard J.

1998-01-01

In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

The Cr dependence problem of eigenvalues of the Laplace operator on domains in the plane

NASA Astrophysics Data System (ADS)

Haddad, Julian; Montenegro, Marcos

2018-03-01

The Cr dependence problem of multiple Dirichlet eigenvalues on domains is discussed for elliptic operators by regarding C r + 1-smooth one-parameter families of C1 perturbations of domains in Rn. As applications of our main theorem (Theorem 1), we provide a fairly complete description for all eigenvalues of the Laplace operator on disks and squares in R2 and also for its second eigenvalue on balls in Rn for any n ≥ 3. The central tool used in our proof is a degenerate implicit function theorem on Banach spaces (Theorem 2) of independent interest.

Solving a Class of Spatial Reasoning Problems: Minimal-Cost Path Planning in the Cartesian Plane.

DTIC Science & Technology

1987-06-01

as in Figure 72. By the Theorem of Pythagoras : Z1 <a z 2 < C Yl(bl+b 2)uI, the cost of going along (a,b,c) is greater that the...preceding lemmas to an indefinite number of boundary-crossing episodes is accomplished by the following theorems . Theorem 1 extends the result of Lemma 1... Theorem 1: Any two Snell’s-law paths within a K-explored wedge defined by Snell’s-law paths RL and R. do not intersect within the K-explored portion of

Longitudinal measurement of chromatic dispersion along an optical fiber transmission system with a new correction factor

NASA Astrophysics Data System (ADS)

Abbasi, Madiha; Imran Baig, Mirza; Shafique Shaikh, Muhammad

2013-12-01

At present existence OTDR based techniques have become a standard practice for measuring chromatic dispersion distribution along an optical fiber transmission link. A constructive measurement technique has been offered in this paper, in which a four wavelength bidirectional optical time domain reflectometer (OTDR) has been used to compute the chromatic dispersion allocation beside an optical fiber transmission system. To improve the correction factor a novel formulation has been developed, which leads to an enhanced and defined measurement. The investigational outcomes obtained are in good harmony.

Basic optics of effect materials.

PubMed

Jones, Steven A

2010-01-01

Effect materials derive their color and effect primarily from thin-film interference. Effect materials have evolved over the decades from simple guanine crystals to the complex multilayer optical structures of today. The development of new complex effect materials requires an understanding of the optics of effect materials. Such an understanding would also benefit the cosmetic formulator as these new effect materials are introduced. The root of this understanding begins with basic optics. This paper covers the nature of light, interference of waves, thin-film interference, color from interference, and color travel.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Discovering Theorems in Abstract Algebra Using the Software "GAP"

ERIC Educational Resources Information Center

Blyth, Russell D.; Rainbolt, Julianne G.

2010-01-01

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

ERIC Educational Resources Information Center

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

Unique Factorization and the Fundamental Theorem of Arithmetic

ERIC Educational Resources Information Center

Sprows, David

2017-01-01

The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

A Physical Proof of the Pythagorean Theorem

ERIC Educational Resources Information Center

Treeby, David

2017-01-01

What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one…

Communication. Kinetics of scavenging of small, nucleating clusters. First nucleation theorem and sum rules

DOE PAGES

Malila, Jussi; McGraw, Robert; Laaksonen, Ari; ...

2015-01-07

Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less

A new blackhole theorem and its applications to cosmology and astrophysics

NASA Astrophysics Data System (ADS)

Wang, Shouhong; Ma, Tian

2015-04-01

We shall present a blackhole theorem and a theorem on the structure of our Universe, proved in a recently published paper, based on 1) the Einstein general theory of relativity, and 2) the cosmological principle that the universe is homogeneous and isotropic. These two theorems are rigorously proved using astrophysical dynamical models coupling fluid dynamics and general relativity based on a symmetry-breaking principle. With the new blackhole theorem, we further demonstrate that both supernovae explosion and AGN jets, as well as many astronomical phenomena including e.g. the recent reported are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Benard type convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to a huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

The detailed balance principle and the reciprocity theorem between photocarrier collection and dark carrier distribution in solar cells

NASA Astrophysics Data System (ADS)

Rau, Uwe; Brendel, Rolf

1998-12-01

It is shown that a recently described general relationship between the local collection efficiency of solar cells and the dark carrier concentration (reciprocity theorem) directly follows from the principle of detailed balance. We derive the relationship for situations where transport of charge carriers occurs between discrete states as well as for the situation where electronic transport is described in terms of continuous functions. Combining both situations allows to extend the range of applicability of the reciprocity theorem to all types of solar cells, including, e.g., metal-insulator-semiconductor-type, electrochemical solar cells, as well as the inclusion of the impurity photovoltaic effect. We generalize the theorem further to situations where the occupation probability of electronic states is governed by Fermi-Dirac statistics instead of Boltzmann statistics as underlying preceding work. In such a situation the reciprocity theorem is restricted to small departures from equilibrium.

Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state.

PubMed

Gieseler, Jan; Quidant, Romain; Dellago, Christoph; Novotny, Lukas

2014-05-01

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance.

Exploiting structure: Introduction and motivation

NASA Technical Reports Server (NTRS)

Xu, Zhong Ling

1994-01-01

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perkins, R. J., E-mail: rperkins@pppl.gov; Bellan, P. M.

Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle inmore » a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.« less

An Integrated Environment for Efficient Formal Design and Verification

NASA Technical Reports Server (NTRS)

1998-01-01

The general goal of this project was to improve the practicality of formal methods by combining techniques from model checking and theorem proving. At the time the project was proposed, the model checking and theorem proving communities were applying different tools to similar problems, but there was not much cross-fertilization. This project involved a group from SRI that had substantial experience in the development and application of theorem-proving technology, and a group at Stanford that specialized in model checking techniques. Now, over five years after the proposal was submitted, there are many research groups working on combining theorem-proving and model checking techniques, and much more communication between the model checking and theorem proving research communities. This project contributed significantly to this research trend. The research work under this project covered a variety of topics: new theory and algorithms; prototype tools; verification methodology; and applications to problems in particular domains.

PHY-DLL dialogue: cross-layer design for optical-wireless OFDM downlink transmission

NASA Astrophysics Data System (ADS)

Wang, Xuguo; Li, Lee

2005-11-01

The use of radio over fiber to provide radio access has a number of advantages including the ability to deploy small, low-cost remote antenna units and ease of upgrade. And due to the great potential for increasing the capacity and quality of service, the combination of Orthogonal Frequency Division Multiplexing (OFDM) modulation and the sub-carrier multiplexed optical transmission is one of the best solutions for the future millimeter-wave mobile communication. And this makes the optimum utility of valuable radio resources essential. This paper devises a cross-layer adaptive algorithm for optical-wireless OFDM system, which takes into consideration not only transmission power limitation in the physical layer, but also traffic scheduling and user fairness at the data-link layer. According to proportional fairness principle and water-pouring theorem, we put forward the complete description of this cross-layer adaptive downlink transmission 6-step algorithm. Simulation results show that the proposed cross-layer algorithm outperforms the mere physical layer adaptive algorithm markedly. The novel scheme is able to improve performance of the packet success rate per time chip and average packet delay, support added active users.

Predicting the performance of linear optical detectors in free space laser communication links

NASA Astrophysics Data System (ADS)

Farrell, Thomas C.

2018-05-01

While the fundamental performance limit for optical communications is set by the quantum nature of light, in practical systems background light, dark current, and thermal noise of the electronics also degrade performance. In this paper, we derive a set of equations predicting the performance of PIN diodes and linear mode avalanche photo diodes (APDs) in the presence of such noise sources. Electrons generated by signal, background, and dark current shot noise are well modeled in PIN diodes as Poissonian statistical processes. In APDs, on the other hand, the amplifying effects of the device result in statistics that are distinctly non-Poissonian. Thermal noise is well modeled as Gaussian. In this paper, we appeal to the central limit theorem and treat both the variability of the signal and the sum of noise sources as Gaussian. Comparison against Monte-Carlo simulation of PIN diode performance (where we do model shot noise with draws from a Poissonian distribution) validates the legitimacy of this approximation. On-off keying, M-ary pulse position, and binary differential phase shift keying modulation are modeled. We conclude with examples showing how the equations may be used in a link budget to estimate the performance of optical links using linear receivers.

Sampling and Reconstruction of the Pupil and Electric Field for Phase Retrieval

NASA Technical Reports Server (NTRS)

Dean, Bruce; Smith, Jeffrey; Aronstein, David

2012-01-01

This technology is based on sampling considerations for a band-limited function, which has application to optical estimation generally, and to phase retrieval specifically. The analysis begins with the observation that the Fourier transform of an optical aperture function (pupil) can be implemented with minimal aliasing for Q values down to Q = 1. The sampling ratio, Q, is defined as the ratio of the sampling frequency to the band-limited cut-off frequency. The analytical results are given using a 1-d aperture function, and with the electric field defined by the band-limited sinc(x) function. Perfect reconstruction of the Fourier transform (electric field) is derived using the Whittaker-Shannon sampling theorem for 1

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

A gauge-theoretic approach to gravity

PubMed Central

Krasnov, Kirill

2012-01-01

Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach. PMID:22792040

A network dynamics approach to chemical reaction networks

NASA Astrophysics Data System (ADS)

van der Schaft, A. J.; Rao, S.; Jayawardhana, B.

2016-04-01

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

The effects of facilitation and competition on group foraging in patches

PubMed Central

Laguë, Marysa; Tania, Nessy; Heath, Joel; Edelstein-Keshet, Leah

2012-01-01

Significant progress has been made towards understanding the social behaviour of animal groups, but the patch model, a foundation of foraging theory, has received little attention in a social context. The effect of competition on the optimal time to leave a foraging patch was considered as early as the original formulation of the marginal value theorem, but surprisingly, the role of facilitation (where foraging in groups decreases the time to find food in patches), has not been incorporated. Here we adapt the classic patch model to consider how the trade-off between facilitation and competition influence optimal group size. Using simple assumptions about the effect of group size on the food-finding time and the sharing of resources, we find conditions for existence of optima in patch residence time and in group size. When patches are close together (low travel times), larger group sizes are optimal. Groups are predicted to exploit patches differently than individual foragers and the degree of patch depletion at departure depends on the details of the trade-off between competition and facilitation. A variety of currencies and group-size effects are also considered and compared. Using our simple formulation, we also study the effects of social foraging on patch exploitation which to date have received little empirical study. PMID:22743132

The effects of facilitation and competition on group foraging in patches.

PubMed

Laguë, Marysa; Tania, Nessy; Heath, Joel; Edelstein-Keshet, Leah

2012-10-07

Significant progress has been made towards understanding the social behaviour of animal groups, but the patch model, a foundation of foraging theory, has received little attention in a social context. The effect of competition on the optimal time to leave a foraging patch was considered as early as the original formulation of the marginal value theorem, but surprisingly, the role of facilitation (where foraging in groups decreases the time to find food in patches), has not been incorporated. Here we adapt the classic patch model to consider how the trade-off between facilitation and competition influences optimal group size. Using simple assumptions about the effect of group size on the food-finding time and the sharing of resources, we find conditions for existence of optima in patch residence time and in group size. When patches are close together (low travel times), larger group sizes are optimal. Groups are predicted to exploit patches differently than individual foragers and the degree of patch depletion at departure depends on the details of the trade-off between competition and facilitation. A variety of currencies and group-size effects are also considered and compared. Using our simple formulation, we also study the effects of social foraging on patch exploitation which to date have received little empirical study. Copyright © 2012 Elsevier Ltd. All rights reserved.