A modified dual-level algorithm for large-scale three-dimensional Laplace and Helmholtz equation

NASA Astrophysics Data System (ADS)

Li, Junpu; Chen, Wen; Fu, Zhuojia

2018-01-01

A modified dual-level algorithm is proposed in the article. By the help of the dual level structure, the fully-populated interpolation matrix on the fine level is transformed to a local supported sparse matrix to solve the highly ill-conditioning and excessive storage requirement resulting from fully-populated interpolation matrix. The kernel-independent fast multipole method is adopted to expediting the solving process of the linear equations on the coarse level. Numerical experiments up to 2-million fine-level nodes have successfully been achieved. It is noted that the proposed algorithm merely needs to place 2-3 coarse-level nodes in each wavelength per direction to obtain the reasonable solution, which almost down to the minimum requirement allowed by the Shannon's sampling theorem. In the real human head model example, it is observed that the proposed algorithm can simulate well computationally very challenging exterior high-frequency harmonic acoustic wave propagation up to 20,000 Hz.

Helmholtz's early empiricism and the Erhaltung der Kraft.

PubMed

Jurkowitz, Edward

2010-01-01

Hermann Helmholtz has often been understood to have started research under the influence of Kant, and then to have made a transition to a later mature empiricist phase. Without claiming that in 1847 Helmholtz held the same positions that he later espoused, I suggest that already in his 1847 'Uber die Erhaltung der Kraft' one may find important aspects of his later empiricism. I highlight the ways in which, from early on, Helmholtz turned Kant to use in developing an empirical program of inquiry into possible basic natural causes. To that end, I indicate how, throughout his arguments, Helmholtz employed, sometimes explicitly, but often tacitly, an empiricist logic, one that ran contrary to any form of transcendental deduction, and even to all a priori knowledge. Instead of deriving aspects about the ultimate constituents of nature, Helmholtz aimed to define the proper project for physical natural science. The first part of the paper describes the context of discussion in which Helmholtz entered. The bulk of the paper then analyzes Helmholtz's arguments in order to make space between (1) Kantian, and other, deductions of characteristics that must be true of nature and (2) Helmholtz's delineation of empirically determinable characteristics of presumed ultimate elements of nature, ones that he meant to be specified and delimited through future experimental research. The paper highlights that throughout his discussion Helmholtz meant to define the proper project for physical natural science, a project rife with empiricist aspects.

Experiments with Helmholtz Resonators.

ERIC Educational Resources Information Center

Greenslade, Thomas B., Jr.

1996-01-01

Presents experiments that use Helmholtz resonators and have been designed for a sophomore-level course in oscillations and waves. Discusses the theory of the Helmholtz resonator and resonance curves. (JRH)

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Hermann von Helmholtz's empirico-transcendentalism reconsidered: construction and constitution in Helmholtz's psychology of the object.

PubMed

De Kock, Liesbet

2014-12-01

This paper aims at contributing to the ongoing efforts to get a firmer grasp of the systematic significance of the entanglement of idealism and empiricism in Helmholtz's work. Contrary to existing analyses, however, the focal point of the present exposition is Helmholtz's attempt to articulate a psychological account of objectification. Helmholtz's motive, as well as his solution to the problem of the object are outlined, and interpreted against the background of his scientific practice on the one hand, and that of empiricist and (transcendental) idealist analyses of experience on the other. The specifically psychological angle taken, not only prompts us to consider figures who have hitherto been treated as having only minor import for Helmholtz interpretation (most importantly J.S. Mill and J.G. Fichte), it furthermore sheds new light on some central tenets of the latter's psychological stance that have hitherto remained underappreciated. For one thing, this analysis reveals an explicit voluntarist tendency in Helmholtz's psychological theory. In conclusion, it is argued that the systematic significance of Helmholtz's empirico-transcendentalism with respect to questions of the mind is best understood as an attempt to found his empirical theory of perception in a second order, normative account of epistemic subjectivity.

Helmholtz and Zoellner: nineteenth-century empiricism, spiritism, and the theory of space perception.

PubMed

Stromberg, W H

1989-10-01

J. K. F. Zoellner began writing on "experimental proofs" of a fourth spatial dimension, and of the existence of spirits, in 1878. His arguments caused strong controversy, with rebuttal essays by Wilhelm Wundt and others. The author argues that Zoellner's case that these matters are experimental questions rested on arguments which Hermann von Helmholtz, inveighing against rationalist views of space and space perception, had recently published. Zoellner's use of Helmholtz's arguments to advance and defend his spiritist views occasioned strong criticism of Helmholtz, affected careers and reputations of scholars in Berlin and Leipzig, and caused enduring controversy over the credibility of Helmholtz's empiricist theory of space perception.

Helmholtz, Riemann, and the Sirens: Sound, Color, and the "Problem of Space"

NASA Astrophysics Data System (ADS)

Pesic, Peter

2013-09-01

Emerging from music and the visual arts, questions about hearing and seeing deeply affected Hermann Helmholtz's and Bernhard Riemann's contributions to what became called the "problem of space [ Raumproblem]," which in turn influenced Albert Einstein's approach to general relativity. Helmholtz's physiological investigations measured the time dependence of nerve conduction and mapped the three-dimensional manifold of color sensation. His concurrent studies on hearing illuminated musical evidence through experiments with mechanical sirens that connect audible with visible phenomena, especially how the concept of frequency unifies motion, velocity, and pitch. Riemann's critique of Helmholtz's work on hearing led Helmholtz to respond and study Riemann's then-unpublished lecture on the foundations of geometry. During 1862-1870, Helmholtz applied his findings on the manifolds of hearing and seeing to the Raumproblem by supporting the quadratic distance relation Riemann had assumed as his fundamental hypothesis about geometrical space. Helmholtz also drew a "close analogy … in all essential relations between the musical scale and space." These intersecting studies of hearing and seeing thus led to reconsideration and generalization of the very concept of "space," which Einstein shaped into the general manifold of relativistic space-time.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Calibration of Helmholtz Coils for the characterization of MEMS magnetic sensor using fluxgate magnetometer with DAS1 magnetic range data acquisition system

NASA Astrophysics Data System (ADS)

Ahmad, Farooq; Dennis, John Ojur; Md Khir, Mohd Haris; Hamid, Nor Hisham

2012-09-01

This paper presents the calibration of Helmholtz coils for the characterization of MEMS Magnetic sensor using Fluxgate magnetometer with DAS1 Magnetic Range Data Acquisition System. The Helmholtz coils arrangement is often used to generate a uniform magnetic field in space. In the past, standard magnets were used to calibrate the Helmholtz coils. A method is presented here for calibrating these coils using a Fluxgate magnetometer and known current source, which is easier and results in greater accuracy.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Sound absorption by a Helmholtz resonator

NASA Astrophysics Data System (ADS)

Komkin, A. I.; Mironov, M. A.; Bykov, A. I.

2017-07-01

Absorption characteristics of a Helmholtz resonator positioned at the end wall of a circular duct are considered. The absorption coefficient of the resonator is experimentally investigated as a function of the diameter and length of the resonator neck and the depth of the resonator cavity. Based on experimental data, the linear analytic model of a Helmholtz resonator is verified, and the results of verification are used to determine the dissipative attached length of the resonator neck so as to provide the agreement between experimental and calculated data. Dependences of sound absorption by a Helmholtz resonator on its geometric parameters are obtained.

Experimental realization of extraordinary acoustic transmission using Helmholtz resonators

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

Crow, Brian C.; Cullen, Jordan M.; McKenzie, William W.

2015-02-15

The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR) is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted soundmore » as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.« less

Study of retro reflector array for the polarimeter-interferometer system on EAST Tokamak

NASA Astrophysics Data System (ADS)

Lan, T.; Wang, S. X.; Liu, H. Q.; Liu, J.; Jie, Y. X.; Zou, Z. Y.; Li, W. M.; Gao, X.; Qin, H.

2015-12-01

In this paper, we experimentally verify the feasibility of replacing individual retro reflectors (RRs) with retro reflector array (RRA) in EAST POlarimeter/INTerferometer (POINT) system, by considering mode transformation and power wastage. Being exposed to plasma environment directly, RRs have risks of deformation, erosion and deposition. RRA is preferable because it can be installed within a smaller space and provide a gap of several centimeters for the shutter design. This protective structure can reduce the cost of device maintenance and bring down system errors. According to Helmholtz-Kirchhoff integral theorem, the optimized incident diameter for the RRA, constituted by seven hexagonal RR cells, is 40 mm in POINT system. The corresponding bench tests are carried out by measuring the propagation properties of reflected beams by plane RRA for perpendicular incidence and reflected beams by terrace RRA for oblique incidence. The experimental results illustrate that RRA can be satisfactorily applied in POINT system at the optimized incident diameter. In view of the energy wastage caused by plasma film coating, it is found that RRA has more advantages for diagnostics using shorter wavelengths, such as the case in ITER.

Control of Combustion-Instabilities Through Various Passive Devices

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Nesman, Tom; Canabal, Francisco

2005-01-01

Results of a computational study on the effectiveness of various passive devices for the control of combustion instabilities are presented. An axi-symmetric combustion chamber is considered. The passive control devices investigated are, baffles, Helmholtz resonators and quarter-waves. The results show that a Helmholtz resonator with a smooth orifice achieves the best control results, while a baffle is the least effective for the frequency tested. At high sound pressure levels, the Helmholtz resonator is less effective. It is also found that for a quarter wave, the smoothness of the orifice has the opposite effect than the Helmholtz resonator, i.e. results in less control.

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

Extraordinary acoustic transmission mediated by Helmholtz resonators

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

Koju, Vijay; Rowe, Ebony; Robertson, William M., E-mail: William.Robertson@mtsu.edu

2014-07-15

We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of themore » necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.« less

Erratum: SDO-AIA Observation of Kelvin-helmholtz Instability in the Solar Corona

NASA Technical Reports Server (NTRS)

Ofman, Leon; Thompson, Barbara J.

2012-01-01

The first SDOAIA observation of the KelvinHelmholtz instability in the solar corona in the 2010 April 8 event was reported by Ofman Thompson (2010, 2011). Foullon et al. (2011), which was published prior to Ofman Thompson (2011), claimed the detection of the KelvinHelmholtz instability in a later event (2010 November 3), and should have been cited in Ofman Thompson (2011).

Effect of Helmholtz Oscillation on Auto-shroud for APS Tungsten Carbide Coating

NASA Astrophysics Data System (ADS)

Jin, Younggil; Choi, Sooseok; Yang, Seung Jae; Park, Chong Rae; Kim, Gon-Ho

2013-06-01

The atmospheric-pressure plasma spray (APS) of tungsten coating was performed using tungsten carbide (WC) powder by means of DC plasma torch equipped with a stepped anode nozzle as a potential method of W coating on graphite plasma-facing component of fusion reactors. This nozzle configuration allows Helmholtz oscillation mode dominating in APS arc fluctuation, and the variation of auto-shroud effect with Helmholtz oscillation characteristics can be investigated. Tungsten coating made from WC powder has lower porosity and higher tungsten purity than that made from pure tungsten powder. The porosity and chemical composition of coatings were investigated by mercury intrusion porosimetry and x-ray photoelectron spectroscopy, respectively. The purity of tungsten coating layer is increased with the increasing frequency of Helmholtz oscillation and the increasing arc current. The modulation of Helmholtz oscillation frequency and magnitude may enhance the decarburization of WC to deposit tungsten coating without W-C and W-O bond from WC powder.

Physiological optics and physical geometry.

PubMed

Hyder, D J

2001-09-01

Hermann von Helmholtz's distinction between "pure intuitive" and "physical" geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant's claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz's understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz's development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz's arguments concerning geometry.

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes

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

Koutsoumaris, C. Chr.; Tsamasphyros, G. J.; Vogiatzis, G. G.

2015-12-31

The nonlocal theory of elasticity is employed for the study of the free vibrations of carbon nanotubes (CNT). For the first time, a bi-Helmholtz operator has been used instead of the standard Helmholtz operator in a nonlocal beam model. Alongside the continuum formulation and its numerical solution, atomistic Molecular Dynamics (MD) simulations have been conducted in order to directly evaluate the eigenfrequencies of vibrating CNTs with a minimum of adjustable parameters. Our results show that the bi-Helmholtz operator is the most appropriate one to fit MD simulation results. However, the estimation of vibration eigenfrequencies from molecular simulations still remains anmore » open (albeit well-posed) problem.« less

A validated non-linear Kelvin-Helmholtz benchmark for numerical hydrodynamics

NASA Astrophysics Data System (ADS)

Lecoanet, D.; McCourt, M.; Quataert, E.; Burns, K. J.; Vasil, G. M.; Oishi, J. S.; Brown, B. P.; Stone, J. M.; O'Leary, R. M.

2016-02-01

The non-linear evolution of the Kelvin-Helmholtz instability is a popular test for code verification. To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution. This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem. The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad hoc proxies, e.g. the existence of small-scale structures. This paper proposes well-posed two-dimensional Kelvin-Helmholtz problems with smooth initial conditions and explicit diffusion. We show that in many cases numerical errors/noise can seed spurious small-scale structure in Kelvin-Helmholtz problems. We demonstrate convergence to a reference solution using both ATHENA, a Godunov code, and DEDALUS, a pseudo-spectral code. Problems with constant initial density throughout the domain are relatively straightforward for both codes. However, problems with an initial density jump (which are the norm in astrophysical systems) exhibit rich behaviour and are more computationally challenging. In the latter case, ATHENA simulations are prone to an instability of the inner rolled-up vortex; this instability is seeded by grid-scale errors introduced by the algorithm, and disappears as resolution increases. Both ATHENA and DEDALUS exhibit late-time chaos. Inviscid simulations are riddled with extremely vigorous secondary instabilities which induce more mixing than simulations with explicit diffusion. Our results highlight the importance of running well-posed test problems with demonstrated convergence to a reference solution. To facilitate future comparisons, we include as supplementary material the resolved, converged solutions to the Kelvin-Helmholtz problems in this paper in machine-readable form.

Design and Fabrication of Helmholtz Coils to Study the Effects of Pulsed Electromagnetic Fields on the Healing Process in Periodontitis: Preliminary Animal Results

PubMed Central

Haghnegahdar, A; Khosrovpanah, H; Andisheh-Tadbir, A; Mortazavi, Gh; Saeedi Moghadam, M; Mortazavi, SMJ; Zamani, A; Haghani, M; Shojaei Fard, M; Parsaei, H; Koohi, O

2014-01-01

Background: Effects of electromagnetic fields on healing have been investigated for centuries. Substantial data indicate that exposure to electromagnetic field can lead to enhanced healing in both soft and hard tissues. Helmholtz coils are devices that generate pulsed electromagnetic fields (PEMF). Objective: In this work, a pair of Helmholtz coils for enhancing the healing process in periodontitis was designed and fabricated. Method: An identical pair of square Helmholtz coils generated the 50 Hz magnetic field.  This device was made up of two parallel coaxial circular coils (100 turns in each loop, wound in series) which were separated from each other by a distance equal to the radius of one coil (12.5 cm). The windings of our Helmholtz coil was made of standard 0.95mm wire to provide the maximum possible current. The coil was powered by a function generator.  Results: The Helmholtz Coils generated a uniform magnetic field between its coils. The magnetic field strength at the center of the space between two coils was 97.6 μT. Preliminary biological studies performed on rats show that exposure of laboratory animals to pulsed electromagnetic fields enhanced the healing of periodontitis. Conclusion: Exposure to PEMFs can lead to stimulatory physiological effects on cells and tissues such as enhanced healing of periodontitis. PMID:25505775

Extension of the Helmholtz-Smoluchowski velocity to the hydrophobic microchannels with velocity slip.

PubMed

Park, H M; Kim, T W

2009-01-21

Electrokinetic flows through hydrophobic microchannels experience velocity slip at the microchannel wall, which affects volumetric flow rate and solute retention time. The usual method of predicting the volumetric flow rate and velocity profile for hydrophobic microchannels is to solve the Navier-Stokes equation and the Poisson-Boltzmann equation for the electric potential with the boundary condition of velocity slip expressed by the Navier slip coefficient, which is computationally demanding and defies analytic solutions. In the present investigation, we have devised a simple method of predicting the velocity profiles and volumetric flow rates of electrokinetic flows by extending the concept of the Helmholtz-Smoluchowski velocity to microchannels with Navier slip. The extended Helmholtz-Smoluchowski velocity is simple to use and yields accurate results as compared to the exact solutions. Employing the extended Helmholtz-Smoluchowski velocity, the analytical expressions for volumetric flow rate and velocity profile for electrokinetic flows through rectangular microchannels with Navier slip have been obtained at high values of zeta potential. The range of validity of the extended Helmholtz-Smoluchowski velocity is also investigated.

Number and measure: Hermann von Helmholtz at the crossroads of mathematics, physics, and psychology.

PubMed

Darrigol, Olivier

2003-09-01

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann/Du Bois), on the possibility of quantitative psychology (Fechner/Kries, Wundt/Zeller), and on the meaning of temperature measurement (Maxwell,Mach.). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz's essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem,Campbell). The aim of the present paper is to situate Helmholtz's contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement. 2003 Published by Elsevier Ltd.

Helmholtz and the psychophysiology of time.

PubMed

Debru, C

2001-09-01

After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

Nitsche’s Method For Helmholtz Problems with Embedded Interfaces

PubMed Central

Zou, Zilong; Aquino, Wilkins; Harari, Isaac

2016-01-01

SUMMARY In this work, we use Nitsche’s formulation to weakly enforce kinematic constraints at an embedded interface in Helmholtz problems. Allowing embedded interfaces in a mesh provides significant ease for discretization, especially when material interfaces have complex geometries. We provide analytical results that establish the well-posedness of Helmholtz variational problems and convergence of the corresponding finite element discretizations when Nitsche’s method is used to enforce kinematic constraints. As in the analysis of conventional Helmholtz problems, we show that the inf-sup constant remains positive provided that the Nitsche’s stabilization parameter is judiciously chosen. We then apply our formulation to several 2D plane-wave examples that confirm our analytical findings. Doing so, we demonstrate the asymptotic convergence of the proposed method and show that numerical results are in accordance with the theoretical analysis. PMID:28713177

From Helmholtz to Schlick: The evolution of the sign-theory of perception.

PubMed

Oberdan, Thomas

2015-08-01

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zurȕck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his 'method of coincidences', similar to the 'point-coincidences' featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism. Copyright © 2015 Elsevier Ltd. All rights reserved.

A full-wave Helmholtz model for continuous-wave ultrasound transmission.

PubMed

Huttunen, Tomi; Malinen, Matti; Kaipio, Jari P; White, Phillip Jason; Hynynen, Kullervo

2005-03-01

A full-wave Helmholtz model of continuous-wave (CW) ultrasound fields may offer several attractive features over widely used partial-wave approximations. For example, many full-wave techniques can be easily adjusted for complex geometries, and multiple reflections of sound are automatically taken into account in the model. To date, however, the full-wave modeling of CW fields in general 3D geometries has been avoided due to the large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a full-wave solution of the 3D Helmholtz equation for modeling of continuous-wave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultraweak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but, due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence.

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.

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Analysis of Transient Shear Wave in Lossy Media.

PubMed

Parker, Kevin J; Ormachea, Juvenal; Will, Scott; Hah, Zaegyoo

2018-07-01

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7 m/s in the liver to 2.5 m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity. Copyright © 2018 World Federation for Ultrasound in Medicine and Biology. Published by Elsevier Inc. All rights reserved.

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption.

PubMed

Griffiths, Stéphane; Nennig, Benoit; Job, Stéphane

2017-01-01

A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.

2017-02-01

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Coupled Kelvin-Helmholtz and Tearing Mode Instabilities at the Mercury's Magnetopause

NASA Astrophysics Data System (ADS)

Ivanovski, S. L.; Milillo, A.; Kartalev, M.; Massetti, S.

2018-05-01

A MHD approach for numerical simulations of coupled Kelvin-Helmholtz and tearing mode instabilities has been applied to Mercury’s magnetopause and used to perform a physical parameters study constrained by the MESSENGER data.

Bistable dark solitons of a cubic-quintic Helmholtz equation

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

Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

2010-05-15

We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation andmore » nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.« less

Kelvin Helmholtz Instability at the Equatorial Magnetotail Boundary: MHD Simulation and Comparison with Geotail Observations

NASA Technical Reports Server (NTRS)

Fairfield, Donald H.; Otto, A.

1999-01-01

On March 24, 1995 the Geotail spacecraft observed large fluctuations of the magnetic field and plasma properties in the Low Latitude Boundary Layer (LLBL) about 15 R(sub E) tailward of the dusk meridian. Although the magnetospheric and the magnetosheath field were strongly northward, the B(sub z) component showed strong short duration fluctuations in which B(sub z) could even reach negative values. We have used two-dimensional magnetohydrodynamic simulations with magnetospheric and magnetosheath input parameters specifically chosen for this. Geotail event to identify the processes which cause the observed boundary properties. It is shown that these fluctuations can be explained by the Kelvin-Helmholtz instability if the k vector of the instability has a component along the magnetic field direction. The simulation results show many of the characteristic properties of the Geotail observations. In particular, the quasi-periodic strong fluctuations are well explained by satellite crossings through the Kelvin-Helmholtz vortices. It is illustrated how the interior structure of the Kelvin-Helmholtz vortices leads to the rapid fluctuations in the Geotail observations. Our results suggest an average Kelvin-Helmholtz wavelength of about 5 R(sub E) with a vortex size of close to 2 R(sub E) for an average repetition time of 2.5 minutes. The growth time for these waves implies a source region of about 10 to 16 R(sub E) upstream from the location of the Geotail spacecraft (i.e., near the dusk meridian). The results also indicate a considerable mass transport of magnetosheath material into the magnetosphere by magnetic reconnection in the Kelvin-Helmholtz vortices.

For a statistical interpretation of Helmholtz' thermal displacement

NASA Astrophysics Data System (ADS)

Podio-Guidugli, Paolo

2016-11-01

On moving from the classic papers by Einstein and Langevin on Brownian motion, two consistent statistical interpretations are given for the thermal displacement, a scalar field formally introduced by Helmholtz, whose time derivative is by definition the absolute temperature.

Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain.

PubMed

Ratowsky, R P; Fleck, J A; Feit, M D

1992-01-01

The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

Hydrodynamic Coherence and Vortex Solutions of the Euler-Helmholtz Equation

NASA Astrophysics Data System (ADS)

Fimin, N. N.; Chechetkin, V. M.

2018-03-01

The form of the general solution of the steady-state Euler-Helmholtz equation (reducible to the Joyce-Montgomery one) in arbitrary domains on the plane is considered. This equation describes the dynamics of vortex hydrodynamic structures.

Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

NASA Astrophysics Data System (ADS)

Bernard, Julien

2018-02-01

I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

Suppression of Helmholtz resonance using inside acoustic liner

NASA Astrophysics Data System (ADS)

Hong, Zhiliang; Dai, Xiwen; Zhou, Nianfa; Sun, Xiaofeng; Jing, Xiaodong

2014-08-01

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.

Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction.

PubMed

Ratowsky, R P; Fleck, J A

1991-06-01

The Lanczos recursion algorithm is used to determine forward-propagating solutions for both the paraxial and Helmholtz wave equations for longitudinally invariant refractive indices. By eigenvalue analysis it is demonstrated that the method gives extremely accurate solutions to both equations.

Evidence for Secondary Flux Rope Generated by the Electron Kelvin-Helmholtz Instability in a Magnetic Reconnection Diffusion Region

NASA Astrophysics Data System (ADS)

Zhong, Z. H.; Tang, R. X.; Zhou, M.; Deng, X. H.; Pang, Y.; Paterson, W. R.; Giles, B. L.; Burch, J. L.; Tobert, R. B.; Ergun, R. E.; Khotyaintsev, Y. V.; Lindquist, P.-A.

2018-02-01

Secondary flux ropes are suggested to play important roles in energy dissipation and particle acceleration during magnetic reconnection. However, their generation mechanism is not fully understood. In this Letter, we present the first direct evidence that a secondary flux rope was generated due to the evolution of an electron vortex, which was driven by the electron Kelvin-Helmholtz instability in an ion diffusion region as observed by the Magnetospheric Multiscale mission. The subion scale (less than the ion inertial length) flux rope was embedded within the electron vortex, which contained a secondary electron diffusion region at the trailing edge of the flux rope. We propose that intense electron shear flow produced by reconnection generated the electron Kelvin-Helmholtz vortex, which induced a secondary reconnection in the exhaust of the primary X line and then led to the formation of the flux rope. This result strongly suggests that secondary electron Kelvin-Helmholtz instability is important for reconnection dynamics.

Evidence for Secondary Flux Rope Generated by the Electron Kelvin-Helmholtz Instability in a Magnetic Reconnection Diffusion Region.

PubMed

Zhong, Z H; Tang, R X; Zhou, M; Deng, X H; Pang, Y; Paterson, W R; Giles, B L; Burch, J L; Tobert, R B; Ergun, R E; Khotyaintsev, Y V; Lindquist, P-A

2018-02-16

Secondary flux ropes are suggested to play important roles in energy dissipation and particle acceleration during magnetic reconnection. However, their generation mechanism is not fully understood. In this Letter, we present the first direct evidence that a secondary flux rope was generated due to the evolution of an electron vortex, which was driven by the electron Kelvin-Helmholtz instability in an ion diffusion region as observed by the Magnetospheric Multiscale mission. The subion scale (less than the ion inertial length) flux rope was embedded within the electron vortex, which contained a secondary electron diffusion region at the trailing edge of the flux rope. We propose that intense electron shear flow produced by reconnection generated the electron Kelvin-Helmholtz vortex, which induced a secondary reconnection in the exhaust of the primary X line and then led to the formation of the flux rope. This result strongly suggests that secondary electron Kelvin-Helmholtz instability is important for reconnection dynamics.

Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

NASA Astrophysics Data System (ADS)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

NASA Astrophysics Data System (ADS)

Pozderac, Preston; Leary, Cody

We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

THE KELVIN-HELMHOLTZ INSTABILITY AT CORONAL MASS EJECTION BOUNDARIES IN THE SOLAR CORONA: OBSERVATIONS AND 2.5D MHD SIMULATIONS

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

Moestl, U. V.; Temmer, M.; Veronig, A. M., E-mail: ute.moestl@uni-graz.at

2013-03-20

The Atmospheric Imaging Assembly on board the Solar Dynamics Observatory observed a coronal mass ejection with an embedded filament on 2011 February 24, revealing quasi-periodic vortex-like structures at the northern side of the filament boundary with a wavelength of approximately 14.4 Mm and a propagation speed of about 310 {+-} 20 km s{sup -1}. These structures could result from the Kelvin-Helmholtz instability occurring on the boundary. We perform 2.5D numerical simulations of the Kelvin-Helmholtz instability and compare the simulated characteristic properties of the instability with the observations, where we obtain qualitative as well as quantitative accordance. We study the absencemore » of Kelvin-Helmholtz vortex-like structures on the southern side of the filament boundary and find that a magnetic field component parallel to the boundary with a strength of about 20% of the total magnetic field has stabilizing effects resulting in an asymmetric development of the instability.« less

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

PubMed

Park, H M; Lee, W M

2008-01-15

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

Kelvin-Helmholtz versus Hall magnetoshear instability in astrophysical flows.

PubMed

Gómez, Daniel O; Bejarano, Cecilia; Mininni, Pablo D

2014-05-01

We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well-known macroscopic and ideal shear-driven instability. In sufficiently low-density plasmas, also the microscopic Hall magnetoshear instability can take place. We performed three-dimensional simulations of the Hall-magnetohydrodynamic equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magnetoshear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.

A high-temperature superconducting Helmholtz probe for microscopy at 9.4 T.

PubMed

Hurlston, S E; Brey, W W; Suddarth, S A; Johnson, G A

1999-05-01

The design and operation of a high-temperature superconducting (HTS) probe for magnetic resonance microscopy (MRM) at 400 MHz are presented. The design of the probe includes a Helmholtz coil configuration and a stable open-cycle cooling mechanism. Characterization of coil operating parameters is presented to demonstrate the suitability of cryo-cooled coils for MRM. Specifically, the performance of the probe is evaluated by comparison of signal-to-noise (SNR) performance with that of a copper Helmholtz pair, analysis of B1 field homogeneity, and quantification of thermal stability. Images are presented to demonstrate the SNR advantage of the probe for typical MRM applications.

[Scientific theoretical founding of medicine as a natural science by Hermann von Helmholtz (1821-1894)].

PubMed

Neumann, J N

1994-01-01

In this study an attempt will be made to discuss the epistemological problems in the theory and practice of modern technical medicine in the writings of Hermann von Helmholz. An inquiry into the relationship between von Helmholtz' thinking and the critical philosophy of Immanuel Kant is followed by the characteristics of von Helmholtz' philosophy of science which he himself called "empirical theory". The question of medicine as a science finally leads to the main problem of medical epistemology, viz., the relationship between theoretical knowledge and practice in medicine. In this context the anthropological dimension is brought into consideration.

Kelvin-Helmholtz instability in a single-component atomic superfluid

NASA Astrophysics Data System (ADS)

Baggaley, A. W.; Parker, N. G.

2018-05-01

We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single-component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counterflowing channels, we seed a line of quantized vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behavior of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantized vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.

Active exterior cloaking for the 2D Laplace and Helmholtz equations.

PubMed

Vasquez, Fernando Guevara; Milton, Graeme W; Onofrei, Daniel

2009-08-14

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.

Development of a high-sensitivity and portable cell using Helmholtz resonance for noninvasive blood glucose-level measurement based on photoacoustic spectroscopy.

PubMed

Tachibana, K; Okada, K; Kobayashi, R; Ishihara, Y

2016-08-01

We describe the possibility of high-sensitivity noninvasive blood glucose measurement based on photoacoustic spectroscopy (PAS). The demand for noninvasive blood glucose-level measurement has increased due to the explosive increase in diabetic patients. We have developed a noninvasive blood glucose-level measurement based on PAS. The conventional method uses a straight-type resonant cell. However, the cell volume is large, which results in a low detection sensitivity and difficult portability. In this paper, a small-sized Helmholtz-type resonant cell is proposed to improve detection sensitivity and portability by reducing the cell dead volume. First, the acoustic property of the small-sized Helmholtz-type resonant cell was evaluated by performing an experiment using a silicone rubber. As a result, the detection sensitivity of the small-sized Helmholtz-type resonant cell was approximately two times larger than that of the conventional straight-type resonant cell. In addition, the inside volume was approximately 30 times smaller. Second, the detection limits of glucose concentration were estimated by performing an experiment using glucose solutions. The experimental results showed that a glucose concentration of approximately 1% was detected by the small-sized Helmholtz-type resonant cell. Although these results on the sensitivity of blood glucose-level measurement are currently insufficient, they suggest that miniaturization of a resonance cell is effective in the application of noninvasive blood glucose-level measurement.

Acoustic metamaterial plate embedded with Helmholtz resonators for extraordinary sound transmission loss

NASA Astrophysics Data System (ADS)

Yamamoto, Takashi

2018-06-01

A new acoustic metamaterial plate (AMP) is proposed herein. The plate incorporates Helmholtz resonators that are periodically embedded at intervals shorter than acoustic wavelengths. This metamaterial plate exhibits extraordinary sound transmission loss (STL) at the resonance frequency of the Helmholtz resonators compared to a conventional flat plate. The STL of the AMP can be theoretically analyzed using the effective mass density and flexural rigidity. At the resonant frequency, the dynamic density of the AMP becomes much larger than that of a conventional solid flat plate with the same mass. When the Helmholtz resonant frequency is tuned to the coincidence frequency of the AMP, the dip in transmission loss owing to the coincidence effect is not observed. The frequency band, wherein high STL occurs, is narrow; however, the frequency band can be widened by embedding multiple resonators with slightly different resonant frequencies. Numerical experiments are also performed to demonstrate the acoustic performance of the proposed system. In the simulation, Helmholtz resonators with the 2.1-kHz resonant frequency are embedded at 20-mm intervals inside a 6-mm-thick flat glass plate. Analytical solutions of this system agree well with numerical solutions for various incidence angles of incoming plane waves. In this configuration, we find that the degradation of STL caused by the coincidence effect is nearly eliminated for waves that are incident at random angles.

An efficient calibration method for SQUID measurement system using three orthogonal Helmholtz coils

NASA Astrophysics Data System (ADS)

Hua, Li; Shu-Lin, Zhang; Chao-Xiang, Zhang; Xiang-Yan, Kong; Xiao-Ming, Xie

2016-06-01

For a practical superconducting quantum interference device (SQUID) based measurement system, the Tesla/volt coefficient must be accurately calibrated. In this paper, we propose a highly efficient method of calibrating a SQUID magnetometer system using three orthogonal Helmholtz coils. The Tesla/volt coefficient is regarded as the magnitude of a vector pointing to the normal direction of the pickup coil. By applying magnetic fields through a three-dimensional Helmholtz coil, the Tesla/volt coefficient can be directly calculated from magnetometer responses to the three orthogonally applied magnetic fields. Calibration with alternating current (AC) field is normally used for better signal-to-noise ratio in noisy urban environments and the results are compared with the direct current (DC) calibration to avoid possible effects due to eddy current. In our experiment, a calibration relative error of about 6.89 × 10-4 is obtained, and the error is mainly caused by the non-orthogonality of three axes of the Helmholtz coils. The method does not need precise alignment of the magnetometer inside the Helmholtz coil. It can be used for the multichannel magnetometer system calibration effectively and accurately. Project supported by the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB04020200) and the Shanghai Municipal Science and Technology Commission Project, China (Grant No. 15DZ1940902).

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.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

PubMed

Mitri, Farid G

2015-10-01

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Reconnection properties in Kelvin-Helmholtz instabilities

NASA Astrophysics Data System (ADS)

Vernisse, Y.; Lavraud, B.; Eriksson, S.; Gershman, D. J.; Dorelli, J.; Pollock, C. J.; Giles, B. L.; Aunai, N.; Avanov, L. A.; Burch, J.; Chandler, M. O.; Coffey, V. N.; Dargent, J.; Ergun, R.; Farrugia, C. J.; Genot, V. N.; Graham, D.; Hasegawa, H.; Jacquey, C.; Kacem, I.; Khotyaintsev, Y. V.; Li, W.; Magnes, W.; Marchaudon, A.; Moore, T. E.; Paterson, W. R.; Penou, E.; Phan, T.; Retino, A.; Schwartz, S. J.; Saito, Y.; Sauvaud, J. A.; Schiff, C.; Torbert, R. B.; Wilder, F. D.; Yokota, S.

2017-12-01

Kelvin-Helmholtz instabilities are particular laboratories to study strong guide field reconnection processes. In particular, unlike the usual dayside magnetopause, the conditions across the magnetopause in KH vortices are quasi-symmetric, with low differences in beta and magnetic shear angle. We study these properties by means of statistical analysis of the high-resolution data of the Magnetospheric Multiscale mission. Several events of Kelvin-Helmholtz instabilities pas the terminator plane and a long lasting dayside instabilities event where used in order to produce this statistical analysis. Early results present a consistency between the data and the theory. In addition, the results emphasize the importance of the thickness of the magnetopause as a driver of magnetic reconnection in low magnetic shear events.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

The Riemann-Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas' scheme.

Summary Reviews of Soil Stabilization Processes. Report 7. Electrical Stabilization of Fine-Grained Soils

DTIC Science & Technology

1961-10-01

Observations . . . . . . . .................. 3 Double Layer Theory ................. .... 4 The Electroosmotic Phenomenon in Soils . . . . ... 6 Helmholtz...lL PART III: EFFECTS OF ELECTROOSMOSIS . ............. .. 133 Electroosmotic Dewatering ........ ................ ... 13 Electroosmotic ... electroosmotic flow based on the theories of Helmholtz-Smoluchowski and Schmid are compared. It is apparent that the applicability of the theoretical concepts

Observations of Kelvin-Helmholtz Waves Along the Dusk-Side Boundary of Mercury's Magnetosphere During MESSENGER's Third Flyby

NASA Technical Reports Server (NTRS)

Boardsen, Scott A.; Sundberg, Torgjoern; Slavin, James A.; Anderson, Brian J.; Korth, Haje; Solomon, Sean C.; Blomberg, Lars G.

2010-01-01

During the third MESSENGER flyby of Mercury on 29 September 2009, 15 crossings of the dusk-side magnetopause were observed in the magnetic field data over a 2-min period, during which the spacecraft traveled a distance of 0.2 R(sub M) (where R(sub M) is Mercury's radius). The quasi-periodic nature of the magnetic field variations during the crossings, the characteristic time separations of approx.16 s between pairs of crossings, and the variations of the magnetopause normal directions indicate that the signals are likely the signature of surface waves highly steepened at their leading edge that arose from the Kelvin-Helmholtz instability. At Earth, the Kelvin- Helmholtz instability is believed to lead to the turbulent transport of solar wind plasma into Earth's plasma sheet. This solar wind entry mechanism could also be important at Mercury. Citation: Boardsen, S. A., T. Sundberg, J. A.Slavin, B. J. Anderson, H. Korth, S. C. Solomon, and L. G. Blomberg (2010), Observations of Kelvin-Helmholtz waves along the dusk-side boundary of Mercury s magnetosphere during MESSENGER's third flyby,

Kelvin-Helmholtz waves in extratropical cyclones passing over mountain ranges: KH Waves in Extratropical Cyclones over Mountain Ranges

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

Medina, Socorro; Houze, Robert A.

2016-02-19

Kelvin–Helmholtz billows with horizontal scales of 3–4 km have been observed in midlatitude cyclones moving over the Italian Alps and the Oregon Cascades when the atmosphere was mostly statically stable with high amounts of shear and Ri < 0.25. In one case, data from a mobile radar located within a windward facing valley documented a layer in which the shear between down-valley flow below 1.2 km and strong upslope cross-barrier flow above was large. Several episodes of Kelvin–Helmholtz waves were observed within the shear layer. The occurrence of the waves appears to be related to the strength of the shear:more » when the shear attained large values, an episode of billows occurred, followed by a sharp decrease in the shear. The occurrence of large values of shear and Kelvin–Helmholtz billows over two different mountain ranges suggests that they may be important features occurring when extratropical cyclones with statically stable flow pass over mountain ranges.« less

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.

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Nonexistence of exact solutions agreeing with the Gaussian beam on the beam axis or in the focal plane

NASA Astrophysics Data System (ADS)

Lekner, John; Andrejic, Petar

2018-01-01

Solutions of the Helmholtz equation which describe electromagnetic beams (and also acoustic or particle beams) are discussed. We show that an exact solution which reproduces the Gaussian beam waveform on the beam axis does not exist. This is surprising, since the Gaussian beam is a solution of the paraxial equation, and thus supposedly accurate on and near the beam axis. Likewise, a solution of the Helmholtz equation which exactly reproduces the Gaussian beam in the focal plane does not exist. We show that the last statement also holds for Bessel-Gauss beams. However, solutions of the Helmholtz equation (one of which is discussed in detail) can approximate the Gaussian waveform within the central focal region.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

Kiselev, Aleksei P; Plachenov, Alexandr B

2016-04-01

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell.

PubMed

Meignin, L; Gondret, P; Ruyer-Quil, C; Rabaud, M

2003-06-13

We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.

On finite element methods for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Aziz, A. K.; Werschulz, A. G.

1979-01-01

The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.

Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

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

Morgan, Brandon E.; Schilling, Oleg; Hartland, Tucker A.

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessarymore » to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.« less

Dual-frequency sound-absorbing metasurface based on visco-thermal effects with frequency dependence

NASA Astrophysics Data System (ADS)

Ryoo, H.; Jeon, W.

2018-03-01

We investigate theoretically an acoustic metasurface with a high absorption coefficient at two frequencies and design it from subwavelength structures. We propose the use of a two-dimensional periodic array of four Helmholtz resonators in two types to obtain a metasurface with nearly perfect sound absorption at given target frequencies via interactions between waves emanating from different resonators. By considering how fluid viscosity affects acoustic energy dissipation in the narrow necks of the Helmholtz resonators, we obtain effective complex-valued material properties that depend on frequency and on the geometrical parameters of the resonators. We furthermore derive the effective acoustic impedance of the metasurface from the effective material properties and calculate the absorption spectra from the theoretical model, which we compare with the spectra obtained from a finite-element simulation. As a practical application of the theoretical model, we derive empirical formulas for the geometrical parameters of a metasurface which would yield perfect absorption at a given frequency. While previous works on metasurfaces based on Helmholtz resonators aimed to absorb sound at single frequencies, we use optimization to design a metasurface composed of four different Helmholtz resonators to absorb sound at two distinct frequencies.

Numerical investigation on an array of Helmholtz resonators for the reduction of micro-pressure waves in modern and future high-speed rail tunnel systems

NASA Astrophysics Data System (ADS)

Tebbutt, J. A.; Vahdati, M.; Carolan, D.; Dear, J. P.

2017-07-01

Previous research has proposed that an array of Helmholtz resonators may be an effective method for suppressing the propagation of pressure and sound waves, generated by a high-speed train entering and moving in a tunnel. The array can be used to counteract environmental noise from tunnel portals and also the emergence of a shock wave in the tunnel. The implementation of an array of Helmholtz resonators in current and future high-speed train-tunnel systems is studied. Wave propagation in the tunnel is modelled using a quasi-one-dimensional formulation, accounting for non-linear effects, wall friction and the diffusivity of sound. A multi-objective genetic algorithm is then used to optimise the design of the array, subject to the geometric constraints of a demonstrative tunnel system and the incident wavefront in order to attenuate the propagation of pressure waves. It is shown that an array of Helmholtz resonators can be an effective countermeasure for various tunnel lengths. In addition, the array can be designed to function effectively over a wide operating envelope, ensuring it will still function effectively as train speeds increase into the future.

Effect of grazing flow on the acoustic impedance of Helmholtz resonators consisting of single and clustered orifices

NASA Technical Reports Server (NTRS)

Hersch, A. S.; Walker, B.

1979-01-01

A semiempirical fluid mechanical model is derived for the acoustic behavior of thin-walled single orifice Helmholtz resonators in a grazing flow environment. The incident and cavity sound fields are connected in terms of an orifice discharge coefficient whose values are determined experimentally using the two-microphone method. Measurements show that at high grazing flow speeds, acoustical resistance is almost linearly proportional to the grazing flow speed and almost independent of incident sound pressure. The corresponding values of reactance are much smaller and tend towards zero. For thicker-walled orifice plates, resistance and reactance were observed to be less sensitive to grazing flow as the ratio of plate thickness to orifice diameter increased. Loud tones were observed to radiate from a single orifice Helmholtz resonator due to interaction between the grazing flow shear layer and the resonator cavity. Measurements showed that the tones radiated at a Strouhal number equal to 0.26. The effects of grazing flow on the impedance of Helmholtz resonators consisting of clusters of orifices was also studied. In general, both resistance and reaction were found to be virtually independent of orifice relative spacing and number. These findings are valid with and without grazing flow.

Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

DOE PAGES

Morgan, Brandon E.; Schilling, Oleg; Hartland, Tucker A.

2018-01-10

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessarymore » to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.« less

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)

A low frequency acoustic insulator by using the acoustic metasurface to a Helmholtz resonator

NASA Astrophysics Data System (ADS)

Zhao, Xiang; Cai, Li; Yu, Dianlong; Lu, Zhimiao; Wen, Jihong

2017-06-01

Acoustic metasurfaces (AMSs) are able to manipulate wavefronts at an anomalous angle through a subwavelength layer. Their application provide a new way to control sound waves in addition to traditional materials. In this work, we introduced the AMS into the design of a Helmholtz resonator (HR) and studied the acoustic transmission through the modified HR in a pipe with one branch. The variation of sound insulation capacity with the phase gradient of the AMS was studied, and the results show that the AMS can remarkably lower the frequency band of the sound insulation without increasing the size. Our investigation provides a new degree of freedom for acoustic control with a Helmholtz resonator, which is of great significance in acoustic metasurface theory and sound insulation design.

Acoustic superlens using Helmholtz-resonator-based metamaterials

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

Yang, Xishan; Yin, Jing; Yu, Gaokun, E-mail: gkyu@ouc.edu.cn

2015-11-09

Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between themore » neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range.« less

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.

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.

Lattice-Gas Automata Fluids on Parallel Supercomputers

DTIC Science & Technology

1993-11-23

Kelvin-Helmholtz shear instabil- ity, and the Von Karman vortex shedding instability. Performance of the two machines in terms of both site update... PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Phillips Laboratory,Hanscom Field,MA,01731 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING...Helmholtz shear instability, and the Von Karman vortex shedding instability. Performance of the two machines in terms of both site update rate and

Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

DTIC Science & Technology

2015-09-14

discontinuous Galerkin method for the numerical solution of the Helmholtz equation , J. Comp. Phys., 290, 318–335, 2015. [14] N.C. NGUYEN, J. PERAIRE...approximations of the Helmholtz equation for a very wide range of wave frequencies. Our approach combines the hybridizable discontinuous Galerkin methodology...local approximation spaces of the hybridizable discontinuous Galerkin methods with precomputed phases which are solutions of the eikonal equation in

Uncertainty in Damage Detection, Dynamic Propagation and Just-in-Time Networks

DTIC Science & Technology

2015-08-03

estimated parameter uncertainty in dynamic data sets; high order compact finite difference schemes for Helmholtz equations with discontinuous wave numbers...delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the...schemes for Helmholtz equations with discontinuous wave numbers across interfaces. • We carried out numerical sensitivity analysis with respect to

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.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Can Hall effect trigger Kelvin-Helmholtz instability in sub-Alfvénic flows?

NASA Astrophysics Data System (ADS)

Pandey, B. P.

2018-05-01

In the Hall magnetohydrodynamics, the onset condition of the Kelvin-Helmholtz instability is solely determined by the Hall effect and is independent of the nature of shear flows. In addition, the physical mechanism behind the super- and sub-Alfvénic flows becoming unstable is quite different: the high-frequency right circularly polarized whistler becomes unstable in the super-Alfvénic flows whereas low-frequency, left circularly polarized ion-cyclotron wave becomes unstable in the presence of sub-Alfvénic shear flows. The growth rate of the Kelvin-Helmholtz instability in the super-Alfvénic case is higher than the corresponding ideal magnetohydrodynamic rate. In the sub-Alfvénic case, the Hall effect opens up a new, hitherto inaccessible (to the magnetohydrodynamics) channel through which the partially or fully ionized fluid can become Kelvin-Helmholtz unstable. The instability growth rate in this case is smaller than the super-Alfvénic case owing to the smaller free shear energy content of the flow. When the Hall term is somewhat smaller than the advection term in the induction equation, the Hall effect is also responsible for the appearance of a new overstable mode whose growth rate is smaller than the purely growing Kelvin-Helmholtz mode. On the other hand, when the Hall diffusion dominates the advection term, the growth rate of the instability depends only on the Alfvén -Mach number and is independent of the Hall diffusion coefficient. Further, the growth rate in this case linearly increases with the Alfvén frequency with smaller slope for sub-Alfvénic flows.

Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

PubMed

Solano-Altamirano, J M; Goldman, Saul

2015-12-01

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

NASA Technical Reports Server (NTRS)

Sun, Xian-He; Zhuang, Yu

1997-01-01

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

Investigation of the Helmholtz-Kohlrausch effect using wide-gamut display

NASA Astrophysics Data System (ADS)

Oh, Semin; Kwak, Youngshin

2015-01-01

The aim of this study is to investigate whether the Helmholtz-Kohlrausch effect exists among the images having various luminance and chroma levels. Firstly, five images were selected. Then each image was adjusted to have 4 different average CIECAM02 C and 5 different average CIECAM02 J. In total 20 test images were generated per each image for the psychophysical experiment. The psychophysical experiment was done in a dark room using a LCD display. To evaluate the overall perceived brightness of images a magnitude estimation method was used. Fifteen participants evaluated the brightness of each image comparing with the reference image. As a result, participants tended to evaluate the brightness higher as the average CIECAM02 J and also CIECAM02 C of the image increases proving the Helmholtz- Kohlrausch effect in images.

Dual-band wide-angle metamaterial perfect absorber based on the combination of localized surface plasmon resonance and Helmholtz resonance.

PubMed

Zhang, Changlei; Huang, Cheng; Pu, Mingbo; Song, Jiakun; Zhao, Zeyu; Wu, Xiaoyu; Luo, Xiangang

2017-07-18

In this article, a dual-band wide-angle metamaterial perfect absorber is proposed to achieve absorption at the wavelength where laser radar operates. It is composed of gold ring array and a Helmholtz resonance cavity spaced by a Si dielectric layer. Numerical simulation results reveal that the designed absorber displays two absorption peaks at the target wavelength of 10.6 μm and 1.064 μm with the large frequency ratio and near-unity absorptivity under the normal incidence. The wide-angle absorbing property and the polarization-insensitive feature are also demonstrated. Localized surface plasmons resonance and Helmholtz resonance are introduced to analyze and interpret the absorbing mechanism. The designed perfect absorber can be developed for potential applications in infrared stealth field.

Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

NASA Astrophysics Data System (ADS)

Coelho, Rodrigo C. V.; Mendoza, Miller; Doria, Mauro M.; Herrmann, Hans J.

2017-11-01

We provide numerical evidence that a Kelvin-Helmholtz instability occurs in the Dirac fluid of electrons in graphene and can be detected in current experiments. This instability appears for electrons in the viscous regime passing though a micrometer-scale obstacle and affects measurements on the time scale of nanoseconds. A possible realization with a needle-shaped obstacle is proposed to produce and detect this instability by measuring the electric potential difference between contact points located before and after the obstacle. We also show that, for our setup, the Kelvin-Helmholtz instability leads to the formation of whirlpools similar to the ones reported in Bandurin et al. [Science 351, 1055 (2016), 10.1126/science.aad0201]. To perform the simulations, we develop a lattice Boltzmann method able to recover the full dissipation in a fluid of massless particles.

Bruit généré par un écoulement turbulent affleurant une cavité à faible nombre de Mach : application aux césures de portes automobiles

NASA Astrophysics Data System (ADS)

Da Silva, Arthur; Kribèche, Ali; Loredo, Alexandre

2009-02-01

Noise produced by turbulent grazing flow over a generic cavity representing car door cavities was measured in a semi-anechoic wind tunnel. Two cavities were studied: one 50 mm large (dimension perpendicular to the airflow), functioning as a Helmholtz resonator, reaching sound pressure levels of 136 dB at 1776 Hz, for a downstream velocity of 54 m/s. The other, of scale 250 mm could not be regarded as a Helmholtz resonator although resonance occurred at 1902 Hz, at a level of 125 dB, for the same velocity. In both cases, noise was caused by Kelvin-Helmholtz instabilities in the mixing layer. To cite this article: A. Da Silva et al., C. R. Mecanique 337 (2009).

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.

A numerical analysis of the Born approximation for image formation modeling of differential interference contrast microscopy for human embryos

NASA Astrophysics Data System (ADS)

Trattner, Sigal; Feigin, Micha; Greenspan, Hayit; Sochen, Nir

2008-03-01

The differential interference contrast (DIC) microscope is commonly used for the visualization of live biological specimens. It enables the view of the transparent specimens while preserving their viability, being a non-invasive modality. Fertility clinics often use the DIC microscope for evaluation of human embryos quality. Towards quantification and reconstruction of the visualized specimens, an image formation model for DIC imaging is sought and the interaction of light waves with biological matter is examined. In many image formation models the light-matter interaction is expressed via the first Born approximation. The validity region of this approximation is defined in a theoretical bound which limits its use to very small specimens with low dielectric contrast. In this work the Born approximation is investigated via the Helmholtz equation, which describes the interaction between the specimen and light. A solution on the lens field is derived using the Gaussian Legendre quadrature formulation. This numerical scheme is considered both accurate and efficient and has shortened significantly the computation time as compared to integration methods that required a great amount of sampling for satisfying the Whittaker - Shannon sampling theorem. By comparing the numerical results with the theoretical values it is shown that the theoretical bound is not directly relevant to microscopic imaging and is far too limiting. The numerical exhaustive experiments show that the Born approximation is inappropriate for modeling the visualization of thick human embryos.

Investigating Cell-Material Interactions of Magnetospirillum magneticum as an Approach for Probing Submerged Surface Structural Integrity

DTIC Science & Technology

2012-07-01

developed a microscope- based , offset Helmholtz coil system with a custom-designed microcontroller. We have developed a microfabrication approach for...implemented an experimental model system using ferromagnetic beads. We have applied direct and frequency based magnetic fields for controlling magnetotactic...fields. Expanded Accomplishments We have developed a microscope- based , offset Helmholtz coil system with a custom- designed microcontroller. To be

Distance Estimation to Flashes in a Simulated Night Vision Environment

DTIC Science & Technology

2007-12-01

indirect perception, which has influenced theorists since, is Hermann von Helmholtz’s theory of unconscious conclusions or unconscious inference [6...Goldstein et al. (Eds.), Blackwell handbook of perception (pp. 53-91). Malden, MA: Blackwell Publishers. [6] Helmholtz, H. von (1867/1925). Treatise on...physiological optics (from 3rd German edition, Vol. III). New York: Dover Publications. [7] Helmholtz, H. von (1878/1968). The facts of perception. In

Corrigendum to "Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer" [J. Magn. Reson. 230 (2013) 88-97

NASA Astrophysics Data System (ADS)

Müller, Dirk K.; Pampel, André; Möller, Harald E.

2015-12-01

In the print version of this article initially published, reference to a funding source was missing. The following information should be added to the Acknowledgements section: This work was funded (in part) by the Helmholtz Alliance ICEMED-Imaging and Curing Environmental Metabolic Diseases, through the Initiative and Networking Fund of the Helmholtz Association.

Three-Dimensional Shallow Water Acoustics

DTIC Science & Technology

2015-09-30

converts the Helmholtz wave equation of elliptic type to a one-way wave equation of parabolic type. The conversion allows efficient marching solution ...algorithms for 2 solving the boundary value problem posed by the Helmholtz equation . This can reduce significantly the requirement for computational...Fourier parabolic- equation sound propagation solution scheme," J. Acoust. Soc. Am, vol. 132, pp. EL61-EL67 (2012). [6] Y.-T. Lin, J.M. Collis and T.F

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Pulsation damping of the reciprocating compressor with Helmholtz resonator

NASA Astrophysics Data System (ADS)

Wang, W.; Zhang, Y.; Zhou, Q.; Peng, X.; Feng, J.; Jia, X.

2017-08-01

Research presented in this paper investigated the mounting of a Helmholtz resonator near the valve chamber of a reciprocating compressor to attenuate the gas pulsation in the valve chamber as well as the pipeline downstream. Its attenuation characteristics were simulated with the plane wave theory together with the transfer matrix method, and the damping effect was checked by comparing the pressure pulsation levels before and after mounting the resonator. The results show that the Helmholtz resonator was effective in attenuating the gas pulsation in the valve chamber and piping downstream, and the pulsation level was decreased by 40% in the valve chamber and 30% at maximum in the piping downstream. The damping effect of the resonator was sensitive to its resonant frequency, and various resonators working simultaneously didn’t interfere with each other. When two resonators were mounted in parallel, with resonant frequencies equal to the second and fourth harmonic frequencies, the pressure pulsation components corresponding to the resonant frequencies were remarkably decreased at the same time, while the pulsation levels at other harmonic frequencies kept almost unchanged. After a series of simulations and experiments a design criterion of chock tube and volume parameter has been proposed for the targeted frequencies to be damped. Furthermore, the frequency-adjustable Helmholtz resonator which was applied to the variable speed compressor was investigated.

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…

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.

Generalized Optical Theorem Detection in Random and Complex Media

NASA Astrophysics Data System (ADS)

Tu, Jing

The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar optical theorem theory applies to arbitrary lossless backgrounds and quite general probing fields including near fields which play a key role in super-resolution imaging. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. Furthermore, the generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks, invisible scatterers, and wireless communications. The latter developments have important military applications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a reactive optical theorem related to the reactive power changes. Meanwhile, the developed approach naturally leads to three optical theorem indicators or statistics, which can be used to detect changes or targets in unknown complex media. In addition, the optical theorem theory is generalized in the time domain so that it applies to arbitrary full vector fields, and arbitrary media including anisotropic media, nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The second component of this Ph.D. research program focuses on the application of the optical theorem to change detection. Three different forms of indicators or statistics are developed for change detection in unknown background media: a real power optical theorem detector, a reactive power optical theorem detector, and a total apparent power optical theorem detector. No prior knowledge is required of the background or the change or target. The performance of the three proposed optical theorem detectors is compared with the classical energy detector approach for change detection. The latter uses a mathematical or functional energy while the optical theorem detectors are based on real physical energy. For reference, the optical theorem detectors are also compared with the matched filter approach which (unlike the optical theorem detectors) assumes perfect target and medium information. The practical implementation of the optical theorem detectors is based for certain random and complex media on the exploitation of time reversal focusing ideas developed in the past 20 years in electromagnetics and acoustics. In the final part of the dissertation, we also discuss the implementation of the optical theorem sensors for one-dimensional propagation systems such as transmission lines. We also present a new generalized likelihood ratio test for detection that exploits a prior data constraint based on the optical theorem. Finally, we also address the practical implementation of the optical theorem sensors for optical imaging systems, by means of holography. The later is the first holographic implementation the optical theorem for arbitrary scenes and targets.

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.

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.

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.

Cartridge Casing Catcher With Reduced Firearm Ejection Port Flash and Noise

DTIC Science & Technology

2009-05-26

acoustic tuner structure comprises at least one of a quarter wave tuner, a Quincke tuner, and a Helmholtz tuner. The magnetic material comprises magnetic...of noise) will be attenuated. FIG. 2B illustrates a Herschel- Quincke (usually simply called Quincke ) or interference tuner 10’. The Quincke tnner... Quincke tuner, and a Helmholtz resonator similar to the acoustic tnners illustrated in FIGS. 2(A-C), respectively. The acoustic tnner structure 240 of

On uniformly valid high-frequency far-field asymptotic solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Mcaninch, G. L.

1986-01-01

An asymptotic, large wave number approximation for the Helmholtz equation is derived. The theory is an extension of the geometric acoustic theory, and provides corrections to that theory in the form of multiplicative functions which satisfy parabolic equations. A simple example is used both to illustrate failure of the geometric theory for large propagation distances, and to show the improvement obtained by use of the new theory.

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

NASA Astrophysics Data System (ADS)

Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

2017-12-01

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

Voluntarism in early psychology: the case of Hermann von Helmholtz.

PubMed

De Kock, Liesbet

2014-05-01

The failure to recognize the programmatic similarity between (post-)Kantian German philosophy and early psychology has impoverished psychology's historical self-understanding to a great extent. This article aims to contribute to recent efforts to overcome the gaps in the historiography of contemporary psychology, which are the result of an empiricist bias. To this end, we present an analysis of the way in which Hermann von Helmholtz's theory of perception resonates with Johann Gottlieb Fichte's Ego-doctrine. It will be argued that this indebtedness is particularly clear when focusing on the foundation of the differential awareness of subject and object in perception. In doing so, the widespread reception of Helmholtz's work as proto-positivist or strictly empiricist is challenged, in favor of the claim that important elements of his theorizing can only be understood properly against the background of Fichte's Ego-doctrine. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Magnetic propulsion of a magnetic device using three square-Helmholtz coils and a square-Maxwell coil.

PubMed

Ha, Yong H; Han, Byung H; Lee, Soo Y

2010-02-01

We introduce a square coil system for remote magnetic navigation of a magnetic device without any physical movements of the coils. We used three square-Helmholtz coils and a square-Maxwell coil for magnetic propulsion of a small magnet along the desired path. All the square coils are mountable on a cubic frame that has an opening to accommodate a living subject. The square-Helmholtz coils control the magnetic propulsion direction by generating uniform magnetic field along the desired direction while the square-Maxwell coil controls the propulsion force by generating magnetic gradient field. We performed magnetic propulsion experiments with a down-scaled coil set and a three-channel coil driver. Experimental results demonstrate that we can use the square coil set for magnetic navigation of a magnetic device without any physical movements of the coils.

Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma. [solar wind-magnetosphere interaction

NASA Technical Reports Server (NTRS)

Miura, A.; Pritchett, P. L.

1982-01-01

A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.

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…

Optical Properties of a Bio-Inspired Gradient Refractive Index Polymer Lens

DTIC Science & Technology

2008-07-21

Optical properties of a bio-inspired gradient refractive index polymer lens G. Beadie,1,* James S. Shirk,1 A. Rosenberg,1 Paul A. Lane,1 E. Fleet,1...of magnitude less than the homogeneous glass lens. ©2008 Optical Society of America OCIS codes: (110.2760) Gradient-index lenses; (160.5470...H. von Helmholtz, A. Gullstrand, J. von Kries, and W. Nagel, Helmholtz’s Treatise on Physiological Optics (The Optical Society of America, Rochester

Electromagnetic stress tensor for an amorphous metamaterial medium

NASA Astrophysics Data System (ADS)

Wang, Neng; Wang, Shubo; Ng, Jack

2018-03-01

We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.

Analysis of Double Layer and Adsorption Effects at the Alkaline Polymer Electrolyte-Electrode Interface

DTIC Science & Technology

2011-10-05

anion exchange mem - branes (AEM) are an attractive alternative to proton exchange mem - brane (PEM) fuel cells.1, 2 From electrocatalysts standpoint...gener- ally broken down into three distinct regions: the inner Helmholtz plane (IHP), the outer Helmholtz plane ( OHP ), and the diffuse layer. Figure 11...closest approach and is defined as OHP at a distance, x2. Nonspecifically adsorbed ions are distributed in a three dimensional region, called diffuse layer

Large-Scale Integration of Solid-State Microfluidic Valves With No Moving Parts

DTIC Science & Technology

2005-01-01

compact and diffuse layer is called outer Helmholtz plane ( OHP ). Potential drop across the diffusion layer is called the zeta potential, ζ. As the...Gouy-Chapman model. This is shown in Fig. 3. The plane at x2 is called the outer Helmholtz plane ( OHP ). Then the total double layer capacitance Cd...Enhanced Electro-Osmotic Pumping With Liquid Bridge and Field Effect Flow Rectification, ” Presented in IEEE MEMS 2004 Conference, Maastricht, The

On the solution of the Helmholtz equation on regions with corners.

PubMed

Serkh, Kirill; Rokhlin, Vladimir

2016-08-16

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

Excitation of Kelvin Helmholtz instability by an ion beam in a plasma with negatively charged dust grains

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

Rani, Kavita; Sharma, Suresh C.

2015-02-15

An ion beam propagating through a magnetized dusty plasma drives Kelvin Helmholtz Instability (KHI) via Cerenkov interaction. The frequency of the unstable wave increases with the relative density of negatively charged dust grains. It is observed that the beam has stabilizing effect on the growth rate of KHI for low shear parameter, but for high shear parameter, the instability is destabilized with relative density of negatively charged dust grains.

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

On the solution of the Helmholtz equation on regions with corners

PubMed Central

Serkh, Kirill; Rokhlin, Vladimir

2016-01-01

In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples. PMID:27482110

Assessing the role of the Kelvin-Helmholtz instability at the QCD cosmological transition

NASA Astrophysics Data System (ADS)

Mourão Roque, V. R. C.; Lugones, G.

2018-03-01

We performed numerical simulations with the PLUTO code in order to analyze the non-linear behavior of the Kelvin-Helmholtz instability in non-magnetized relativistic fluids. The relevance of the instability at the cosmological QCD phase transition was explored using an equation of state based on lattice QCD results with the addition of leptons. The results of the simulations were compared with the theoretical predictions of the linearized theory. For small Mach numbers up to Ms ~ 0.1 we find that both results are in good agreement. However, for higher Mach numbers, non-linear effects are significant. In particular, many initial conditions that look stable according to the linear analysis are shown to be unstable according to the full calculation. Since according to lattice calculations the cosmological QCD transition is a smooth crossover, violent fluid motions are not expected. Thus, in order to assess the role of the Kelvin-Helmholtz instability at the QCD epoch, we focus on simulations with low shear velocity and use monochromatic as well as random perturbations to trigger the instability. We find that the Kelvin-Helmholtz instability can strongly amplify turbulence in the primordial plasma and as a consequence it may increase the amount of primordial gravitational radiation. Such turbulence may be relevant for the evolution of the Universe at later stages and may have an impact in the stochastic gravitational wave background.

The role of elastic stored energy in controlling the long term rheological behaviour of the lithosphere

NASA Astrophysics Data System (ADS)

Regenauer-Lieb, Klaus; Weinberg, Roberto F.; Rosenbaum, Gideon

2012-04-01

The traditional definition of lithospheric strength is derived from the differential stresses required to form brittle and ductile structures at a constant strain rate. This definition is based on dissipative brittle and ductile deformation and does not take into account the ability of the lithosphere to store elastic strain. Here we show the important role of elasticity in controlling the long-term behaviour of the lithosphere. This is particularly evident when describing deformation in a thermodynamic framework, which differentiates between stored (Helmholtz free energy) and dissipative (entropy) energy potentials. In our model calculations we stretch a continental lithosphere with a wide range of crustal thickness (30-60 km) and heat flow (50-80 mW/m2) at a constant velocity. We show that the Helmholtz free energy, which in our simple calculation describes the energy stored elastically, converges for all models within a 25% range, while the dissipated energy varies over an order of magnitude. This variation stems from complex patterns in the local strain distributions of the different models, which together operate to minimize the Helmholtz free energy. This energy minimization is a fundamental material behaviour of the lithosphere, which in our simple case is defined by its elastic properties. We conclude from this result that elasticity (more generally Helmholtz free energy) is an important regulator of the long-term geological strength of the lithosphere.

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

NASA Technical Reports Server (NTRS)

Rogers, Michael M.; Moser, Robert D.

1991-01-01

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Observation of single-mode, Kelvin-Helmholtz instability in a supersonic flow

DOE PAGES

Wan, W. C.; Malamud, Guy; Shimony, A.; ...

2015-10-01

This manuscript reports the first observations of the Kelvin-Helmholtz instability evolving from well-characterized seed perturbations in a steady, supersonic flow. The Kelvin-Helmholtz instability occurs when two fluids move parallel to one another at different velocities, and contributes to an intermixing of fluids and transition to turbulence. It is ubiquitous in nature and engineering, including terrestrial systems such as cloud formations, astrophysical systems such as supernovae, and laboratory systems such as fusion experiments. In a supersonic flow, the growth rate of the instability is inhibited due to effects of compressibility. These effects are still not fully understood, and hold the motivationmore » for the current work. The data presented here were obtained by developing a novel experimental platform capable of sustaining a steady shockwave over a precision-machined interface for unprecedented durations. The chosen interface was a well-characterized, single-mode sine wave, allowing us to document the evolution of individual vortices at high resolution. Understanding the behavior of individual vortices is the first of two fundamental steps towards developing a comprehensive model for the Kelvin-Helmholtz instability in a compressible flow. The results of this experiment were well reproduced with 2D hydrodynamic simulations. The platform has been extended to additional experiments, which study the evolution of different hydrodynamic instabilities in steady, supersonic flows.« less

Observation of single-mode, Kelvin-Helmholtz instability in a supersonic flow

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

Wan, W. C.; Malamud, Guy; Shimony, A.

This manuscript reports the first observations of the Kelvin-Helmholtz instability evolving from well-characterized seed perturbations in a steady, supersonic flow. The Kelvin-Helmholtz instability occurs when two fluids move parallel to one another at different velocities, and contributes to an intermixing of fluids and transition to turbulence. It is ubiquitous in nature and engineering, including terrestrial systems such as cloud formations, astrophysical systems such as supernovae, and laboratory systems such as fusion experiments. In a supersonic flow, the growth rate of the instability is inhibited due to effects of compressibility. These effects are still not fully understood, and hold the motivationmore » for the current work. The data presented here were obtained by developing a novel experimental platform capable of sustaining a steady shockwave over a precision-machined interface for unprecedented durations. The chosen interface was a well-characterized, single-mode sine wave, allowing us to document the evolution of individual vortices at high resolution. Understanding the behavior of individual vortices is the first of two fundamental steps towards developing a comprehensive model for the Kelvin-Helmholtz instability in a compressible flow. The results of this experiment were well reproduced with 2D hydrodynamic simulations. The platform has been extended to additional experiments, which study the evolution of different hydrodynamic instabilities in steady, supersonic flows.« less

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].

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

FY92 Progress Report for the Gyrotron Backward-Wave-Oscillator Experiment

DTIC Science & Technology

1993-07-01

C. SAMPLE CABLE CALIBRATION 23 D. ASYST CHANNEL SETUPS 26 E. SAMPLE MAGNET INPUT DATA DECK FOR THE GYRO-BWO 32 F. SAMPLE EGUN INPUT DATA DECK FOR THE...of the first coil of the Helmholtz pair; zero also corresponds to the diode end of the experiment). Another computer code used was the EGUN code (Ref...a short computer program was written to superimpose the two magnetic fields; DC and Helmholtz). An example of an EGUN input data file is included in

Spectral multigrid methods for the solution of homogeneous turbulence problems

NASA Technical Reports Server (NTRS)

Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

1987-01-01

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Diffraction of Electromagnetic Waves on a Waveguide Joint

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid; Tyutyunnik, Anastasiya; Nikolaev, Nikolai

2018-02-01

In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn't reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the "Hamiltonian form" to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

Nonlinear Evolution of the Kelvin-Helmholtz Instability in the High Latitude Ionosphere.

DTIC Science & Technology

1987-12-21

field. Both cases have been studied in the MHD [Mikhailovskii, 1974; Sen, 1964; -. Southwood, 19681 and electrostatic [D’Angelo, 1965; Smith and von ...1293, 1964. Smith, C.G. and S. von Goeler, Kelviri-Helmholtz instability for a collisionless plasma model, Phys. Fluids, 11, 2665,1968. Southwood...ELECTRIC COMPANY P.O. BOX 85154 SPACE DIVISION SAN DIEGO, CA 92138 VALLEY FORGE SPACE CENTER OCY ATTN J.L. SPERLING GODDARD BLVD KING OF PRUSSIA P.O. BOX

Magneto-mechanical modeling of electrical steel sheets

NASA Astrophysics Data System (ADS)

Aydin, U.; Rasilo, P.; Martin, F.; Singh, D.; Daniel, L.; Belahcen, A.; Rekik, M.; Hubert, O.; Kouhia, R.; Arkkio, A.

2017-10-01

A simplified multiscale approach and a Helmholtz free energy based approach for modeling the magneto-mechanical behavior of electrical steel sheets are compared. The models are identified from uniaxial magneto-mechanical measurements of two different electrical steel sheets which show different magneto-elastic behavior. Comparison with the available measurement data of the materials shows that both models successfully model the magneto-mechanical behavior of one of the studied materials, whereas for the second material only the Helmholtz free energy based approach is successful.

A transverse Kelvin-Helmholtz instability in a magnetized plasma

NASA Technical Reports Server (NTRS)

Kintner, P.; Dangelo, N.

1977-01-01

An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.

PubMed

Lin, Ying-Tsong; Duda, Timothy F

2012-08-01

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

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.

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.

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

NASA Astrophysics Data System (ADS)

Conway, John T.; Cohl, Howard S.

2010-06-01

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

Ammonia synthesis using magnetic induction method (MIM)

NASA Astrophysics Data System (ADS)

Puspitasari, P.; Razak, J. Abd; Yahya, N.

2012-09-01

The most challenging issues for ammonia synthesis is to get the high yield. New approach of ammonia synthesis by using Magnetic Induction Method (MIM) and the Helmholtz Coils has been proposed. The ammonia detection was done by using Kjeldahl Method and FTIR. The system was designed by using Autocad software. The magnetic field of MIM was vary from 100mT-200mT and the magnetic field for the Helmholtz coils was 14mT. The FTIR result shows that ammonia has been successfully formed at stretching peaks 1097,1119,1162,1236, 1377, and 1464 cm-1. UV-VIS result shows the ammonia bond at 195nm of wavelength. The ammonia yield was increase to 244.72μmole/g.h by using the MIM and six pairs of Helmholtz coils. Therefore this new method will be a new promising method to achieve the high yield ammonia at ambient condition (at 25δC and 1atm), under the Magnetic Induction Method (MIM).

Linear stability analysis of particle-laden hypopycnal plumes

NASA Astrophysics Data System (ADS)

Farenzena, Bruno Avila; Silvestrini, Jorge Hugo

2017-12-01

Gravity-driven riverine outflows are responsible for carrying sediments to the coastal waters. The turbulent mixing in these flows is associated with shear and gravitational instabilities such as Kelvin-Helmholtz, Holmboe, and Rayleigh-Taylor. Results from temporal linear stability analysis of a two-layer stratified flow are presented, investigating the behavior of settling particles and mixing region thickness on the flow stability in the presence of ambient shear. The particles are considered suspended in the transport fluid, and its sedimentation is modeled with a constant valued settling velocity. Three scenarios, regarding the mixing region thickness, were identified: the poorly mixed environment, the strong mixed environment, and intermediate scenario. It was observed that Kelvin-Helmholtz and settling convection modes are the two fastest growing modes depending on the particles settling velocity and the total Richardson number. The second scenario presents a modified Rayleigh-Taylor instability, which is the dominant mode. The third case can have Kelvin-Helmholtz, settling convection, and modified Rayleigh-Taylor modes as the fastest growing mode depending on the combination of parameters.

Turbulent mass transfer caused by vortex induced reconnection in collisionless magnetospheric plasmas.

PubMed

Nakamura, T K M; Hasegawa, H; Daughton, W; Eriksson, S; Li, W Y; Nakamura, R

2017-11-17

Magnetic reconnection is believed to be the main driver to transport solar wind into the Earth's magnetosphere when the magnetopause features a large magnetic shear. However, even when the magnetic shear is too small for spontaneous reconnection, the Kelvin-Helmholtz instability driven by a super-Alfvénic velocity shear is expected to facilitate the transport. Although previous kinetic simulations have demonstrated that the non-linear vortex flows from the Kelvin-Helmholtz instability gives rise to vortex-induced reconnection and resulting plasma transport, the system sizes of these simulations were too small to allow the reconnection to evolve much beyond the electron scale as recently observed by the Magnetospheric Multiscale (MMS) spacecraft. Here, based on a large-scale kinetic simulation and its comparison with MMS observations, we show for the first time that ion-scale jets from vortex-induced reconnection rapidly decay through self-generated turbulence, leading to a mass transfer rate nearly one order higher than previous expectations for the Kelvin-Helmholtz instability.

Investigations on an electroactive polymer based tunable Helmholtz resonator

NASA Astrophysics Data System (ADS)

Abbad, A.; Rabenorosoa, K.; Ouisse, M.; Atalla, N.

2017-04-01

A Helmholtz resonator is a passive acoustic resonator classically used to control a single frequency resulting from the cavity volume and the resonator neck size. The aim of the proposed study is to present a new concept and strategy allowing real-time tunability of the Helmholtz resonator in order to enhance acoustic absorption performances at low frequencies (< 500 Hz). The proposed concept consists in replacing the resonator rigid front plate by an electroactive polymer (EAP) membrane. The first proposed strategy consists on a change in the mechanical properties of the membrane resulting from the applied electric field. This induces a resonance frequency shift. A second strategy is based on a well-located spring, which could direct the membrane deformation following the axis of the resonator to obtain a cavity volume variation. Both strategies allow variation of the resonance frequency of the device. Experimental measurements are performed to determine the potential of this concept for improvement of low-frequency performances of the acoustic devices.

Quantitative Reappraisal of the Helmholtz-Guyton Resonance Theory of Frequency Tuning in the Cochlea

PubMed Central

Babbs, Charles F.

2011-01-01

To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories. PMID:22028708

Kelvin-Helmholtz Instability: Lessons Learned and Ways Forward

NASA Astrophysics Data System (ADS)

Masson, A.; Nykyri, K.

2018-06-01

The Kelvin-Helmholtz instability (KHI) is a ubiquitous phenomenon across the Universe, observed from 500 m deep in the oceans on Earth to the Orion molecular cloud. Over the past two decades, several space missions have enabled a leap forward in our understanding of this phenomenon at the Earth's magnetopause. Key results obtained by these missions are first presented, with a special emphasis on Cluster and THEMIS. In particular, as an ideal instability, the KHI was not expected to produce mass transport. Simulations, later confirmed by spacecraft observations, indicate that plasma transport in Kelvin-Helmholtz (KH) vortices can arise during non-linear stage of its development via secondary process. In addition to plasma transport, spacecraft observations have revealed that KHI can also lead to significant ion heating due to enhanced ion-scale wave activity driven by the KHI. Finally, we describe what are the upcoming observational opportunities in 2018-2020, thanks to a unique constellation of multi-spacecraft missions including: MMS, Cluster, THEMIS, Van Allen Probes and Swarm.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

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.

Single-Mode, Supersonic Kelvin-Helmholtz Instability Experiment on OMEGA-EP

NASA Astrophysics Data System (ADS)

Wan, Wesley; Malamud, G.; Di Stefano, C.; Kuranz, C. C.; Drake, R.

2013-06-01

Laboratory laser experiments are able to produce and study phenomena that occur in astrophysical systems, allowing us to study mechanisms relevant to the formation, interaction, and destruction processes of stars and planets. These dynamic processes are strongly affected by hydrodynamic instabilities such as the Kelvin-Helmholtz instability, which arises when shear flow at an interface causes mixing between fluid layers. This instability is commonly observed at the boundary of cloud bands among gas planets, and can act as an atmospheric loss mechanism on planets with little to no intrinsic magnetic field. It is also observed in simulations of astrophysical systems including supernovae and wind-driven clumps. This poster discusses an upcoming experiment for the OMEGA-EP system that will produce a supersonic Kelvin-Helmholtz instability in the high-energy-density regime. This experiment will use a long laser pulse to create a sustained shock through two stratified layers separated by a seeded, single-mode perturbation. A high Mach number is believed to suppress the growth of the Kelvin-Helmholtz instability and, if sufficiently high, prevent growth entirely. We will be quantifying these effects using x-ray radiography. This work is funded by the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-FG52-09NA29548, and by the National Laser User Facility Program, grant number DE-NA0000850, with additional support provided under Cooperative Agreement No. DE-FC52-08NA28302 through the Laboratory for Laser Energetics, University of Rochester.

Equation of state and Helmholtz free energy for the atomic system of the repulsive Lennard-Jones particles.

PubMed

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2017-12-07

Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6≤T * ≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.

Equation of state and Helmholtz free energy for the atomic system of the repulsive Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2017-12-01

Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6 ≤T*≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.

Spiking neuron network Helmholtz machine.

PubMed

Sountsov, Pavel; Miller, Paul

2015-01-01

An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule.

Of the Helmholtz Club, South-Californian seedbed for visual and cognitive neuroscience, and its patron Francis Crick

PubMed Central

Aicardi, Christine

2014-01-01

Taking up the view that semi-institutional gatherings such as clubs, societies, research schools, have been instrumental in creating sheltered spaces from which many a 20th-century project-driven interdisciplinary research programme could develop and become established within the institutions of science, the paper explores the history of one such gathering from its inception in the early 1980s into the 2000s, the Helmholtz Club, which brought together scientists from such various research fields as neuroanatomy, neurophysiology, psychophysics, computer science and engineering, who all had an interest in the study of the visual system and of higher cognitive functions relying on visual perception such as visual consciousness. It argues that British molecular biologist turned South Californian neuroscientist Francis Crick had an early and lasting influence over the Helmholtz Club of which he was a founding pillar, and that from its inception, the club served as a constitutive element in his long-term plans for a neuroscience of vision and of cognition. Further, it argues that in this role, the Helmholtz Club served many purposes, the primary of which was to be a social forum for interdisciplinary discussion, where ‘discussion’ was not mere talk but was imbued with an epistemic value and as such, carefully cultivated. Finally, it questions what counts as ‘doing science’ and in turn, definitions of success and failure—and provides some material evidence towards re-appraising the successfulness of Crick’s contribution to the neurosciences. PMID:24384229

Coherent structures and flow topology of transitional separated-reattached flow over two and three dimensional geometrical shapes

NASA Astrophysics Data System (ADS)

Diabil, Hayder Azeez; Li, Xin Kai; Abdalla, Ibrahim Elrayah

2017-09-01

Large-scale organized motions (commonly referred to coherent structures) and flow topology of a transitional separated-reattached flow have been visualised and investigated using flow visualisation techniques. Two geometrical shapes including two-dimensional flat plate with rectangular leading edge and three-dimensional square cylinder are chosen to shed a light on the flow topology and present coherent structures of the flow over these shapes. For both geometries and in the early stage of the transition, two-dimensional Kelvin-Helmholtz rolls are formed downstream of the leading edge. They are observed to be twisting around the square cylinder while they stay flat in the case of the two-dimensional flat plate. For both geometrical shapes, the two-dimensional Kelvin-Helmholtz rolls move downstream of the leading edge and they are subjected to distortion to form three-dimensional hairpin structures. The flow topology in the flat plate is different from that in the square cylinder. For the flat plate, there is a merging process by a pairing of the Kelvin-Helmholtz rolls to form a large structure that breaks down directly into many hairpin structures. For the squire cylinder case, the Kelvin-Helmholtz roll evolves topologically to form a hairpin structure. In the squire cylinder case, the reattachment length is much shorter and a forming of the three-dimensional structures is closer to the leading edge than that in the flat plate case.

Spiking neuron network Helmholtz machine

PubMed Central

Sountsov, Pavel; Miller, Paul

2015-01-01

An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule. PMID:25954191

Limitations of correlation-based redatuming methods

NASA Astrophysics Data System (ADS)

Barrera P, D. F.; Schleicher, J.; van der Neut, J.

2017-12-01

Redatuming aims to correct seismic data for the consequences of an acquisition far from the target. That includes the effects of an irregular acquisition surface and of complex geological structures in the overburden such as strong lateral heterogeneities or layers with low or very high velocity. Interferometric techniques can be used to relocate sources to positions where only receivers are available and have been used to move acquisition geometries to the ocean bottom or transform data between surface-seismic and vertical seismic profiles. Even if no receivers are available at the new datum, the acquisition system can be relocated to any datum in the subsurface to which the propagation of waves can be modeled with sufficient accuracy. By correlating the modeled wavefield with seismic surface data, one can carry the seismic acquisition geometry from the surface closer to geologic horizons of interest. Specifically, we show the derivation and approximation of the one-sided seismic interferometry equation for surface-data redatuming, conveniently using Green’s theorem for the Helmholtz equation with density variation. Our numerical examples demonstrate that correlation-based single-boundary redatuming works perfectly in a homogeneous overburden. If the overburden is inhomogeneous, primary reflections from deeper interfaces are still repositioned with satisfactory accuracy. However, in this case artifacts are generated as a consequence of incorrectly redatumed overburden multiples. These artifacts get even worse if the complete wavefield is used instead of the direct wavefield. Therefore, we conclude that correlation-based interferometric redatuming of surface-seismic data should always be applied using direct waves only, which can be approximated with sufficient quality if a smooth velocity model for the overburden is available.

Bistability in the chemical master equation for dual phosphorylation cycles.

PubMed

Bazzani, Armando; Castellani, Gastone C; Giampieri, Enrico; Remondini, Daniel; Cooper, Leon N

2012-06-21

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory, and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed at elucidating the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional chemical master equation for a well-known model of a two step phospho/dephosphorylation cycle using the quasi-steady state approximation of enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the external field derived from the generation and recombination transition rates, can be decomposed by the Helmholtz theorem, into a conservative and a rotational (irreversible) part. Moreover, this decomposition allows to compute the stationary distribution via a perturbative approach. For a finite number of molecules there exists diffusion dynamics in a macroscopic region of the state space where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

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

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

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)

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)).

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

A remark on the energy conditions for Hawking's area theorem

NASA Astrophysics Data System (ADS)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

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.

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.

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.

Martian cave air-movement via Helmholtz resonance

USGS Publications Warehouse

Williams, Kaj; Titus, Timothy N.; Okubo, Chris; Cushing, Glen

2017-01-01

Infrasonic resonance has previously been measured in terrestrial caves by other researchers, where Helmholtz resonance has been suggested as the plausible mechanism resulting in periodic wind reversals within cave entrances. We extend this reasoning to possible Martian caves, where we examine the characteristics of four atypical pit craters (APCs) on Tharsis, suggested as candidate cave entrance locations. The results show that, for several possible cave air movement periods, we are able to infer the approximate cave volumes. The utility of inferring cave volumes for planetary cave exploration is discussed.

Absolute Helmholtz free energy of highly anharmonic crystals: theory vs Monte Carlo.

PubMed

Yakub, Lydia; Yakub, Eugene

2012-04-14

We discuss the problem of the quantitative theoretical prediction of the absolute free energy for classical highly anharmonic solids. Helmholtz free energy of the Lennard-Jones (LJ) crystal is calculated accurately while accounting for both the anharmonicity of atomic vibrations and the pair and triple correlations in displacements of the atoms from their lattice sites. The comparison with most precise computer simulation data on sublimation and melting lines revealed that theoretical predictions are in excellent agreement with Monte Carlo simulation data in the whole range of temperatures and densities studied.

Exact nonparaxial beams of the scalar Helmholtz equation.

PubMed

Rodríguez-Morales, Gustavo; Chávez-Cerda, Sabino

2004-03-01

It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.

Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

NASA Astrophysics Data System (ADS)

Rumyantseva, O. D.; Shurup, A. S.

2017-01-01

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.

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.

A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers

NASA Technical Reports Server (NTRS)

Piepmeier, J. R.; Simon, N. K.

2004-01-01

The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.

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

Development of ultrasonic electrostatic microjets for distributed propulsion and microflight

NASA Astrophysics Data System (ADS)

Amirparviz, Babak

This dissertation details the first attempt to design and fabricate a distributed micro propulsion system based on acoustic streaming. A novel micro propulsion method is suggested by combining Helmholtz resonance, acoustic streaming and flow entrainment and thrust augmentation. In this method, oscillatory motion of an electrostatically actuated diaphragm creates a high frequency acoustic field inside the cavity of a Helmholtz resonator. The initial fluid motion velocity is amplified by the Helmholtz resonator structure and creates a jet flow at the exit nozzle. Acoustic streaming is the phenomenon responsible for primary jet stream creation. Primary jets produced by a few resonators can be combined in an ejector configuration to induce flow entrainment and thrust augmentation. Basic governing equations for the electrostatic actuator, deformation of the diaphragm and the fluid flow inside the resonator are derived. These equations are linearized and used to derive an equivalent electrical circuit model for the operation of the device. Numerical solution of the governing equations and simulation of the circuit model are used to predict the performance of the experimental systems. Thrust values as high as 30.3muN are expected per resonator. A micro machined electrostatically-driven high frequency Helmholtz resonator prototype is designed and fabricated. A new micro fabrication technique is developed for bulk micromachining and in particular fabrication of the resonator. Geometric stops for wet anisotropic etching of silicon are introduced for the fist time for structure formation. Arrays of high frequency (>60kHz) micro Helmholtz resonators are fabricated. In one sample more than 1000 resonators cover the surface of a four-inch silicon wafer and in effect convert it to a distributed propulsion system. A high yield (>85%) micro fabrication process is presented for realization of this propulsion system taking advantage of newly developed deep glass micromachining and lithography on thin (15mum) silicon methods. Extensive test and characterization are performed on the micro jets using current frequency component analysis, laser interferometry, acoustic measurements, hot-wire anemometers, video particle imaging and load cells. The occurrence of acoustic streaming at jet nozzles is verified and flow velocities exceeding 1m/s are measured at the 15mum x 330mum jet exit nozzle.

Connecting science and the musical arts in teaching tone quality: Integrating Helmholtz motion and master violin teachers' pedagogies

NASA Astrophysics Data System (ADS)

Collins, Cheri D.

Is it possible for students to achieve better tone quality from even their factory-made violins? All violins, regardless of cost, have a common capacity for good tone in certain frequencies. These signature modes outline the first position range of a violin (196-600 hertz). To activate this basic capacity of all violins, the string must fully vibrate. To accomplish this the bow must be pulled across the string with enough pressure (relative to its speed and contact point) for the horsehairs to catch. This friction permits the string to vibrate in Helmholtz Motion, which produces a corner that travels along the edge of the string between the bridge and the nut. Creating this corner is the most fundamental technique for achieving good tone. The findings of celebrated scientists Ernest Chladni, Hermann von Helmholtz, and John Schelleng will be discussed and the tone-production pedagogy of master teachers Carl Flesch, Ivan Galamian, Robert Gerle, and Simon Fischer will be investigated. Important connections between the insights of these scientists and master teachers are evident. Integrating science and art can provide teachers with a better understanding of the characteristics of good tone. This can help their students achieve the best possible sound from their instruments. In the private studio the master teacher may not use the words "Helmholtz Motion." Yet through modeling and listening students are able to understand and create a quality tone. Music teachers without experience in string performance may be assigned to teach strings in classroom and ensembles settings. As a result modeling good tone is not always possible. However, all teachers and conductors can understand the fundamental behavior of string vibration and adapt their instruction strategies towards student success. Better tonal quality for any string instrument is ultimately achieved. Mastery and use of the Helmholtz Motion benefits teachers and students alike. Simple practice exercises for teaching and conducting, based on student discovery rather than modeling, are presented in Appendix A: Application. This approach to teaching good tone can be applied successfully in all string settings and levels.

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.

Of the Helmholtz Club, South-Californian seedbed for visual and cognitive neuroscience, and its patron Francis Crick.

PubMed

Aicardi, Christine

2014-03-01

Taking up the view that semi-institutional gatherings such as clubs, societies, research schools, have been instrumental in creating sheltered spaces from which many a 20th-century project-driven interdisciplinary research programme could develop and become established within the institutions of science, the paper explores the history of one such gathering from its inception in the early 1980s into the 2000s, the Helmholtz Club, which brought together scientists from such various research fields as neuroanatomy, neurophysiology, psychophysics, computer science and engineering, who all had an interest in the study of the visual system and of higher cognitive functions relying on visual perception such as visual consciousness. It argues that British molecular biologist turned South Californian neuroscientist Francis Crick had an early and lasting influence over the Helmholtz Club of which he was a founding pillar, and that from its inception, the club served as a constitutive element in his long-term plans for a neuroscience of vision and of cognition. Further, it argues that in this role, the Helmholtz Club served many purposes, the primary of which was to be a social forum for interdisciplinary discussion, where 'discussion' was not mere talk but was imbued with an epistemic value and as such, carefully cultivated. Finally, it questions what counts as 'doing science' and in turn, definitions of success and failure-and provides some material evidence towards re-appraising the successfulness of Crick's contribution to the neurosciences. Copyright © 2013 The Author. Published by Elsevier Ltd.. All rights reserved.

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.

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

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 nonrelativistic 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.

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

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.

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.

destiny: diffusion maps for large-scale single-cell data in R.

PubMed

Angerer, Philipp; Haghverdi, Laleh; Büttner, Maren; Theis, Fabian J; Marr, Carsten; Buettner, Florian

2016-04-15

: Diffusion maps are a spectral method for non-linear dimension reduction and have recently been adapted for the visualization of single-cell expression data. Here we present destiny, an efficient R implementation of the diffusion map algorithm. Our package includes a single-cell specific noise model allowing for missing and censored values. In contrast to previous implementations, we further present an efficient nearest-neighbour approximation that allows for the processing of hundreds of thousands of cells and a functionality for projecting new data on existing diffusion maps. We exemplarily apply destiny to a recent time-resolved mass cytometry dataset of cellular reprogramming. destiny is an open-source R/Bioconductor package "bioconductor.org/packages/destiny" also available at www.helmholtz-muenchen.de/icb/destiny A detailed vignette describing functions and workflows is provided with the package. carsten.marr@helmholtz-muenchen.de or f.buettner@helmholtz-muenchen.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Turbulent mass transfer caused by vortex induced reconnection in collisionless magnetospheric plasmas

DOE PAGES

Nakamura, T. K. M.; Hasegawa, H.; Daughton, William Scott; ...

2017-11-17

Magnetic reconnection is believed to be the main driver to transport solar wind into the Earth’s magnetosphere when the magnetopause features a large magnetic shear. However, even when the magnetic shear is too small for spontaneous reconnection, the Kelvin–Helmholtz instability driven by a super-Alfvénic velocity shear is expected to facilitate the transport. Although previous kinetic simulations have demonstrated that the non-linear vortex flows from the Kelvin–Helmholtz instability gives rise to vortex-induced reconnection and resulting plasma transport, the system sizes of these simulations were too small to allow the reconnection to evolve much beyond the electron scale as recently observed bymore » the Magnetospheric Multiscale (MMS) spacecraft. Here in this paper, based on a large-scale kinetic simulation and its comparison with MMS observations, we show for the first time that ion-scale jets from vortex-induced reconnection rapidly decay through self-generated turbulence, leading to a mass transfer rate nearly one order higher than previous expectations for the Kelvin–Helmholtz instability.« less

Turbulent mass transfer caused by vortex induced reconnection in collisionless magnetospheric plasmas

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

Nakamura, T. K. M.; Hasegawa, H.; Daughton, William Scott

Magnetic reconnection is believed to be the main driver to transport solar wind into the Earth’s magnetosphere when the magnetopause features a large magnetic shear. However, even when the magnetic shear is too small for spontaneous reconnection, the Kelvin–Helmholtz instability driven by a super-Alfvénic velocity shear is expected to facilitate the transport. Although previous kinetic simulations have demonstrated that the non-linear vortex flows from the Kelvin–Helmholtz instability gives rise to vortex-induced reconnection and resulting plasma transport, the system sizes of these simulations were too small to allow the reconnection to evolve much beyond the electron scale as recently observed bymore » the Magnetospheric Multiscale (MMS) spacecraft. Here in this paper, based on a large-scale kinetic simulation and its comparison with MMS observations, we show for the first time that ion-scale jets from vortex-induced reconnection rapidly decay through self-generated turbulence, leading to a mass transfer rate nearly one order higher than previous expectations for the Kelvin–Helmholtz instability.« less

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: polyampholyte and polyelectrolyte solutions.

PubMed

Jiang, Hao; Adidharma, Hertanto

2014-11-07

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

PREFACE: Special section on vortex rings Special section on vortex rings

NASA Astrophysics Data System (ADS)

Fukumoto, Yasuhide

2009-10-01

This special section of Fluid Dynamics Research includes five articles on vortex rings in both classical and quantum fluids. The leading scientists of the field describe the trends in and the state-of-the-art development of experiments, theories and numerical simulations of vortex rings. The year 2008 was the 150th anniversary of 'vortex motion' since Hermann von Helmholtz opened up this field. In 1858, Helmholtz published a paper in Crelle's Journal which put forward the concept of 'vorticity' and made the first analysis of vortex motion. Fluid mechanics before that was limited to irrotational motion. In the absence of vorticity, the motion of an incompressible homogeneous fluid is virtually equivalent to a rigid-body motion in the sense that the fluid motion is determined once the boundary configuration is specified. Helmholtz proved, among other things, that, without viscosity, a vortex line is frozen into the fluid. This Helmholtz's law immediately implies the preservation of knots and links of vortex lines and its implication is enormous. One of the major trends of fluid mechanics since the latter half of the 20th century is to clarify the topological meaning of Helmholtz's law and to exploit it to develop theoretical and numerical methods to find the solutions of the Euler equations and to develop experimental techniques to gain an insight into fluid motion. Vortex rings are prominent coherent structures in a variety of fluid motions from the microscopic scale, through human and mesoscale to astrophysical scales, and have attracted people's interest. The late professor Philip G Saffman (1981) emphasized the significance of studies on vortex rings. One particular motion exemplifies the whole range of problems of vortex motion and is also a commonly known phenomenon, namely the vortex ring or smoke ring. Vortex rings are easily produced by dropping drops of one liquid into another, or by puffing fluid out of a hole, or by exhaling smoke if one has the skill. Their formation is a problem of vortex sheet dynamics, the steady state is a problem of existence, their duration is a problem of stability, and if there are several we have the problem of vortex interactions. Helmholtz himself, in the same paper (1858), devoted a few pages to an analysis of the motion of a vortex ring, and made substantial contributions. Since then, theoretical, experimental and numerical treatments of vortex rings have been developing continuously, yet we encounter mysteries and novel phenomena, with which vortex rings find new applications in, say, bio-fluid mechanics. Recently vortex rings have enlarged their scope beyond classical fluids to encompass super-fluids and Bose-Einstein condensates. On the occasion of the 150th anniversary of Helmholtz's theory on a vortex ring, it is worthwhile to bring together, in one issue, the latest understandings of and open problems in vortex rings from various aspects. The topics in this issue include development of theories and experiments for motion of vortex rings and their interaction with other vortex rings, flows and boundaries, with application to vortex-ring manipulation for flow control, original experiments on collision of vortex rings with a porous boundary, a novel numerical technique to simulate three-dimensional motion of vortex rings and new theories of dynamics of quantum vortex rings governed by nonlinear Schrödinger equations. I hope that this special section gives a sketch, in some proportion, of the current frontier of the field and provides a means to tackle future problems. References Saffman P G 1981 Dynamics of vorticity J. Fluid Mech. 106 49-58 von Helmholtz H 1858 Über Integrale der hydrodynamischen Gleichungen welche den Wirbelbewegungen entsprechen J. Reine Angew. Math. 55 25-55 (Engl. transl.: Tait P G 1867 On the integrals of the hydrodynamical equations which express vortex-motion Phil. Mag. 33 (4) 485-512)

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…

Parametric design of tri-axial nested Helmholtz coils

NASA Astrophysics Data System (ADS)

Abbott, Jake J.

2015-05-01

This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

Parametric design of tri-axial nested Helmholtz coils.

PubMed

Abbott, Jake J

2015-05-01

This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

Parametric design of tri-axial nested Helmholtz coils

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

Abbott, Jake J., E-mail: jake.abbott@utah.edu

This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

Low frequency acoustic and electromagnetic scattering

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Maccamy, R. C.

1986-01-01

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

NASA Astrophysics Data System (ADS)

Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix

2018-03-01

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

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

Ciraolo, Giulio, E-mail: g.ciraolo@math.unipa.it; Gargano, Francesco, E-mail: gargano@math.unipa.it; Sciacca, Vincenzo, E-mail: sciacca@math.unipa.it

2013-08-01

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

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.

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.

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.

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.

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.

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.

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

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…

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.

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.

Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: Mathematical modeling.

PubMed

Tripathi, Dharmendra; Yadav, Ashu; Bég, O Anwar

2017-01-01

Analytical solutions are developed for the electro-kinetic flow of a viscoelastic biological liquid in a finite length cylindrical capillary geometry under peristaltic waves. The Jefferys' non-Newtonian constitutive model is employed to characterize rheological properties of the fluid. The unsteady conservation equations for mass and momentum with electro-kinetic and Darcian porous medium drag force terms are reduced to a system of steady linearized conservation equations in an axisymmetric coordinate system. The long wavelength, creeping (low Reynolds number) and Debye-Hückel linearization approximations are utilized. The resulting boundary value problem is shown to be controlled by a number of parameters including the electro-osmotic parameter, Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity), and Jefferys' first parameter (ratio of relaxation and retardation time), wave amplitude. The influence of these parameters and also time on axial velocity, pressure difference, maximum volumetric flow rate and streamline distributions (for elucidating trapping phenomena) is visualized graphically and interpreted in detail. Pressure difference magnitudes are enhanced consistently with both increasing electro-osmotic parameter and Helmholtz-Smoluchowski velocity, whereas they are only elevated with increasing Jefferys' first parameter for positive volumetric flow rates. Maximum time averaged flow rate is enhanced with increasing electro-osmotic parameter, Helmholtz-Smoluchowski velocity and Jefferys' first parameter. Axial flow is accelerated in the core (plug) region of the conduit with greater values of electro-osmotic parameter and Helmholtz-Smoluchowski velocity whereas it is significantly decelerated with increasing Jefferys' first parameter. The simulations find applications in electro-osmotic (EO) transport processes in capillary physiology and also bio-inspired EO pump devices in chemical and aerospace engineering. Copyright © 2016 Elsevier Inc. All rights reserved.

A Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation

NASA Astrophysics Data System (ADS)

Cho, Min Hyung; Cai, Wei

2010-12-01

A Wideband Fast Multipole Method (FMM) for the 2D Helmholtz equation is presented. It can evaluate the interactions between N particles governed by the fundamental solution of 2D complex Helmholtz equation in a fast manner for a wide range of complex wave number k, which was not easy with the original FMM due to the instability of the diagonalized conversion operator. This paper includes the description of theoretical backgrounds, the FMM algorithm, software structures, and some test runs. Program summaryProgram title: 2D-WFMM Catalogue identifier: AEHI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4636 No. of bytes in distributed program, including test data, etc.: 82 582 Distribution format: tar.gz Programming language: C Computer: Any Operating system: Any operating system with gcc version 4.2 or newer Has the code been vectorized or parallelized?: Multi-core processors with shared memory RAM: Depending on the number of particles N and the wave number k Classification: 4.8, 4.12 External routines: OpenMP ( http://openmp.org/wp/) Nature of problem: Evaluate interaction between N particles governed by the fundamental solution of 2D Helmholtz equation with complex k. Solution method: Multilevel Fast Multipole Algorithm in a hierarchical quad-tree structure with cutoff level which combines low frequency method and high frequency method. Running time: Depending on the number of particles N, wave number k, and number of cores in CPU. CPU time increases as N log N.

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.

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.

Systematic Approaches to Experimentation: The Case of Pick's Theorem

ERIC Educational Resources Information Center

Papadopoulos, Ioannis; Iatridou, Maria

2010-01-01

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

Topology and the Lay of the Land: A Mathematician on the Topographer's Turf.

ERIC Educational Resources Information Center

Shubin, Mikhail

1992-01-01

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

Weak Compactness and Control Measures in the Space of Unbounded Measures

PubMed Central

Brooks, James K.; Dinculeanu, Nicolae

1972-01-01

We present a synthesis theorem for a family of locally equivalent measures defined on a ring of sets. This theorem is then used to exhibit a control measure for weakly compact sets of unbounded measures. In addition, the existence of a local control measure for locally strongly bounded vector measures is proved by means of the synthesis theorem. PMID:16591980

A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

ERIC Educational Resources Information Center

Raychaudhuri, D.

2007-01-01

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

Erratum: Correction to: Information Transmission and Criticality in the Contact Process

NASA Astrophysics Data System (ADS)

Cassandro, M.; Galves, A.; Löcherbach, E.

2018-01-01

The original publication of the article unfortunately contained a mistake in the first sentence of Theorem 1 and in the second part of the proof of Theorem 1. The corrected statement of Theorem as well as the corrected proof are given below. The full text of the corrected version is available at http://arxiv.org/abs/1705.11150.

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

PubMed Central

Zhang, Likun; Marston, Philip L.

2013-01-01

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam. PMID:24049681

Republication of: A theorem on Petrov types

NASA Astrophysics Data System (ADS)

Goldberg, J. N.; Sachs, R. K.

2009-02-01

This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

Electrostatic Hellmann-Feynman theorem applied to long-range interatomic forces - The hydrogen molecule.

NASA Technical Reports Server (NTRS)

Steiner, E.

1973-01-01

The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.

Tree-manipulating systems and Church-Rosser theorems.

NASA Technical Reports Server (NTRS)

Rosen, B. K.

1973-01-01

Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.

Quantum voting and violation of Arrow's impossibility theorem

NASA Astrophysics Data System (ADS)

Bao, Ning; Yunger Halpern, Nicole

2017-06-01

We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions

NASA Astrophysics Data System (ADS)

Hussain, N.

2008-02-01

The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

PubMed

Gillespie, Dirk

2014-11-01

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Study of noise reduction characteristics of multilayered panels and dual pane windows with Helmholtz resonators

NASA Technical Reports Server (NTRS)

Navaneethan, R.

1981-01-01

The experimental noise attenuation characteristics of flat, general aviation type, multilayered panels are discussed. Experimental results of stiffened panels, damping tape, honeycomb materials and sound absorption materials are presented. Single degree of freedom theoretical models were developed for sandwich type panels with both shear resistant and non-shear resistant core material. The concept of Helmholtz resonators used in conjunction with dual panel windows in increasing the noise reduction around a small range of frequency was tested. It is concluded that the stiffening of the panels either by stiffeners or by sandwich construction increases the low frequency noise reduction.

Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II.

PubMed

Lushnikov, Pavel M; Zubarev, Nikolay M

2018-05-18

Relative motion of the normal and superfluid components of helium II results in the quantum Kelvin-Helmholtz instability (KHI) at their common free surface. We found the integrability and exact growing solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two classical fluids, the dynamics of a helium II free surface allows reduction to the Laplace growth equation, which has an infinite number of exact solutions, including the generic formation of sharp cusps at the free surface in a finite time.

Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel M.; Zubarev, Nikolay M.

2018-05-01

Relative motion of the normal and superfluid components of helium II results in the quantum Kelvin-Helmholtz instability (KHI) at their common free surface. We found the integrability and exact growing solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two classical fluids, the dynamics of a helium II free surface allows reduction to the Laplace growth equation, which has an infinite number of exact solutions, including the generic formation of sharp cusps at the free surface in a finite time.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Numerical modeling of interaction in the dynamic system "gas-structure" with harmonic motion of the piston in the variable section pipe

NASA Astrophysics Data System (ADS)

Butymova, L. N.; Modorskii, V. Ya.; Petrov, V. Yu.

2016-10-01

The Helmholtz resonator is an instrument to create low-frequency natural oscillations whose wavelength is substantially larger than the dimensions of the resonator itself. Some modern insulating materials are a set of Helmholtz resonators made in the form of a multilayer composite structure with a layer of cells between the carrier layers. The cells have an outlet hole drilled in the support layer. Improving effectiveness of such structures in terms of noise reduction is an urgent task [1 - 7]. It is found that the resonator with a throat of higher surface roughness damps noise more effectively.

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

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

Linton, C. M., E-mail: C.M.Linton@lboro.ac.uk

2015-01-15

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

Collocation for an integral equation arising in duct acoustics

NASA Technical Reports Server (NTRS)

Moss, W. F.

1986-01-01

A mathematical model is developed to describe the effect of aircraft-engine inlet geometry on the reflected and radiated acoustic field without flow, as studied experimentally using a spinning-mode synthesizer by Silcox (1983). The acoustic pressure in the inlet interior and exterior is modeled by a pure cylindrical azimuthal mode for the Helmholtz equation with hardwall boundary and by the Helmholtz equation and the radiation condition at infinity, respectively. The analytical approach to the solution of the resulting boundary-value problem and the program implementation are explained; numerical results are presented in tables and graphs; and the uniqueness of the problem is demonstrated.

Fully vectorial accelerating diffraction-free Helmholtz beams.

PubMed

Aleahmad, Parinaz; Miri, Mohammad-Ali; Mills, Matthew S; Kaminer, Ido; Segev, Mordechai; Christodoulides, Demetrios N

2012-11-16

We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.

Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields

NASA Technical Reports Server (NTRS)

Rasband, S. N.; Turner, L.

1981-01-01

It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.

A multiple degree of freedom electromechanical Helmholtz resonator.

PubMed

Liu, Fei; Horowitz, Stephen; Nishida, Toshikazu; Cattafesta, Louis; Sheplak, Mark

2007-07-01

The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads.

Asymmetric Kelvin-Helmholtz Instability at Jupiter's Magnetopause Boundary: Implications for Corotation-Dominated Systems

NASA Astrophysics Data System (ADS)

Zhang, B.; Delamere, P. A.; Ma, X.; Burkholder, B.; Wiltberger, M.; Lyon, J. G.; Merkin, V. G.; Sorathia, K. A.

2018-01-01

The multifluid Lyon-Fedder-Mobarry (MFLFM) global magnetosphere model is used to study the interactions between solar wind and rapidly rotating, internally driven Jupiter magnetosphere. The MFLFM model is the first global simulation of Jupiter magnetosphere that captures the Kelvin-Helmholtz instability (KHI) in the critically important subsolar region. Observations indicate that Kelvin-Helmholtz vortices are found predominantly in the dusk sector. Our simulations explain that this distribution is driven by the growth of KHI modes in the prenoon and subsolar region (e.g., >10 local time) that are advected by magnetospheric flows to the dusk sector. The period of density fluctuations at the dusk terminator flank (18 magnetic local time, MLT) is roughly 1.4 h compared with 7.2 h at the dawn flank (6 MLT). Although the simulations are only performed using parameters of the Jupiter's magnetosphere, the results may also have implications for solar wind-magnetosphere interactions at other corotation-dominated systems such as Saturn. For instance, the simulated average azimuthal speed of magnetosheath flows exhibit significant dawn-dusk asymmetry, consistent with recent observations at Saturn. The results are particularly relevant for the ongoing Juno mission and the analysis of dawnside magnetopause boundary crossings for other planetary missions.

Helmholtz and Gibbs ensembles, thermodynamic limit and bistability in polymer lattice models

NASA Astrophysics Data System (ADS)

Giordano, Stefano

2017-12-01

Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics have not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force-extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force-extension response, whereas the isometric condition causes a sawtooth-like force-extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions

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

Jiang, Hao; Adidharma, Hertanto, E-mail: adidharm@uwyo.edu

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must thereforemore » be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.« less

A Third Note: Helmholtz, Palestrina, and the Early History of Musicology.

PubMed

Kursell, Julia

2015-06-01

This contribution focuses on Hermann von Helmholtz's work on Renaissance composer Giovanni Pierluigi da Palestrina. Helmholtz used his scientific concept of distortion to analyze this music and, reversely, to find corroboration for the concept in his musical analyses. In this, his work interlocked with nineteenth-century aesthetic and scholarly ideals. His eagerness to use the latest products of historical scholarship in early music reveals a specific view of music history. Historical documents of music provide the opportunity for the discovery of new experimental research topics and thereby also reveal insights into hearing under different conditions. The essay argues that this work occupies a peculiar position in the history of musicology; it falls under the header of "systematic musicology," which eventually emerged as a discipline of musicology at the end of the nineteenth century. That this discipline has a history at all is easily overlooked, as many of its contributors were scientists with an interest in music. A history of musicology therefore must consider at least the following two caveats: parts of it take place outside the institutionalized field of musicology, and any history of musicology must, in the last instance, be embedded in a history of music.

A Microsoft® Excel Simulation Illustrating the Central Limit Theorem's Appropriateness for Comparing the Difference between the Means of Any Two Populations

ERIC Educational Resources Information Center

Moen, David H.; Powell, John E.

2008-01-01

Using Microsoft® Excel, several interactive, computerized learning modules are developed to illustrate the Central Limit Theorem's appropriateness for comparing the difference between the means of any two populations. These modules are used in the classroom to enhance the comprehension of this theorem as well as the concepts that provide the…

Optimal Repairman Allocation Models

DTIC Science & Technology

1976-03-01

state X under policy ir. Then lim {k1’ lC0 (^)I) e.(X,k) - 0 k*0 *’-’ (3.1.1) Proof; The result is proven by induction on |CQ(X...following theorem. Theorem 3.1 D. Under the conditions of theorem 3.1 A, define g1[ 1) (X) - g^U), then lim k- lC0 W l-mle (XHkl00^ Ig*11 (X

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

ERIC Educational Resources Information Center

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

A Converse of Fermat's Little Theorem

ERIC Educational Resources Information Center

Bruckman, P. S.

2007-01-01

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

Bayes' Theorem: An Old Tool Applicable to Today's Classroom Measurement Needs. ERIC/AE Digest.

ERIC Educational Resources Information Center

Rudner, Lawrence M.

This digest introduces ways of responding to the call for criterion-referenced information using Bayes' Theorem, a method that was coupled with criterion-referenced testing in the early 1970s (see R. Hambleton and M. Novick, 1973). To illustrate Bayes' Theorem, an example is given in which the goal is to classify an examinee as being a master or…

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

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.

Reciprocity relations in aerodynamics

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Spreiter, John R

1953-01-01

Reverse flow theorems in aerodynamics are shown to be based on the same general concepts involved in many reciprocity theorems in the physical sciences. Reciprocal theorems for both steady and unsteady motion are found as a logical consequence of this approach. No restrictions on wing plan form or flight Mach number are made beyond those required in linearized compressible-flow analysis. A number of examples are listed, including general integral theorems for lifting, rolling, and pitching wings and for wings in nonuniform downwash fields. Correspondence is also established between the buildup of circulation with time of a wing starting impulsively from rest and the buildup of lift of the same wing moving in the reverse direction into a sharp-edged gust.

Fluctuation theorem for channel-facilitated membrane transport of interacting and noninteracting solutes.

PubMed

Berezhkovskii, Alexander M; Bezrukov, Sergey M

2008-05-15

In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

A coupled mode formulation by reciprocity and a variational principle

NASA Technical Reports Server (NTRS)

Chuang, Shun-Lien

1987-01-01

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions satisfying Maxwell's equations and the boundary conditions in two different media, respectively, is derived. Based on the generalized reciprocity theorem, the coupled mode equations can then be formulated. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the 'conventional' and the new coupling coefficients are derived. It is shown analytically that the present formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer (1985, 1986) theory by 0.033 percent, for example.

Does the Coase theorem hold in real markets? An application to the negotiations between waterworks and farmers in Denmark.

PubMed

Abildtrup, Jens; Jensen, Frank; Dubgaard, Alex

2012-01-01

The Coase theorem depends on a number of assumptions, among others, perfect information about each other's payoff function, maximising behaviour and zero transaction costs. An important question is whether the Coase theorem holds for real market transactions when these assumptions are violated. This is the question examined in this paper. We consider the results of Danish waterworks' attempts to establish voluntary cultivation agreements with Danish farmers. A survey of these negotiations shows that the Coase theorem is not robust in the presence of imperfect information, non-maximising behaviour and transaction costs. Thus, negotiations between Danish waterworks and farmers may not be a suitable mechanism to achieve efficiency in the protection of groundwater quality due to violations of the assumptions of the Coase theorem. The use of standard schemes or government intervention (e.g. expropriation) may, under some conditions, be a more effective and cost efficient approach for the protection of vulnerable groundwater resources in Denmark. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-06-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Quantum Mechanics, Can It Be Consistent with Locality?

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe; Sestito, Angela

2011-07-01

We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, and identify the implied extensions of quantum correlations. Then we prove that the theorem of Bell, and the non-locality theorems without inequalities, fail if the new extensions are adopted. Therefore, these theorems can be interpreted as arguments against the wide interpretation of the criterion of reality rather than as a violation of locality.

Specification Improvement Through Analysis of Proof Structure (SITAPS): High Assurance Software Development

DTIC Science & Technology

2016-02-01

proof in mathematics. For example, consider the proof of the Pythagorean Theorem illustrated at: http://www.cut-the-knot.org/ pythagoras / where 112...methods and tools have made significant progress in their ability to model software designs and prove correctness theorems about the systems modeled...assumption criticality” or “ theorem root set size” SITAPS detects potentially brittle verification cases. SITAPS provides tools and techniques that

Delaunay Refinement Mesh Generation

DTIC Science & Technology

1997-05-18

edge is locally Delaunay; thus, by Lemma 3, every edge is Delaunay. Theorem 5 Let V be a set of three or more vertices in the plane that are not all...this document. Delaunay triangulations are valuable in part because they have the following optimality properties. Theorem 6 Among all triangulations of...no locally Delaunay edges. By Theorem 5, a triangulation with no locally Delaunay edges is the Delaunay triangulation. The property of max-min

Development of a Dependency Theory Toolbox for Database Design.

DTIC Science & Technology

1987-12-01

published algorithms and theorems , and hand simulating these algorithms can be a tedious and error prone chore. Additionally, since the process of...to design and study relational databases exists in the form of published algorithms and theorems . However, hand simulating these algorithms can be a...published algorithms and theorems . Hand simulating these algorithms can be a tedious and error prone chore. Therefore, a toolbox of algorithms and

Field Computation and Nonpropositional Knowledge.

DTIC Science & Technology

1987-09-01

field computer It is based on xeneralization of Taylor’s theorem to continuous dimensional vector spaces. 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21...generalization of Taylor’s theorem to continuous dimensional vector -5paces A number of field computations are illustrated, including several Lransforma...paradigm. The "old" Al has been quite successful in performing a number of difficult tasks, such as theorem prov- ing, chess playing, medical diagnosis and

Ignoring the Innocent: Non-combatants in Urban Operations and in Military Models and Simulations

DTIC Science & Technology

2006-01-01

such a model yields is a sufficiency theorem , a single run does not provide any information on the robustness of such theorems . That is, given that...often formally resolvable via inspection, simple differentiation, the implicit function theorem , comparative statistics, and so on. The only way to... Pythagoras , and Bactowars. For each, Grieger discusses model parameters, data collection, terrain, and other features. Grieger also discusses

Some functional limit theorems for compound Cox processes

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

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

NASA Astrophysics Data System (ADS)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

Reduction theorems for optimal unambiguous state discrimination of density matrices

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

Raynal, Philippe; Luetkenhaus, Norbert; Enk, Steven J. van

2003-08-01

We present reduction theorems for the problem of optimal unambiguous state discrimination of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank n and are described in a Hilbert space of dimensions 2n. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N{>=}2)

Proof of factorization using background field method of QCD

NASA Astrophysics Data System (ADS)

Nayak, Gouranga C.

2010-02-01

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof.

Proof of factorization using background field method of QCD

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

Nayak, Gouranga C.

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof.

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

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.

Sound-proof Sandwich Panel Design via Metamaterial Concept

NASA Astrophysics Data System (ADS)

Sui, Ni

Sandwich panels consisting of hollow core cells and two face-sheets bonded on both sides have been widely used as lightweight and strong structures in practical engineering applications, but with poor acoustic performance especially at low frequency regime. Basic sound-proof methods for the sandwich panel design are spontaneously categorized as sound insulation and sound absorption. Motivated by metamaterial concept, this dissertation presents two sandwich panel designs without sacrificing weight or size penalty: A lightweight yet sound-proof honeycomb acoustic metamateiral can be used as core material for honeycomb sandwich panels to block sound and break the mass law to realize minimum sound transmission; the other sandwich panel design is based on coupled Helmholtz resonators and can achieve perfect sound absorption without sound reflection. Based on the honeycomb sandwich panel, the mechanical properties of the honeycomb core structure were studied first. By incorporating a thin membrane on top of each honeycomb core, the traditional honeycomb core turns into honeycomb acoustic metamaterial. The basic theory for such kind of membrane-type acoustic metamaterial is demonstrated by a lumped model with infinite periodic oscillator system, and the negative dynamic effective mass density for clamped membrane is analyzed under the membrane resonance condition. Evanescent wave mode caused by negative dynamic effective mass density and impedance methods are utilized to interpret the physical phenomenon of honeycomb acoustic metamaterials at resonance. The honeycomb metamaterials can extraordinarily improve low-frequency sound transmission loss below the first resonant frequency of the membrane. The property of the membrane, the tension of the membrane and the numbers of attached membranes can impact the sound transmission loss, which are observed by numerical simulations and validated by experiments. The sandwich panel which incorporates the honeycomb metamateiral as the core material maintains the mechanical property and yields a sound transmission loss that is consistently greater than 50 dB at low frequencies. Furthermore, the absorption property of the proposed honeycomb sandwich panel was experimentally studied. The honeycomb sandwich panel shows an excellent sound absorbing performance at high frequencies by using reinforced glass fiber without adding too much mass. The effect of the panel size and the stiffness of the grid-like frame effect of the honeycomb sandwich structures on sound transmission are discussed lastly. For the second sound-proof sandwich panel design, each unit cell of the sandwich panel is replaced by a Helmholtz resonator by perforating a small hole on the top face sheet. A perfect sound absorber sandwich panel with coupled Helmholtz resonators is proposed by two types: single identical Helmholtz resonator in each unit cell and dual Helmholtz resonators with different orifices, arranged in each cell arranged periodically. The soundproof sandwich panel is modelled as a panel embedded in rigid panel and assumed as a semiinfinite space with hard boundary condition. The net/mutual impedance model is first proposed and derived by solving Kirchhoff-Helmholtz integral by using the Green's function. The thermal-viscous energy dissipation at the thermal boundary layer dominates the total energy consumed. Two types of perfect sound absorber sandwich panel are designed in the last part. Two theoretical methods: the average energy and the equivalent surface impedance method are used to predict sound absorption performance. The geometry for perfect sound absorber sandwich panel at a target frequency can be obtained when the all the Helmholtz resonators are at resonance and the surface impedance of the sandwich panel matches the air impedance. The bandwidth for the identical sandwich panel mainly depends on the neck radius. The absorptive property of the dual Helmholtz resonators type of sandwich panel is studied by investigating the coupling effects between HRs. The theoretical results can be verified by numerical simulations through finite element method. The absorption bandwidth can be tuned by incorporating more HRs in each unit cell. Both sound-proof sandwich panel designs possess extraordinary acoustic performance for noise reduction at low frequency range with sub-wavelength structures. The sound absorber panel design can also achieve broadband sound attenuation at low frequencies.

Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Shiu, Gary

2018-05-01

We show that the soft photon, gluon, and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented.

Teaching the Jahn-Teller Theorem: A Simple Exercise That Illustrates How the Magnitude of Distortion Depends on the Number of Electrons and Their Occupation of the Degenerate Energy Level

ERIC Educational Resources Information Center

Johansson, Adam Johannes

2013-01-01

Teaching the Jahn-Teller theorem offers several challenges. For many students, the first encounter comes in coordination chemistry, which can be difficult due to the already complicated nature of transition-metal complexes. Moreover, a deep understanding of the Jahn-Teller theorem requires that one is well acquainted with quantum mechanics and…

Research on Quantum Algorithms at the Institute for Quantum Information

DTIC Science & Technology

2009-10-17

accuracy threshold theorem for the one-way quantum computer. Their proof is based on a novel scheme, in which a noisy cluster state in three spatial...detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated...proved quantum threshold theorems for long-range correlated non-Markovian noise, for leakage faults, for the one-way quantum computer, for postselected

Deductive Synthesis of the Unification Algorithm,

DTIC Science & Technology

1981-06-01

DEDUCTIVE SYNTHESIS OF THE I - UNIFICATION ALGORITHM Zohar Manna Richard Waldinger I F? Computer Science Department Artificial Intelligence Center...theorem proving," Artificial Intelligence Journal, Vol. 9, No. 1, pp. 1-35. Boyer, R. S. and J S. Moore [Jan. 19751, "Proving theorems about LISP...d’Intelligence Artificielle , U.E.R. de Luminy, Universit6 d’ Aix-Marseille II. Green, C. C. [May 1969], "Application of theorem proving to problem

Generalized Synchronization in AN Array of Nonlinear Dynamic Systems with Applications to Chaotic Cnn

NASA Astrophysics Data System (ADS)

Min, Lequan; Chen, Guanrong

This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.

Fixed-point theorems for families of weakly non-expansive maps

NASA Astrophysics Data System (ADS)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction

PubMed Central

Handa, Amrish

2014-01-01

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688

Transactions of the Conference of Army Mathematicians (25th).

DTIC Science & Technology

1980-01-01

pothesis (see description of H in Theorem 1). It follows from (4.16) and (4.17) that CT v Hv(4.18) CFT < MCT V V and, since the greatest eigenvalue of H is...0 (3.15)’ 𔃺 2 (ar) = 0 -138- Tr1W 𔃾A WlO (0,T) = a + 2 t1 W ( , T) = - - 2 r H* f* (3.16)� 2 W12 ( CfT ) = f 2 O T at + (a212) Hi - 2 If* 12 3 W2...Theorem 8.10 and Theorem 8.11. For these tables, use of (8.36) to get bounds for I aml is not possible. It will be noted that Theorems 8.10 and 8.11 give

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing.

PubMed

Satorra, Albert; Neudecker, Heinz

2015-12-01

This paper develops a theorem that facilitates computing the degrees of freedom of Wald-type chi-square tests for moment restrictions when there is rank deficiency of key matrices involved in the definition of the test. An if and only if (iff) condition is developed for a simple rule of difference of ranks to be used when computing the desired degrees of freedom of the test. The theorem is developed exploiting basics tools of matrix algebra. The theorem is shown to play a key role in proving the asymptotic chi-squaredness of a goodness of fit test in moment structure analysis, and in finding the degrees of freedom of this chi-square statistic.

A Systematic Study of Kelvin-Helmholtz Instability in Galaxy Clusters

NASA Astrophysics Data System (ADS)

Su, Yuanyuan

2017-09-01

Kelvin-Helmholtz instabilities (KHI) were observed at cold fronts in a handful of clusters. KHI are predicted at all cold fronts in hydro simulation of intracluster medium (ICM). Their presence and absence provides a unique probe of transport processes in the hot plasma, which are essential to the dissipation and redistribution of the energy in the ICM. We propose the first systematic study of the prevalence of KHI in galaxy clusters by analyzing the archived Chandra observations of a sample of 50 nearby galaxy clusters. We will associate the occurrence and properties of KHI rolls with various cluster parameters such as their gas temperature and density, and put constraints on effective transport coefficients in the ICM

Nonlocal description of sound propagation through an array of Helmholtz resonators

NASA Astrophysics Data System (ADS)

Nemati, Navid; Kumar, Anshuman; Lafarge, Denis; Fang, Nicholas X.

2015-12-01

A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory, which enables the description of resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties, such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, related to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures. xml:lang="fr"

Adsorption of organic molecules on a porous polymer surface modified with the supramolecular structure of melamine-cyanuric acid

NASA Astrophysics Data System (ADS)

Gainullina, Yu. Yu.; Guskov, V. Yu.

2017-10-01

The adsorption of organic molecules on the surface of a porous polymeric sorbent modified with a mixed cyanuric acid-melamine supramolecular structure is studied. The parameters of thermodynamic adsorption are considered and the contributions from intermolecular interactions to the Helmholtz energy of adsorption are assessed. Analysis of the molar changes in internal energy and adsorption entropy shows that the supramolecular structure formed on the surface could not exhibit dimension effects, indicating there were no cavities. The contributions from nonspecific interactions to the Helmholtz energy of adsorption generally fall, while those of specific interactions increase, indicating an increase in the polarity of the sorbent surface.

Black and gray Helmholtz-Kerr soliton refraction

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

Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposalmore » of positive or negative lensing operations on soliton arrays at planar boundaries.« less

Lattice vibrational contribution to equation of state for tetrahedral compounds

NASA Astrophysics Data System (ADS)

Kagaya, H.-Matsuo; Kotoku, H.; Soma, T.

1989-02-01

The lattice vibrational contributions to the Helmholtz free energy and the thermal pressure of tetrahedral compounds such as GaP, InP, ZnS, ZnSe, ZnTe and CdTe are investigated from the electronic theory of solids in the dynamical treatment based on our presented binding force. The temperature dependence of Helmholtz free energy and thermal pressure from lattice vibrational term are quantitatively obtained, and vibrational contributions to free energy are small compared with the static crystal energy. The influence of the thermal pressure is important to the equation of state in high temperatures, and the reformulation of the volume scale for the pressure-volume relation is given by considering the thermal pressure.

A DRBEM for steady infiltration from periodic semi-circular channels with two different types of roots distribution

NASA Astrophysics Data System (ADS)

Solekhudin, Imam; Sumardi

2017-05-01

In this study, problems involving steady Infiltration from periodic semicircular channels with root-water uptake function are considered. These problems are governed by Richards equation. This equation can be studied more conveniently by transforming the equation into a modified Helmholtz equation. In these problems, two different types of root-water uptake are considered. A dual reciprocity boundary element method (DRBEM) with a predictor-corrector scheme is used to solve the modified Helmholtz equation numerically. Using the solution obtained, numerical values of suction potential and root-water uptake function can be computed. In addition, amount of water absorbed by the different plant roots distribution can also be computed and compared.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

NASA Astrophysics Data System (ADS)

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-01

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

Diffraction in volume reflection gratings with variable fringe contrast.

PubMed

Brotherton-Ratcliffe, David; Bjelkhagen, Hans; Osanlou, Ardeshir; Excell, Peter

2015-06-01

The PSM model is used to analyze the process of diffraction occurring in volume reflection gratings in which fringe contrast is an arbitrary function of distance within the grating. General analytic expressions for diffraction efficiency at Bragg resonance are obtained for unslanted panchromatic lossless reflection gratings at oblique incidence. These formulas are then checked for several diverse fringe contrast profiles with numerical solutions of the Helmholtz equation, where exceptionally good agreement is observed. Away from Bragg resonance, the case of the hyperbolically decaying fringe contrast profile is shown to lead to an analytic expression for the diffraction efficiency and this is again compared successfully with numerical solutions of the Helmholtz equation.

Computational method for exact frequency-dependent rays on the basis of the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Protasov, M.; Gadylshin, K.

2017-07-01

A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analysed and compared with classical ray theory and with the method of finite-difference modelling for the first time. In this paper, we study the dependence of these rays on the frequency of signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones that are impenetrable for classical rays.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

Tomographic Processing of Synthetic Aperture Radar Signals for Enhanced Resolution

DTIC Science & Technology

1989-11-01

to image 3 larger scenes, this problem becomes more important. A byproduct of this investigation is a duality theorem which is a generalization of the...well-known Projection-Slice Theorem . The second prob- - lem proposed is that of imaging a rapidly-spinning object, for example in inverse SAR mode...slices is absent. There is a possible connection of the word to the Projection-Slice Theorem , but, as seen in Chapter 4, even this is absent in the

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Influence of a density increase on the evolution of the Kelvin-Helmholtz instability and vortices

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

Amerstorfer, U. V.; Erkaev, N. V.; Institute of Computational Modelling, 660036 Krasnoyarsk

2010-07-15

Results of two-dimensional nonlinear numerical simulations of the magnetohydrodynamic Kelvin-Helmholtz instability are presented. A boundary layer of a certain width is assumed, which separates the plasma in the upper layer from the plasma in the lower layer. A special focus is given on the influence of a density increase toward the lower layer. The evolution of the Kelvin-Helmholtz instability can be divided into three different phases, namely, a linear growth phase at the beginning, followed by a nonlinear phase with regular structures of the vortices, and finally, a turbulent phase with nonregular structures. The spatial scales of the vortices aremore » about five times the initial width of the boundary layer. The considered configuration is similar to the situation around unmagnetized planets, where the solar wind (upper plasma layer) streams past the ionosphere (lower plasma layer), and thus the plasma density increases toward the planet. The evolving vortices might detach around the terminator of the planet and eventually so-called plasma clouds might be formed, through which ionospheric material can be lost. For the special case of a Venus-like planet, loss rates are estimated, which are of the order of estimated loss rates from observations at Venus.« less

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

NASA Astrophysics Data System (ADS)

Stolk, Christiaan C.

2016-06-01

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

Performance evaluation of power transmission coils for powering endoscopic wireless capsules.

PubMed

Basar, Md Rubel; Ahmad, Mohd Yazed; Cho, Jongman; Ibrahim, Fatimah

2015-01-01

This paper presents an analysis of H-field generated by a simple solenoid, pair of solenoids, pair of double-layer solenoids, segmented-solenoid, and Helmholtz power transmission coils (PTCs) to power an endoscopic wireless capsule (WC). The H-fields were computed using finite element analysis based on partial differential equations. Three parameters were considered in the analysis: i) the maximum level of H-field (Hmax) to which the patient's body would be exposed, ii) the minimum level of H-field (Hmin) effective for power transmission, and iii) uniformity of H-field. We validated our analysis by comparing the computed data with data measured from a fabricated Helmholtz PTC. This analysis disclosed that at the same excitation power, all the PTCs are able to transfer same amount of minimum usable power since they generated almost equal value of Hmin. The level of electromagnetic exposure and power transfer stability across all the PTCs would vary significantly which is mainly due to the different level of Hmax and H-field uniformity. The segmented solenoid PTC would cause the lowest exposure and this PTC can transfer the maximum amount of power. The Helmholtz PTC would be able to transfer the most stable power with a moderate level of exposure.

An Orientation Dependent Size Illusion Is Underpinned by Processing in the Extrastriate Visual Area, LO1.

PubMed

Mikellidou, Kyriaki; Gouws, André D; Clawson, Hannah; Thompson, Peter; Morland, Antony B; Keefe, Bruce D

2016-01-01

We use the simple, but prominent Helmholtz's squares illusion in which a vertically striped square appears wider than a horizontally striped square of identical physical dimensions to determine whether functional magnetic resonance imaging (fMRI) BOLD responses in V1 underpin illusions of size. We report that these simple stimuli which differ in only one parameter, orientation, to which V1 neurons are highly selective elicited activity in V1 that followed their physical, not perceived size. To further probe the role of V1 in the illusion and investigate plausible extrastriate visual areas responsible for eliciting the Helmholtz squares illusion, we performed a follow-up transcranial magnetic stimulation (TMS) experiment in which we compared perceptual judgments about the aspect ratio of perceptually identical Helmholtz squares when no TMS was applied against selective stimulation of V1, LO1, or LO2. In agreement with fMRI results, we report that TMS of area V1 does not compromise the strength of the illusion. Only stimulation of area LO1, and not LO2, compromised significantly the strength of the illusion, consistent with previous research that LO1 plays a role in the processing of orientation information. These results demonstrate the involvement of a specific extrastriate area in an illusory percept of size.

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

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

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able tomore » extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.« less

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

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com; Plastino, A., E-mail: plastino@fisica.unlp.edu.ar

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS linkmore » and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.« less

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

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.

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Stochastic Version of the Noether Theorem

NASA Astrophysics Data System (ADS)

González Lezcano, Alfredo; Cabo Montes de Oca, Alejandro

2018-06-01

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

Noether’s second theorem and Ward identities for gauge symmetries

DOE PAGES

Avery, Steven G.; Schwab, Burkhard U. W.

2016-02-04

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less

A mathematical proof and example that Bayes's Theorem is fundamental to actuarial estimates of sexual recidivism risk.

PubMed

Donaldson, Theodore; Wollert, Richard

2008-06-01

Expert witnesses in sexually violent predator (SVP) cases often rely on actuarial instruments to make risk determinations. Many questions surround their use, however. Bayes's Theorem holds much promise for addressing these questions. Some experts nonetheless claim that Bayesian analyses are inadmissible in SVP cases because they are not accepted by the relevant scientific community. This position is illogical because Bayes's Theorem is simply a probabilistic restatement of the way that frequency data are combined to arrive at whatever recidivism rates are paired with each test score in an actuarial table. This article presents a mathematical proof and example validating this assertion. The advantages and implications of a logic model that combines Bayes's Theorem and the null hypothesis are also discussed.

Sharp comparison theorems for the Klein-Gordon equation in d dimensions

NASA Astrophysics Data System (ADS)

Hall, Richard L.; Zorin, Petr

2016-06-01

We establish sharp (or ’refined’) comparison theorems for the Klein-Gordon equation. We show that the condition Va ≤ Vb, which leads to Ea ≤ Eb, can be replaced by the weaker assumption Ua ≤ Ub which still implies the spectral ordering Ea ≤ Eb. In the simplest case, for d = 1, Ui(x) =∫0xV i(t)dt, i = a or b and for d > 1, Ui(r) =∫0rV i(t)td-1dt, i = a or b. We also consider sharp comparison theorems in the presence of a scalar potential S (a ‘variable mass’) in addition to the vector term V (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.

Logical errors on proving theorem

NASA Astrophysics Data System (ADS)

Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.

2018-01-01

In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.

Necessary and sufficient conditions for the stability of a sleeping top described by three forms of dynamic equations

NASA Astrophysics Data System (ADS)

Ge, Zheng-Ming

2008-04-01

Necessary and sufficient conditions for the stability of a sleeping top described by dynamic equations of six state variables, Euler equations, and Poisson equations, by a two-degree-of-freedom system, Krylov equations, and by a one-degree-of-freedom system, nutation angle equation, is obtained by the Lyapunov direct method, Ge-Liu second instability theorem, an instability theorem, and a Ge-Yao-Chen partial region stability theorem without using the first approximation theory altogether.

Twelve years before the quantum no-cloning theorem

NASA Astrophysics Data System (ADS)

Ortigoso, Juan

2018-03-01

The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.

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.

A Pseudo-Reversing Theorem for Rotation and its Application to Orientation Theory

DTIC Science & Technology

2012-03-01

approach to the task of constructing the appropriate course a ship must steer in order for the wind to appear to come from some given direction with some...axes, although the theorem doesn’t actually require such axes. The Pseudo-Reversing Theorem can often be invoked to give a different pedagogical basis to...of validity will quickly become obvious when it’s implemented on a computer. It does not seem to me that a great deal of pedagogical effort has found

Naval Research Logistics Quarterly. Volume 28. Number 1,

DTIC Science & Technology

1981-03-01

doing %%e forfeit the contraction property and must base our analysis on other procedures t)ualit. theor. and the Perron - Frobenius theorem are the main...and the Perron - Frobenius theorem (see Varga [16] or Seneta 1141). 2. NOTATION AND PRELIMINARY RESULTS Let v and v be two vectors. Write x > .j...x). If P is a square matrix, p(P) will denote the spectral radius of P. If P > 0 and square then the Perron - Frobenius theorem gives us that Pv = p(P)x

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.

Advanced Wireless Integrated Navy Network

DTIC Science & Technology

2005-03-01

transmitter and the receiver (do), the height of the setup above the floor can be estimated using Pythagoras ’ theorem : 4 The destination’s deck can also...single-unit resource model. Theorem I (RUA’s Blocking Time) Under RUA with the single-unit resource model, a task T, can be blocked for at most the...wait-free objects. Theorem 2 (Comparison of RUA’s Sojourn Times) Under RUA, as the critical section tac: of a task T, becomes longer, the difference

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas

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

Tan, Shina

2008-12-15

For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al. A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure to the case of imbalanced populations.

Event Oriented Design and Adaptive Multiprocessing

DTIC Science & Technology

1991-08-31

System 5 2.3 The Classification 5 2.4 Real-Time Systems 7 2.5 Non Real-Time Systems 10 2.6 Common Characterizations of all Software Systems 10 2.7... Non -Optimal Guarantee Test Theorem 37 6.3.2 Chetto’s Optimal Guarantee Test Theorem 37 6.3.3 Multistate Case: An Extended Guarantee 39 Test Theorem...which subdivides all software systems according to the way in which they operate, such as interactive, non interactive, real-time, etc. Having defined

Hiproofs

NASA Technical Reports Server (NTRS)

Denney, Ewen; Power, John

2003-01-01

We introduce a hierarchical notion of formal proof, useful in the implementation of theorem provers, which we call highproofs. Two alternative definitions are given, motivated by existing notations used in theorem proving research. We define transformations between these two forms of hiproof, develop notions of underlying proof, and give a suitable definition of refinement in order to model incremental proof development. We show that our transformations preserve both underlying proofs and refinement. The relationship of our theory to existing theorem proving systems is discussed, as is its future extension.

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

Chen, Yong, E-mail: 83229994@qq.com; Ge, Hao, E-mail: haoge@pku.edu.cn; Xiong, Jie, E-mail: jiexiong@umac.mo

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions agree with the numerical results of the quantum Chirikov map.

[A wireless power transmission system for capsule endoscope].

PubMed

Xin, Wenhui; Yan, Guozheng; Wang, Wenxing

2010-06-01

In order to deliver power to the capsule endoscope, whose position and orientation are always changing when traveling along the alimentary tract, a wireless power transmission system based on electromagnetic coupling was proposed. The system is composed of Helmholtz transmitting coil and three-dimensional receiving coil. Helmholtz coil outside the body generates a uniform magnetic field covering the whole alimentary tract; three-dimensional coil inside retrieves stable power regardless of its position and orientation. The transmitter and receiver were designed and implemented, and the experiments validated the feasibility of the system. The results show that at least 320 mW of usable power can be transmitted to capsule endoscope when its position and orientation are changing at random and the transmitting power is 25W.

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

A new relativistic viscous hydrodynamics code and its application to the Kelvin–Helmholtz instability in high-energy heavy-ion collisions

DOE PAGES

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-09

Here, we construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We also split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. Furthemore, we check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken’s flow and the Israel–Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin–Helmholtz instability inmore » high-energy heavy-ion collisions.« less

Observations of Large-Amplitude, Parallel, Electrostatic Waves Associated with the Kelvin-Helmholtz Instability by the Magnetospheric Multiscale Mission

NASA Technical Reports Server (NTRS)

Wilder, F. D.; Ergun, R. E.; Schwartz, S. J.; Newman, D. L.; Eriksson, S.; Stawarz, J. E.; Goldman, M. V.; Goodrich, K. A.; Gershman, D. J.; Malaspina, D.;

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.

PubMed

Achilleos, V; Richoux, O; Theocharis, G; Frantzeskakis, D J

2015-02-01

We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid

NASA Astrophysics Data System (ADS)

Sastre, Francisco; Moreno-Hilario, Elizabeth; Sotelo-Serna, Maria Guadalupe; Gil-Villegas, Alejandro

2018-02-01

The microcanonical-ensemble computer simulation method (MCE) is used to evaluate the perturbation terms Ai of the Helmholtz free energy of a square-well (SW) fluid. The MCE method offers a very efficient and accurate procedure for the determination of perturbation terms of discrete-potential systems such as the SW fluid and surpass the standard NVT canonical ensemble Monte Carlo method, allowing the calculation of the first six expansion terms. Results are presented for the case of a SW potential with attractive ranges 1.1 ≤ λ ≤ 1.8. Using semi-empirical representation of the MCE values for Ai, we also discuss the accuracy in the determination of the phase diagram of this system.

Seafloor identification in sonar imagery via simulations of Helmholtz equations and discrete optimization

NASA Astrophysics Data System (ADS)

Engquist, Björn; Frederick, Christina; Huynh, Quyen; Zhou, Haomin

2017-06-01

We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates multiscale simulations, by coupling Helmholtz equations and geometrical optics for a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including material type. Simulated backscattered data is generated using numerical microlocal analysis techniques. In order to lower the computational cost of the large-scale simulations in the inversion process, we take advantage of a pre-computed library of representative acoustic responses from various seafloor parameterizations.

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Magnetic reconnection driven by Gekko XII lasers with a Helmholtz capacitor-coil target

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

Pei, X. X.; University of Chinese Academy of Sciences, Beijing 100049; Zhong, J. Y., E-mail: jyzhong@bnu.edu.cn, E-mail: gzhao@bao.ac.cn

2016-03-15

We demonstrate a novel plasma device for magnetic reconnection, driven by Gekko XII lasers irradiating a double-turn Helmholtz capacitor-coil target. Optical probing revealed an accumulated plasma plume near the magnetic reconnection outflow. The background electron density and magnetic field were measured to be approximately 10{sup 18 }cm{sup −3} and 60 T by using Nomarski interferometry and the Faraday effect, respectively. In contrast with experiments on magnetic reconnection constructed by the Biermann battery effect, which produced high beta values, our beta value was much lower than one, which greatly extends the parameter regime of laser-driven magnetic reconnection and reveals its potential in astrophysicalmore » plasma applications.« less

Exploring the distinction between experimental resonant modes and theoretical eigenmodes: from vibrating plates to laser cavities.

PubMed

Tuan, P H; Wen, C P; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2014-02-01

Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

Effect of triangular element orientation on finite element solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1986-01-01

The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Generalized Bezout's Theorem and its applications in coding theory

NASA Technical Reports Server (NTRS)

Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

Profiling procedure for disk cutter to generate the male rotor, screw compressors component, using the “Substitute Family Circle” - graphic method in AUTOCAD environment

NASA Astrophysics Data System (ADS)

Popa, CL; Popa, V.

2016-11-01

This paper proposes a profiling method for the tool which generates the helical groove of male rotor, screw compressor component. The method is based on a complementary theorem of surfaces enveloping - "Substitute Family Circles Method”. The specific theorem of family circles of substitution has been applied using AUTOCAD graphics design environment facility. The frontal view of the male rotor, screw compressor component, has been determinate knowing the transverse profile of female rotor, and using this theorem of "Substitute Family Circle". The three-dimensional model of the rotor makes possible to apply the same theorem, leading to the surface of revolution enveloping the helical surface. An application will be also presented to determine the axial profile of the disk cutter, numeric and graphics, following the proposed algorithm.

Model Checking Failed Conjectures in Theorem Proving: A Case Study

NASA Technical Reports Server (NTRS)

Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

2004-01-01

Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

Kochen-Specker theorem studied with neutron interferometer.

PubMed

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Verification of the FtCayuga fault-tolerant microprocessor system. Volume 2: Formal specification and correctness theorems

NASA Technical Reports Server (NTRS)

Bickford, Mark; Srivas, Mandayam

1991-01-01

Presented here is a formal specification and verification of a property of a quadruplicately redundant fault tolerant microprocessor system design. A complete listing of the formal specification of the system and the correctness theorems that are proved are given. The system performs the task of obtaining interactive consistency among the processors using a special instruction on the processors. The design is based on an algorithm proposed by Pease, Shostak, and Lamport. The property verified insures that an execution of the special instruction by the processors correctly accomplishes interactive consistency, providing certain preconditions hold, using a computer aided design verification tool, Spectool, and the theorem prover, Clio. A major contribution of the work is the demonstration of a significant fault tolerant hardware design that is mechanically verified by a theorem prover.

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

Fixed point theorems for generalized contractions in ordered metric spaces

NASA Astrophysics Data System (ADS)

O'Regan, Donal; Petrusel, Adrian

2008-05-01

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

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.

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

Matching factorization theorems with an inverse-error weighting

NASA Astrophysics Data System (ADS)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

2018-06-01

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

A Minimum Path Algorithm Among 3D-Polyhedral Objects

NASA Astrophysics Data System (ADS)

Yeltekin, Aysin

1989-03-01

In this work we introduce a minimum path theorem for 3D case. We also develop an algorithm based on the theorem we prove. The algorithm will be implemented on the software package we develop using C language. The theorem we introduce states that; "Given the initial point I, final point F and S be the set of finite number of static obstacles then an optimal path P from I to F, such that PA S = 0 is composed of straight line segments which are perpendicular to the edge segments of the objects." We prove the theorem as well as we develop the following algorithm depending on the theorem to find the minimum path among 3D-polyhedral objects. The algorithm generates the point Qi on edge ei such that at Qi one can find the line which is perpendicular to the edge and the IF line. The algorithm iteratively provides a new set of initial points from Qi and exploits all possible paths. Then the algorithm chooses the minimum path among the possible ones. The flowchart of the program as well as the examination of its numerical properties are included.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Matching factorization theorems with an inverse-error weighting

DOE PAGES

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; ...

2018-04-03

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

Discrete Jordan curve theorem

NASA Astrophysics Data System (ADS)

Chen, Li

1999-09-01

According to a general definition of discrete curves, surfaces, and manifolds (Li Chen, 'Generalized discrete object tracking algorithms and implementations, ' In Melter, Wu, and Latecki ed, Vision Geometry VI, SPIE Vol. 3168, pp 184 - 195, 1997.). This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected surface into two components. Based on the definition of discrete surfaces, we give three reasonable definitions of simply connected spaces. Theoretically, these three definition shall be equivalent. We have proved the Jordan curve theorem under the third definition of simply connected spaces. The Jordan theorem shows the relationship among an object, its boundary, and its outside area. In continuous space, the boundary of an mD manifold is an (m - 1)D manifold. The similar result does apply to regular discrete manifolds. The concept of a new regular nD-cell is developed based on the regular surface point in 2D, and well-composed objects in 2D and 3D given by Latecki (L. Latecki, '3D well-composed pictures,' In Melter, Wu, and Latecki ed, Vision Geometry IV, SPIE Vol 2573, pp 196 - 203, 1995.).

Matching factorization theorems with an inverse-error weighting

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

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

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.

On the locality of the no hair conjection and the measure of the universe

NASA Technical Reports Server (NTRS)

Pacher, Tibor; Stein-Schabes, Jaime A.

1988-01-01

The reently proposed proof by Jensen and Stein-Schabes of the No Hair Theorem for inhomogeneous spacetimes is analyzed, putting a special emphasis on the asymptotic behavior of the shear and curvature. It is concluded that the theorem only holds locally, and the minimum size a region should be is estimated in order for it to inflate. The assumptions used in the theorem are discussed in detail. The last section speculates about the possible measure of the set of spacetimes that would undergo inflation.

FAST TRACK COMMUNICATION: Singularity theorems based on trapped submanifolds of arbitrary co-dimension

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Senovilla, José M. M.

2010-08-01

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to an arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of the co-dimension 1, 2 or n.

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

Causality and a -theorem constraints on Ricci polynomial and Riemann cubic gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Lü, H.; Wu, Jun-Bao

2018-01-01

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost-free, exhibiting an a -theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost-free and a -theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

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

Mundt, Michael; Kuemmel, Stephan; Leeuwen, Robert van

2007-05-15

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

DTIC Science & Technology

2009-08-01

easily by Pythagoras theorem (i.e., (2r)2 = r2 + x21 for the triangle enclosed by h, x, c in Fig. 7a): x = ( √ (2r)2 − r2, 0) = ( √ 3r, 0) . (4...region [10]. Most notably, the separation proof in Section 4.7 is by overapproximation and tolerates asymmetric distances to c (Fig. 7b). Theorem 1... Theorem 1 is already sufficiently general, but the computational complexity high. It would be interesting future work to see if the informal robustness

A Review of Maximum Entropy Spectral Analysis and Applications to Fourier Spectroscopy.

DTIC Science & Technology

1985-04-03

1 From Pythagoras to Fourier 3 2. 2 The Periodogram as Introduced by Sir Arthur Schuster 6 2. 3 The Slutzky Effect and the Work of Yule 7 2.4 The...Transform 27 4. 2 The Z-Transform Convolution Theorem 29 4. 3 The Wiener -Khintchmne , Theorem 31 4.4 The Z-Transform of el. 3 5. A COMPARISON BETWEEN...the Convolution I’heoreni, the Wiene i-Khintrbitte Theorem , aind the conventional ;pp roach of Il1ac km in and Tuke-,. Finally, it should he

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem

NASA Astrophysics Data System (ADS)

Wong, Chun-Shang; Goree, J.; Gopalakrishnan, Ranganathan

2018-05-01

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-μ m sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-13

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

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

Gao, Kai; Fu, Shubin; Chung, Eric T.

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

Magnetic field homogeneity of a conical coaxial coil pair.

PubMed

Salazar, F J; Nieves, F J; Bayón, A; Gascón, F

2017-09-01

An analytical study of the magnetic field created by a double-conical conducting sheet is presented. The analysis is based on the expansion of the magnetic field in terms of Legendre polynomials. It is demonstrated analytically that the angle of the conical surface that produces a nearly homogeneous magnetic field coincides with that of a pair of loops that fulfills the Helmholtz condition. From the results obtained, we propose an electric circuit formed by pairs of isolated conducting loops tightly wound around a pair of conical surfaces, calculating numerically the magnetic field produced by this system and its heterogeneity. An experimental setup of the proposed circuit was constructed and its magnetic field was measured. The results were compared with those obtained by numerical calculation, finding a good agreement. The numerical results demonstrate a significant improvement in homogeneity in the field of the proposed pair of conical coils compared with that achieved with a simple pair of Helmholtz loops or with a double solenoid. Moreover, a new design of a double pair of conical coils based on Braunbek's four loops is also proposed to achieve greater homogeneity. Regarding homogeneity, the rating of the analyzed configurations from best to worst is as follows: (1) double pair of conical coils, (2) pair of conical coils, (3) Braunbek's four loops, (4) Helmholtz pair, and (5) solenoid pair.

Magnetic field homogeneity of a conical coaxial coil pair

NASA Astrophysics Data System (ADS)

Salazar, F. J.; Nieves, F. J.; Bayón, A.; Gascón, F.

2017-09-01

An analytical study of the magnetic field created by a double-conical conducting sheet is presented. The analysis is based on the expansion of the magnetic field in terms of Legendre polynomials. It is demonstrated analytically that the angle of the conical surface that produces a nearly homogeneous magnetic field coincides with that of a pair of loops that fulfills the Helmholtz condition. From the results obtained, we propose an electric circuit formed by pairs of isolated conducting loops tightly wound around a pair of conical surfaces, calculating numerically the magnetic field produced by this system and its heterogeneity. An experimental setup of the proposed circuit was constructed and its magnetic field was measured. The results were compared with those obtained by numerical calculation, finding a good agreement. The numerical results demonstrate a significant improvement in homogeneity in the field of the proposed pair of conical coils compared with that achieved with a simple pair of Helmholtz loops or with a double solenoid. Moreover, a new design of a double pair of conical coils based on Braunbek's four loops is also proposed to achieve greater homogeneity. Regarding homogeneity, the rating of the analyzed configurations from best to worst is as follows: (1) double pair of conical coils, (2) pair of conical coils, (3) Braunbek's four loops, (4) Helmholtz pair, and (5) solenoid pair.

Chamber music: an unusual Helmholtz resonator for song amplification in a Neotropical bush-cricket (Orthoptera, Tettigoniidae).

PubMed

Jonsson, Thorin; Chivers, Benedict D; Robson Brown, Kate; Sarria-S, Fabio A; Walker, Matthew; Montealegre-Z, Fernando

2017-08-15

Animals use sound for communication, with high-amplitude signals being selected for attracting mates or deterring rivals. High amplitudes are attained by employing primary resonators in sound-producing structures to amplify the signal (e.g. avian syrinx). Some species actively exploit acoustic properties of natural structures to enhance signal transmission by using these as secondary resonators (e.g. tree-hole frogs). Male bush-crickets produce sound by tegminal stridulation and often use specialised wing areas as primary resonators. Interestingly, Acanthacara acuta , a Neotropical bush-cricket, exhibits an unusual pronotal inflation, forming a chamber covering the wings. It has been suggested that such pronotal chambers enhance amplitude and tuning of the signal by constituting a (secondary) Helmholtz resonator. If true, the intact system - when stimulated sympathetically with broadband sound - should show clear resonance around the song carrier frequency which should be largely independent of pronotum material, and change when the system is destroyed. Using laser Doppler vibrometry on living and preserved specimens, microcomputed tomography, 3D-printed models and finite element modelling, we show that the pronotal chamber not only functions as a Helmholtz resonator owing to its intact morphology but also resonates at frequencies of the calling song on itself, making song production a three-resonator system. © 2017. Published by The Company of Biologists Ltd.

On Multiple Hall-Like Electron Currents and Tripolar Guide Magnetic Field Perturbations During Kelvin-Helmholtz Waves

NASA Astrophysics Data System (ADS)

Sturner, Andrew P.; Eriksson, Stefan; Nakamura, Takuma; Gershman, Daniel J.; Plaschke, Ferdinand; Ergun, Robert E.; Wilder, Frederick D.; Giles, Barbara; Pollock, Craig; Paterson, William R.; Strangeway, Robert J.; Baumjohann, Wolfgang; Burch, James L.

2018-02-01

Two magnetopause current sheet crossings with tripolar guide magnetic field signatures were observed by multiple Magnetosphere Multiscale (MMS) spacecraft during Kelvin-Helmholtz wave activity. The two out-of-plane magnetic field depressions of the tripolar guide magnetic field are largely supported by the observed in-plane electron currents, which are reminiscent of two clockwise Hall current loop systems. A comparison with a three-dimensional kinetic simulation of Kelvin-Helmholtz waves and vortex-induced reconnection suggests that MMS likely encountered the two Hall magnetic field depressions on either side of a magnetic reconnection X-line. Moreover, MMS observed an out-of-plane current reversal and a corresponding in-plane magnetic field rotation at the center of one of the current sheets, suggesting the presence of two adjacent flux ropes. The region inside one of the ion-scale flux ropes was characterized by an observed decrease of the total magnetic field, a strong axial current, and significant enhancements of electron density and parallel electron temperature. The flux rope boundary was characterized by currents opposite this axial current, strong in-plane and converging electric fields, parallel electric fields, and weak electron-frame Joule dissipation. These return current region observations may reflect a need to support the axial current rather than representing local reconnection signatures in the absence of any exhausts.

Helmholtz and Goethe -- controversies at the birth of modern neuroscience.

PubMed

Kesselring, Jürg

2013-01-01

Hermann von Helmholtz (1821-1894), a great German scientist and philosopher, made his mark during the exciting twilight period from the Enlightenment and Romanticism to the beginnings of modern neuroscience and offered new perspectives through his work. His early inclination was for physics, which he found more attractive than purely geometric and algebraic studies, but his father was not able to make it possible for him to study physics, and so he studied medicine in order to earn a living. His lecture before the Physical Society in Berlin on July 23, 1847, 'about the conservation of the force' marked an epochal turn, even though his intention had been to deliver 'merely, some critical investigations and arrangement of facts in favor of the physiologists' as well as good arguments for the refusal of the theory of 'vitality'. Even though these new concepts were at first dismissed as fantastic speculation by some of the authorities in physics and philosophy of the day, they were enthusiastically welcomed by younger students of philosophy and the older men soon had to allow themselves to be persuaded that the effectiveness of vitality, though great and beautiful, is actually always dependent on some source of energy. Helmholtz critically assessed Goethe as a physical scientist but he did not dispute his great importance as a poet. Copyright © 2012 S. Karger AG, Basel.

CBM Collaboration

NASA Astrophysics Data System (ADS)

Ablyazimov, T.; Abuhoza, A.; Adak, R.; Adamczewski-Musch, J.; Adamczyk, M.; Aggarwal, M. M.; Ahammed, Z.; Ahmad, F.; Ahmad, N.; Ahmad, S.; Akindinov, A.; Akishin, P.; Akishina, E.; Akishina, T.; Akishina, V.; Al-Turany, M.; Alexandrov, E.; Alexandrov, I.; Amar-Youcef, S.; Anđelić, M.; Andreeva, O.; Andrei, C.; Andronic, A.; Anisimov, Yu.; Appelshäuser, H.; Arend, A.; Argintaru, D.; Atkin, E.; Avdeev, S.; Averbeck, R.; Azmi, M. D.; Baban, V.; Bach, M.; Badura, E.; Baginyan, S.; Balle, T.; Balog, T.; Bandyopadhyay, S.; Banerjee, P.; Baranova, N.; Barczyk, T.; Bartoş, D.; Bashir, S.; Basrak, Z.; Baszczyk, M.; Batenkov, O.; Baublis, V.; Baumann, C.; Baznat, M.; Becker, K.-H.; Bel, T.; Belogurov, S.; Bendarouach, J.; Berceanu, I.; Bercuci, A.; Berdermann, E.; Berdnikov, A.; Berdnikov, Y.; Berendes, R.; Bergmann, C.; Bertini, D.; Bertini, O.; Beşliu, C.; Bezshyyko, O.; Bhaduri, P. P.; Bhasin, A.; Bhati, A. K.; Bhattacharjee, B.; Bhattacharyya, A.; Bhattacharyya, T. K.; Biswas, S.; Blau, D.; Blume, C.; Bocharov, Yu.; Böttger, S.; Borysova, M.; Breitner, T.; Brüning, U.; Brzychczyk, J.; Bubak, A.; Büsching, H.; Bychkov, A.; Byszuk, A.; Cai, Xu; Cãlin, M.; Cao, Ping; Čaplar, R.; Caragheorgheopol, G.; Carević, I.; Cătănescu, V.; Chakrabarti, A.; Chatterji, S.; Chattopadhyay, Sanatan; Chattopadhyay, Subhasis; Chen, Hongfang; Cheng, Jianping; Chepurnov, V.; Chernenko, S.; Chernogorov, A.; Choi, Kyung-Eon; Ciobanu, M. I.; Claus, G.; Constantin, F.; Covlea, V.; Csanád, M.; D'Ascenzo, N.; Das, S.; Davkov, K.; Davkov, V.; de Cuveland, J.; Debnath, B.; Dementiev, D.; Deng, Zhi; Deppe, H.; Deppner, I.; Derenovskaya, O.; Deveaux, C. A.; Deveaux, M.; Dey, K.; Dey, M.; Dillenseger, P.; Dobyrn, V.; Doering, D.; Dorokhov, A.; Drozd, A.; Dubey, A. K.; Dubnichka, S.; Dubnichkova, A.; Dürr, M.; Dulinski, W.; Dutka, L.; Dželalija, M.; Emschermann, D.; Engel, H.; Eremin, V.; Eşanu, T.; Eschke, J.; Eschweiler, D.; Eum, Jongsik; Fan, Huanhuan; Fateev, O.; Filozova, I.; Finogeev, D.; Fischer, P.; Flemming, H.; Frankenfeld, U.; Friese, V.; Friske, E.; Fröhlich, I.; Frühauf, J.; Fülöp, Á.; Gajda, J.; Galatyuk, T.; Galkin, A.; Galkin, V.; Gangopadhyay, G.; García Chávez, C.; Gašparić, I.; Gebelein, J.; Ghosh, P.; Ghosh, S. K.; Goffe, M.; Golinka-Bezshyyko, L.; Golovatyuk, V.; Golovnya, S.; Golovtsov, V.; Golubeva, M.; Golubkov, D.; Gómez Ramírez, A.; Gorbunov, S.; Gorokhov, S.; Gottschalk, D.; Gryboś, P.; Grzeszczuk, A.; Guber, F.; Gudima, K.; Gupta, A.; Gusakov, Yu.; Haldar, A.; Haldar, S.; Hartmann, H.; Hehner, J.; Heidel, K.; Heine, N.; Hellbär, E.; Herghelegiu, A.; Herrmann, N.; Heß, B.; Heuser, J. M.; Himmi, A.; Höhne, C.; Holzmann, R.; Huang, Guangming; Huang, Xinjie; Hutsch, J.; Hutter, D.; Iakovleva, E.; Ierusalimov, A.; Ilgenfritz, E.-M.; Irfan, M.; Ivanov, M.; Ivanov, Valery; Ivanov, Victor; Ivanov, Vladimir; Ivashkin, A.; Jaaskelainen, K.; Jahan, H.; Jain, V.; Jakovlev, V.; Janson, T.; Jipa, A.; Kadenko, I.; Kämpfer, B.; Kalcher, S.; Kalinin, V.; Kampert, K.-H.; Kang, Tae Im; Kaptur, E.; Karabowicz, R.; Karavichev, O.; Karavicheva, T.; Karmanov, D.; Karnaukhov, V.; Karpechev, E.; Kasiński, K.; Kasprowicz, G.; Kaur, M.; Kazantsev, A.; Kebschull, U.; Kekelidze, G.; Khan, M. M.; Khan, S. A.; Khanzadeev, A.; Khasanov, F.; Khvorostukhin, A.; Kirakosyan, V.; Kirejczyk, M.; Kiryakov, A.; Kiš, M.; Kisel, I.; Kisel, P.; Kiselev, S.; Kiss, A.; Kiss, T.; Klaus, P.; Kłeczek, R.; Klein-Bösing, Ch.; Kleipa, V.; Kmon, P.; Koch, K.; Kochenda, L.; Koczoń, P.; König, W.; Kohn, M.; Kolb, B. W.; Kolosova, A.; Komkov, B.; Kopfer, J. M.; Korolev, M.; Korolko, I.; Kotte, R.; Kotynia, A.; Kovalchuk, A.; Kowalski, S.; Koziel, M.; Kozlov, G.; Kravtsov, P.; Krebs, E.; Kreidl, C.; Kresan, D.; Kretschmar, G.; Kretz, M.; Krieger, M.; Kryshen, E.; Kucewicz, W.; Kudin, L.; Kugler, A.; Kulakov, I.; Kunkel, J.; Kurepin, A.; Kurilkin, P.; Kushpil, V.; Kyva, V.; Ladygin, V.; Lara, C.; Larionov, P.; Laso Garcia, A.; Lavrik, E.; Lazanu, I.; Lebedev, A.; Lebedev, S.; Lebedeva, E.; Lehnert, J.; Lehrbach, J.; Lemke, F.; Li, Cheng; Li, Jin; Li, Qiyan; Li, Yuanjing; Li, Yulan; Lindenstruth, V.; Linev, S.; Linnik, B.; Litvinenko, E.; Liu, Feng; Lobanov, I.; Lobanova, E.; Löchner, S.; Loizeau, P.-A.; Lucio Martínez, J. A.; Lymanets, A.; Maevskaya, A.; Mahajan, S.; Mahapatra, D. P.; Mahmoud, T.; Maj, P.; Majka, Z.; Malakhov, A.; Malankin, E.; Malkevich, D.; Malyatina, O.; Malygina, H.; Mandal, S.; Manko, V.; Manz, S.; Marin, V.; Marin Garcia, A. M.; Markert, J.; Masciocchi, S.; Matulewicz, T.; Merkin, M.; Mialkovski, V.; Michel, J.; Miftakhov, N.; Mikhailov, K.; Mikhaylov, V.; Milanović, B.; Militsija, V.; Mir, M. F.; Miskowiec, D.; Morhardt, T.; Müller, W. F. J.; Müntz, C.; Murin, Yu.; Najman, R.; Naumann, L.; Nayak, T.; Nedosekin, A.; Neumann, B.; Niebur, W.; Nikulin, V.; Normanov, D.; Nüssle, M.; Oancea, A.; Oh, Kunsu; Onishchuk, Y.; Osipov, D.; Ososkov, G.; Ossetski, D.; Otfinowski, P.; Ovcharenko, E.; Pal, S.; Panasenko, I.; Panda, N. R.; Parzhitskiy, S.; Pauly, C.; Peng, Haiping; Peric, I.; Peshekhonov, D.; Peshekhonov, V.; Petráček, V.; Petriş, M.; Petrovici, A.; Petrovici, M.; Petrovskiy, A.; Petukhov, O.; Piasecki, K.; Pieper, J.; Pietraszko, J.; Płaneta, R.; Plekhanov, E.; Plotnikov, V.; Plujko, V.; Pluta, J.; Poliakov, V.; Polozov, P.; Pop, A.; Popov, V.; Pospisil, V.; Potukuchi, B. V. K. S.; Pouryamout, J.; Poźniak, K.; Prakash, A.; Prokudin, M.; Pshenichnov, I.; Pugach, M.; Pugatch, V.; Querchfeld, S.; Radulescu, L.; Raha, S.; Raja, W.; Rami, F.; Raniwala, R.; Raniwala, S.; Raportirenko, A.; Rautenberg, J.; Rauza, J.; Ray, R.; Razin, S.; Reichelt, P.; Reinecke, S.; Reshetin, A.; Ristea, C.; Ristea, O.; Roether, F.; Romaniuk, R.; Rost, A.; Rostchin, E.; Rostovtseva, I.; Roy, A.; Rożynek, J.; Ryabov, Yu.; Rykalin, V.; Sadovsky, A.; Sadovsky, S.; Sahoo, R.; Sahu, P. K.; Saini, J.; Samanta, S.; Sambyal, S. S.; Samsonov, V.; Sánchez Rosado, J.; Sau, S.; Saveliev, V.; Schatral, S.; Schiaua, C.; Schmidt, C. J.; Schmidt, H. R.; Schmidt, K.; Schweda, K.; Scurtu, A.; Seck, F.; Seddiki, S.; Selyuzhenkov, I.; Semennikov, A.; Senger, A.; Senger, P.; Shabunov, A.; Shao, Ming; Sharma, M. K.; Shumeiko, N.; Shumikhin, V.; Sikora, B.; Simakov, A.; Simon, C.; Simons, C.; Singaraju, R. N.; Singh, A. K.; Singh, B. K.; Singh, C. P.; Singhal, V.; Siwek-Wilczyńska, K.; Škoda, L.; Skwira-Chalot, I.; Som, I.; Song, Jihye; Sorokin, I.; Sosin, Z.; Soyk, D.; Staszel, P.; Stavinskiy, A.; Stephan, E.; Storozhyk, D.; Strikhanov, M.; Strohauer, S.; Stroth, J.; Sturm, C.; Sultanov, R.; Sun, Yongjie; Svoboda, O.; Szczygieł, R.; Talukdar, R.; Tang, Zebo; Tanha, M.; Tarasiuk, J.; Tarassenkova, O.; Târzilă, M.-G.; Tiflov, V.; Tischler, T.; Tlustý, P.; Toia, A.; Tolyhi, T.; Topil'skaya, N.; Trageser, C.; Trivedy, P.; Tsakov, I.; Tsyupa, Yu.; Turowiecki, A.; Uhlig, F.; Usenko, E.; Valin, I.; Vasiliev, T.; Vassiliev, I.; Verbitskaya, E.; Verhoeven, W.; Veshikov, A.; Visinka, R.; Viyogi, Y. P.; Volkov, S.; Volkov, Yu.; Vorobiev, A.; Voronin, A.; Vovchenko, V.; Vznuzdaev, E.; Vznuzdaev, M.; Wang, Dong; Wang, Yaping; Yi, Wang; Wendisch, C.; Wessels, J. P.; Wiebusch, M.; Wiechula, J.; Wiedemann, B.; Wielanek, D.; Wieloch, A.; Winckler, N.; Winter, M.; Wiśniewski, K.; Wohlfeld, D.; Wolf, Gy.; Sanguk, Won; Wüstenfeld, J.; Xiang, Changzhou; Nu, Xu; Yi, Jun-Gyu; Yin, Zhongbao; Yoo, In-Kwon; Yue, Qian; Yuldashev, B.; Yushmanov, I.; Zabołotny, W.; Zaitsev, Yu.; Zanevsky, Yu.; Zhalov, M.; Zhang, Ya Peng; Zhang, Yifei; Zhou, Daicui; Zhu, Xianglei; Zinchenko, A.; Zipper, W.; Żoładź, M.; Zrelov, P.; Zryuev, V.; Zumbruch, P.; Zyzak, M.

2014-11-01

We acknowledge support by the Seventh Framework Programme (FP7) of the European Commission through projects AIDA, CRISP and HadronPhysics3; the Bundesministerium für Bildung und Forschung, Germany, through the grants 05P09PXFC5, 05P12PXFCE, 05P12RFFC7, 05P12RFFCM, 05P12RFFCP, 05P12RGFCG,05P12RGGHM, 05P12VHFCE, 05P12VHFCF, 05PRVHFC7, and 06HD9123I; the Deutsche Forschungsgemeinschaft, Germany, grant GRK 1039; the Hessian Loewe Initiative through the Helmholtz International Center for FAIR (HIC4FAIR); the Helmholtz Graduate School HIRe; the Helmholtz Research School H-QM; the GSI Helmholzzentrum für Schwerionenforschung mbH, Germany, through F&E cooperations with Goethe-Universität Frankfurt, Justus-Liebig-Universität Gießen and Bergische Universität Wuppertal (WKAMPE1012); the Department of Science and Technology, Government of India; the Department of Atomic Energy, Government of India; the Council of Scientific and Industrial Research, Government of India; the University Grants Commission, Government of India; the Indo-FAIR Co-ordination Centre, Bose Institute, Kolkata, India; the Strategic Grants POSDRU/89/1.5/S/58852 and PN-II-ID-PCE-IDEI 34/05.10.2011, Romania; the NASR/CAPACITATI-Modul III, Romania, contract nr. 179EU; the NASR/NUCLEU Project PN09370103, Romania; the FAIR Russia Research Center (FRRC), Russia; and the Federal Agency for Atomic Research (Rosatom), Russia.

B1 transmit phase gradient coil for single-axis TRASE RF encoding.

PubMed

Deng, Qunli; King, Scott B; Volotovskyy, Vyacheslav; Tomanek, Boguslaw; Sharp, Jonathan C

2013-07-01

TRASE (Transmit Array Spatial Encoding) MRI uses RF transmit phase gradients instead of B0 field gradients for k-space traversal and high-resolution MR image formation. Transmit coil performance is a key determinant of TRASE image quality. The purpose of this work is to design an optimized RF transmit phase gradient array for spatial encoding in a transverse direction (x- or y- axis) for a 0.2T vertical B0 field MRI system, using a single transmitter channel. This requires the generation of two transmit B1 RF fields with uniform amplitude and positive and negative linear phase gradients respectively over the imaging volume. A two-element array consisting of a double Maxwell-type coil and a Helmholtz-type coil was designed using 3D field simulations. The phase gradient polarity is set by the relative phase of the RF signals driving the simultaneously energized elements. Field mapping and 1D TRASE imaging experiments confirmed that the constructed coil produced the fields and operated as designed. A substantially larger imaging volume relative to that obtainable from a non-optimized Maxwell-Helmholtz design was achieved. The Maxwell (sine)-Helmholtz (cosine) approach has proven successful for a horizontal phase gradient coil. A similar approach may be useful for other phase-gradient coil designs. Copyright © 2013 Elsevier Inc. All rights reserved.

The Common Data Acquisition Platform in the Helmholtz Association

NASA Astrophysics Data System (ADS)

Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

2017-04-01

Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ``Matter and Technology'': ``Detector Technology and Systems'' and ``Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Forest Carbon Uptake and the Fundamental Theorem of Calculus

ERIC Educational Resources Information Center

Zobitz, John

2013-01-01

Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.

RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

DTIC Science & Technology

Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

Nonuniform sampling theorems for random signals in the linear canonical transform domain

NASA Astrophysics Data System (ADS)

Shuiqing, Xu; Congmei, Jiang; Yi, Chai; Youqiang, Hu; Lei, Huang

2018-06-01

Nonuniform sampling can be encountered in various practical processes because of random events or poor timebase. The analysis and applications of the nonuniform sampling for deterministic signals related to the linear canonical transform (LCT) have been well considered and researched, but up to now no papers have been published regarding the various nonuniform sampling theorems for random signals related to the LCT. The aim of this article is to explore the nonuniform sampling and reconstruction of random signals associated with the LCT. First, some special nonuniform sampling models are briefly introduced. Second, based on these models, some reconstruction theorems for random signals from various nonuniform samples associated with the LCT have been derived. Finally, the simulation results are made to prove the accuracy of the sampling theorems. In addition, the latent real practices of the nonuniform sampling for random signals have been also discussed.

John S. Bell's concept of local causality

NASA Astrophysics Data System (ADS)

Norsen, Travis

2011-12-01

John Stewart Bell's famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many workers assert that Bell's theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with ``hidden'' variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently--as establishing an ``essential conflict'' between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell's own views more widely known and to explain Bell's little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell's formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.

John S. Bell's concept of local causality

NASA Astrophysics Data System (ADS)

Norsen, Travis

2011-12-01

John Stewart Bell's famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many workers assert that Bell's theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with "hidden" variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an "essential conflict" between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell's own views more widely known and to explain Bell's little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell's formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering.

PubMed

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-08-26

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

Cone and trumpet concentrators in light of the general edge-ray theorem

NASA Astrophysics Data System (ADS)

Ries, Harald; Spirkl, Wolfgang; Winston, Roland

1995-08-01

Cone and trumpet are nonimaging concentrators which do not obey the traditional edge-ray principle. The latter states that edge rays from the source should be transferred to the edge of the target. These concentrators have traditionally been described in terms of the heuristic flow line principle. The edge-ray theorem has been generalized to include nonimaging reflectors with multiple reflections. One includes all multiply reflected rays as an auxiliary domain. The general edge-ray theorem then states that the edge rays to the union of source and auxiliary domain must be reflected to edge of the union of target and auxiliary domain by the first reflection. We show the setup for which cone and trumpet constitute perfect nonimaging concentrators in the light of the generalized edge-ray theorem. We discuss the cases where cones are very good approximations for the solutions of nonimaging problems.

Adiabatic Theorem for Quantum Spin Systems

NASA Astrophysics Data System (ADS)

Bachmann, S.; De Roeck, W.; Fraas, M.

2017-08-01

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

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

Periodic solution of neutral Lotka-Volterra system with periodic delays

NASA Astrophysics Data System (ADS)

Liu, Zhijun; Chen, Lansun

2006-12-01

A nonautonomous n-species Lotka-Volterra system with neutral delays is investigated. A set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this Lotka-Volterra system by applying an existence theorem and some analysis techniques, where the assumptions of the existence theorem are different from that of Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and that of abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969]. Moreover, a problem proposed by Freedman and Wu [H.I. Freedman, J. Wu, Periodic solution of single species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701] is answered.

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

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

According to the no-hair theorem, astrophysical black holes are uniquely described by their masses and spins. An observational test of the no-hair theorem can be performed by measuring at least three different multipole moments of the spacetime of a black hole and verifying whether their values are consistent with the unique combinations of the Kerr solution. In this paper, we study quasi-periodic variability observed in the emission from black holes across the electromagnetic spectrum as a test of the no-hair theorem. We derive expressions for the Keplerian and epicyclic frequencies in a quasi-Kerr spacetime, in which the quadrupole moment ismore » a free parameter in addition to mass and spin. We show that, for moderate spins, the Keplerian frequency is practically independent of small deviations of the quadrupole moment from the Kerr value, while the epicyclic frequencies exhibit significant variations. We apply this framework to quasi-periodic oscillations (QPOs) in black hole X-ray binaries in two different scenarios. In the case that a pair of QPOs can be identified as the fundamental g- and c-modes in the accretion disk, we show that the no-hair theorem can be tested in conjunction with an independent mass measurement. If pairs of oscillations are identified with non-parametric resonance of dynamical frequencies in the accretion disk, then testing the no-hair theorem also requires an independent measurement of the black hole spin. In addition, we argue that VLBI observations of Sgr A* may test the no-hair theorem through a combination of imaging observations and the detection of quasi-periodic variability.« less

Applications of square-related theorems

NASA Astrophysics Data System (ADS)

Srinivasan, V. K.

2014-04-01

The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.

[ ] 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.

Remarks on the Acceptance of Proofs: The Case of Some Recently Tackled Major Theorems.

ERIC Educational Resources Information Center

Neubrand, Michael

1989-01-01

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Trace theorem for quasi-Fuchsian groups

NASA Astrophysics Data System (ADS)

Connes, A.; Sukochev, F. A.; Zanin, D. V.

2017-10-01

We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322-325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.

On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator

ERIC Educational Resources Information Center

Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru

2009-01-01

The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

Nested Helmholtz coil design for producing homogeneous transient rotating magnetic fields

NASA Astrophysics Data System (ADS)

Podaru, George; Moore, John; Dani, Raj Kumar; Prakash, Punit; Chikan, Viktor

2015-03-01

Electromagnets that can produce strong rotating magnetic fields at kHz frequencies are potentially very useful to exert rotating force on magnetic nanoparticles as small as few nanometers in size. In this article, the construction of a pulsed high-voltage rotating electromagnet is demonstrated based on a nested Helmholtz coil design. The energy for the coils is provided by two high-voltage discharge capacitors. The triggered spark gaps used in the experiments show sufficient accuracy to achieve the high frequency rotating magnetic field. The measured strength of the rotating magnetic field is 200 mT. This magnetic field is scalable by increasing the number of turns on the coils, by reducing the dimensions of the coils and by increasing the discharge current/voltage of the capacitors.

Kelvin-Helmholtz Instability at Dayside Magnetopause, View from Local 3-D MHD Simulations

NASA Astrophysics Data System (ADS)

Ma, X.; Otto, A.; Delamere, P. A.

2014-12-01

During the past decade, Kelvin-Helmholtz (KH) modes have gained increasing attention for the interaction between the magnetosphere and the solar wind particularly for northward IMF. Recently, several studies showed that the KH mode may also operate near the equatorial plane under southward IMF conditions as well as at high latitudes for IMF mostly along the GSE y direction. It was also demonstrated that three-dimensional aspects are of critical importance for this process. This presentation will particularly address the mass transport rate and the amount of open magnetic flux created by reconnection driven by nonlinear KH modes as a function of IMF orientation. We will also discuss the plausible in situ and ground auroral observation signatures of the interaction between the KH waves and magnetic reconnection.

Some experiments related to L-star instability in rocket motors

NASA Technical Reports Server (NTRS)

Kumar, R. N.; Mcnamara, R. P.

1973-01-01

The role of solid phase heterogeneity on the low-pressure L-star instability of nonmetallized AP/PBAN propellants is explored. Four particle size distributions are employed in propellants that are otherwise identical. Over one hundred test firings were conducted in the 21/2 in. diameter L-star burner. Pressure time histories in the chamber and color movies of two firings constitute the raw data. An economical firing program was used which enables the interesting range of L-star values to be covered during a single firing (at a set mean pressure), through the variations in the depleting propellant volume. Time-independent combustion, Helmholtz mode, chuff mode, and the pressure-burst phenomena are revealed as the principal signatures. Of these, the Helmholtz mode is found to be the most ordered form of instability.

Effects of the Kelvin-Helmholtz surface instability on supersonic jets

NASA Technical Reports Server (NTRS)

Hardee, P. E.

1982-01-01

An exact numerical calculation is provided for of linear growth and phase velocity of Kelvin-Helmholtz unstable wave modes on a supersonic jet of cylindrical cross section. An expression for the maximally unstable wavenumber of each wave mode is found. Provided a sharp velocity discontinuity exists all wave modes are unstable. A combination of rapid jet expansion and velocity shear across a jet can effectively stabilize all wave modes. The more likely case of slow jet expansion and of velocity shear at the jet surface allows wave modes with maximally unstable wavelength longer than or on the order of the jet radius to grow. The relative energy in different wave modes and effect on the jet is investigated. Energy input into a jet resulting from surface instability is discussed.

Observation of dual-mode, Kelvin-Helmholtz instability vortex merger in a compressible flow

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

Wan, W. C.; Malamud, Guy; Shimony, A.

Here, we report the first observations of Kelvin-Helmholtz vortices evolving from well-characterized, dual-mode initial conditions in a steady, supersonic flow. The results provide the first measurements of the instability's vortex merger rate and supplement data on the inhibition of the instability's growth rate in a compressible flow. These experimental data were obtained by sustaining a shockwave over a foam-plastic interface with a precision-machined seed perturbation. This technique produced a strong shear layer between two plasmas at high-energy-density conditions. The system was diagnosed using x-ray radiography and was well-reproduced using hydrodynamic simulations. Experimental measurements imply that we observed the anticipated vortexmore » merger rate and growth inhibition for supersonic shear flow.« less

Observation of dual-mode, Kelvin-Helmholtz instability vortex merger in a compressible flow

DOE PAGES

Wan, W. C.; Malamud, Guy; Shimony, A.; ...

2017-04-25

Here, we report the first observations of Kelvin-Helmholtz vortices evolving from well-characterized, dual-mode initial conditions in a steady, supersonic flow. The results provide the first measurements of the instability's vortex merger rate and supplement data on the inhibition of the instability's growth rate in a compressible flow. These experimental data were obtained by sustaining a shockwave over a foam-plastic interface with a precision-machined seed perturbation. This technique produced a strong shear layer between two plasmas at high-energy-density conditions. The system was diagnosed using x-ray radiography and was well-reproduced using hydrodynamic simulations. Experimental measurements imply that we observed the anticipated vortexmore » merger rate and growth inhibition for supersonic shear flow.« less

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Evolution of the magnetic field generated by the Kelvin-Helmholtz instability

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

Modestov, M.; Bychkov, V.; Brodin, G.

2014-07-15

The Kelvin-Helmholtz instability in an ionized plasma is studied with a focus on the magnetic field generation via the Biermann battery (baroclinic) mechanism. The problem is solved by using direct numerical simulations of two counter-directed flows in 2D geometry. The simulations demonstrate the formation of eddies and their further interaction and merging resulting in a large single vortex. In contrast to general belief, it is found that the instability generated magnetic field may exhibit significantly different structures from the vorticity field, despite the mathematically identical equations controlling the magnetic field and vorticity evolution. At later stages of the nonlinear instabilitymore » development, the magnetic field may keep growing even after the hydrodynamic vortex strength has reached its maximum and started decaying due to dissipation.« less

Double-reconnected magnetic structures driven by Kelvin-Helmholtz vortices at the Earth's magnetosphere

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

Borgogno, D.; Califano, F.; Pegoraro, F.

2015-03-15

In an almost collisionless magnetohydrodynamic plasma in a relatively strong magnetic field, stresses can be conveyed far from the region where they are exerted, e.g., through the propagation of Alfvèn waves. The forced dynamics of line-tied magnetic structures in solar and stellar coronae (see, e.g., A. F. Rappazzo and E. N. Parker, Astrophys. J. 773, L2 (2013) and references therein) is a paradigmatic case. Here, we investigate how this action at a distance develops from the equatorial region of the Kelvin-Helmholtz unstable flanks of the Earth's magnetosphere leading to the onset, at mid latitude in both hemispheres, of correlated doublemore » magnetic field line reconnection events that can allow the solar wind plasma to enter the Earth's magnetosphere.« less

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics

NASA Technical Reports Server (NTRS)

Gingold, H.

1991-01-01

A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.

Stochastic stability

NASA Technical Reports Server (NTRS)

Kushner, H. J.

1972-01-01

The field of stochastic stability is surveyed, with emphasis on the invariance theorems and their potential application to systems with randomly varying coefficients. Some of the basic ideas are reviewed, which underlie the stochastic Liapunov function approach to stochastic stability. The invariance theorems are discussed in detail.

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.