Efficient numerical method for solving Cauchy problem for the Gamma equation

NASA Astrophysics Data System (ADS)

Koleva, Miglena N.

2011-12-01

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

Smooth solutions of the Navier-Stokes equations

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

Pokhozhaev, S I

2014-02-28

We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R{sup 3}. We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles.

Convection Regularization of High Wavenumbers in Turbulence ANS Shocks

DTIC Science & Technology

2011-07-31

dynamics of particles that adhere to one another upon collision and has been studied as a simple cosmological model for describing the nonlinear formation of...solution we mean a solution to the Cauchy problem in the following sense. Definition 5.1. A function u : R × [0, T ] 7→ RN is a weak solution of the...step 2 the limit function in the α → 0 limit is shown to satisfy the definition of a weak solution for the Cauchy problem. Without loss of generality

An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

NASA Astrophysics Data System (ADS)

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime

NASA Astrophysics Data System (ADS)

Gérard, C.; Wrochna, M.

2015-07-01

We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

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

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

Cauchy horizon stability in a collapsing spherical dust cloud: II. Energy bounds for test fields and odd-parity gravitational perturbations

NASA Astrophysics Data System (ADS)

Ortiz, Néstor; Sarbach, Olivier

2018-01-01

We analyze the stability of the Cauchy horizon associated with a globally naked, shell-focussing singularity arising from the complete gravitational collapse of a spherical dust cloud. In a previous work, we have studied the dynamics of spherical test scalar fields on such a background. In particular, we proved that such fields cannot develop any divergences which propagate along the Cauchy horizon. In the present work, we extend our analysis to the more general case of test fields without symmetries and to linearized gravitational perturbations with odd parity. To this purpose, we first consider test fields possessing a divergence-free stress-energy tensor satisfying the dominant energy condition, and we prove that a suitable energy norm is uniformly bounded in the domain of dependence of the initial slice. In particular, this result implies that free-falling observers co-moving with the dust particles measure a finite energy of the field, even as they cross the Cauchy horizon at points lying arbitrarily close to the central singularity. Next, for the case of Klein–Gordon fields, we derive point-wise bounds from our energy estimates which imply that the scalar field cannot diverge at the Cauchy horizon, except possibly at the central singular point. Finally, we analyze the behaviour of odd-parity, linear gravitational and dust perturbations of the collapsing spacetime. Similarly to the scalar field case, we prove that the relevant gauge-invariant combinations of the metric perturbations stay bounded away from the central singularity, implying that no divergences can propagate in the vacuum region. Our results are in accordance with previous numerical studies and analytic work in the self-similar case.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

PubMed

Suk, Heejun

2016-07-01

MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.

On the membrane approximation in isothermal film casting

NASA Astrophysics Data System (ADS)

Hagen, Thomas

2014-08-01

In this work, a one-dimensional model for isothermal film casting is studied. Film casting is an important engineering process to manufacture thin films and sheets from a highly viscous polymer melt. The model equations account for variations in film width and film thickness, and arise from thinness and kinematic assumptions for the free liquid film. The first aspect of our study is a rigorous discussion of the existence and uniqueness of stationary solutions. This objective is approached via the argument principle, exploiting the homotopy invariance of a family of analytic functions. As our second objective, we analyze the linearization of the governing equations about stationary solutions. It is shown that solutions for the associated boundary-initial value problem are given by a strongly continuous semigroup of bounded linear operators. To reach this result, we cast the relevant Cauchy problem in a more accessible form. These transformed equations allow us insight into the regularity of the semigroup, thus yielding the validity of the spectral mapping theorem for the semigroup and the spectrally determined growth property.

An Obstruction to the Integrability of a Class of Non-linear Wave Equations by 1-Stable Cartan Characteristics

NASA Astrophysics Data System (ADS)

Fackerell, E. D.; Hartley, D.; Tucker, R. W.

We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux's method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

NASA Astrophysics Data System (ADS)

Morisse, Baptiste

2018-04-01

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0 < σ <σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arxiv:arXiv:1611.07225], the instability follows from a long-time Cauchy-Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

Global Well-Posedness of the Incompressible Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Cai, Yuan; Lei, Zhen

2018-06-01

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

On the solutions of fractional order of evolution equations

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-01-01

In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2005-12-01

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

A regularization method for extrapolation of solar potential magnetic fields

NASA Technical Reports Server (NTRS)

Gary, G. A.; Musielak, Z. E.

1992-01-01

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

A Revision on Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials

NASA Astrophysics Data System (ADS)

Alonso, Ricardo J.; Gamba, Irene M.

2011-05-01

This short note complements the recent paper of the authors (Alonso, Gamba in J. Stat. Phys. 137(5-6):1147-1165, 2009). We revisit the results on propagation of regularity and stability using L p estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue's exponent α>1 in the angular part of the collision kernel in order to obtain finiteness in some constants involved in the regularity and stability estimates. As a consequence the L p regularity associated to the Cauchy problem of the space inhomogeneous Boltzmann equation holds for a finite range of p≥1 explicitly determined.

Degenerate Cauchy numbers of the third kind.

PubMed

Pyo, Sung-Soo; Kim, Taekyun; Rim, Seog-Hoon

2018-01-01

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

NASA Astrophysics Data System (ADS)

Chang, Chien-Chieh; Chen, Chia-Shyun

2002-06-01

A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.

An Effective Hybrid Evolutionary Algorithm for Solving the Numerical Optimization Problems

NASA Astrophysics Data System (ADS)

Qian, Xiaohong; Wang, Xumei; Su, Yonghong; He, Liu

2018-04-01

There are many different algorithms for solving complex optimization problems. Each algorithm has been applied successfully in solving some optimization problems, but not efficiently in other problems. In this paper the Cauchy mutation and the multi-parent hybrid operator are combined to propose a hybrid evolutionary algorithm based on the communication (Mixed Evolutionary Algorithm based on Communication), hereinafter referred to as CMEA. The basic idea of the CMEA algorithm is that the initial population is divided into two subpopulations. Cauchy mutation operators and multiple paternal crossover operators are used to perform two subpopulations parallelly to evolve recursively until the downtime conditions are met. While subpopulation is reorganized, the individual is exchanged together with information. The algorithm flow is given and the performance of the algorithm is compared using a number of standard test functions. Simulation results have shown that this algorithm converges significantly faster than FEP (Fast Evolutionary Programming) algorithm, has good performance in global convergence and stability and is superior to other compared algorithms.

Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor

NASA Astrophysics Data System (ADS)

Beyer, Florian; Paetz, Tim-Torben

2018-02-01

The Mars-Simon tensor (MST), which, e.g., plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper, we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a space-like I (i.e., for ∧ > 0). In contrast to the Bianchi equation, the MST equation is of Fuchsian type at I , for which existence and uniqueness results are derived.

The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Liu, Huan

2018-04-01

The Riemann-Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding 3× 3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy problem of the coupled nonlinear Schrödinger equation.

Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation

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

Zhou, Ping; Lv, Youbin; Wang, Hong

Optimal operation of a practical blast furnace (BF) ironmaking process depends largely on a good measurement of molten iron quality (MIQ) indices. However, measuring the MIQ online is not feasible using the available techniques. In this paper, a novel data-driven robust modeling is proposed for online estimation of MIQ using improved random vector functional-link networks (RVFLNs). Since the output weights of traditional RVFLNs are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with outliers. This affects the modeling accuracy of RVFLNs. To solve this problem, a Cauchy distribution weighted M-estimation basedmore » robust RFVLNs is proposed. Since the weights of different outlier data are properly determined by the Cauchy distribution, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Moreover, given that the BF is a complex nonlinear system with numerous coupling variables, the data-driven canonical correlation analysis is employed to identify the most influential components from multitudinous factors that affect the MIQ indices to reduce the model dimension. Finally, experiments using industrial data and comparative studies have demonstrated that the obtained model produces a better modeling and estimating accuracy and stronger robustness than other modeling methods.« less

Stress-intensity factors for a thick-walled cylinder containing an annular imbedded or external or internal surface crack

NASA Technical Reports Server (NTRS)

Erdol, R.; Erdogan, F.

1976-01-01

The elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack is considered. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.

Cauchy flights in confining potentials

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

2010-03-01

We analyze confining mechanisms for Lévy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target pdf (eventually asymptotic) equals the preselected one. To this end, dynamically distinct jump-type processes can be employed. We demonstrate that one “targeted stochasticity” scenario involves Langevin systems with a symmetric stable noise. Another derives from the Lévy-Schrödinger semigroup dynamics (closely linked with topologically induced super-diffusions), which has no standard Langevin representation. For computational and visualization purposes, the Cauchy driver is employed to exemplify our considerations.

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

Donnelly, William; Freidel, Laurent

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Well-posedness and Scattering for the Boltzmann Equations: Soft Potential with Cut-off

NASA Astrophysics Data System (ADS)

He, Lingbing; Jiang, Jin-Cheng

2017-07-01

We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model γ =2-N with initial data small in L^N_{x,v} where N=2,3 is the dimension. The proof relies on the existing inhomogeneous Strichartz estimates for the kinetic equation by Ovcharov (SIAM J Math Anal 43(3):1282-1310, 2011) and convolution-like estimates for the gain term of the Boltzmann collision operator by Alonso et al. (Commun Math Phys 298:293-322, 2010). The global dynamics of the solution is also characterized by showing that the small global solution scatters with respect to the kinetic transport operator in L^N_{x,v}. Also the connection between function spaces and cut-off soft potential model -N<γ <2-N is characterized in the local well-posedness result for the Cauchy problem with large initial data.

J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms

NASA Astrophysics Data System (ADS)

Fackler, Stephan

2017-05-01

An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous forms has maximal regularity if the time dependence is merely assumed to be continuous or even measurable. We give a negative answer to this question and discuss the minimal regularity needed for positive results.

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Analogues of Chernoff's theorem and the Lie-Trotter theorem

NASA Astrophysics Data System (ADS)

Neklyudov, Alexander Yu

2009-10-01

This paper is concerned with the abstract Cauchy problem \\dot x=\\mathrm{A}x, x(0)=x_0\\in\\mathscr{D}(\\mathrm{A}), where \\mathrm{A} is a densely defined linear operator on a Banach space \\mathbf X. It is proved that a solution x(\\,\\cdot\\,) of this problem can be represented as the weak limit \\lim_{n\\to\\infty}\\{\\mathrm F(t/n)^nx_0\\}, where the function \\mathrm F\\colon \\lbrack 0,\\infty)\\mapsto\\mathscr L(\\mathrm X) satisfies the equality \\mathrm F'(0)y=\\mathrm{A}y, y\\in\\mathscr{D}(\\mathrm{A}), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator \\mathrm{C} to be closable and for its closure to be the generator of a C_0-semigroup. Also, we obtain new criteria for the sum of two generators of C_0-semigroups to be the generator of a C_0-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

International Conference on Hyperbolic Problems Theory, Numerics, Applications Held in Stony Brook, New York on 13-17 June 1994

DTIC Science & Technology

1994-07-25

these equations, see Antman [1]. fourth order methods are the only ones that give good results Keyfits and Xranser [(3 considered the string with a...produces a weak solution to the Cauchy problem for arbitrarily large initial data by working in L 2 spaces. [1] Stuart S. Antman , "The Equations for

On homogeneous second order linear general quantum difference equations.

PubMed

Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M

2017-01-01

In this paper, we prove the existence and uniqueness of solutions of the β -Cauchy problem of second order β -difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β , defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β -difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β -difference equation.

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

Local subsystems in gauge theory and gravity

DOE PAGES

Donnelly, William; Freidel, Laurent

2016-09-16

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

The Cauchy problem for space-time monopole equations in Sobolev spaces

NASA Astrophysics Data System (ADS)

Huh, Hyungjin; Yim, Jihyun

2018-04-01

We consider the initial value problem of space-time monopole equations in one space dimension with initial data in Sobolev space Hs. Observing null structures of the system, we prove local well-posedness in almost critical space. Unconditional uniqueness and global existence are proved for s ≥ 0. Moreover, we show that the H1 Sobolev norm grows at a rate of at most c exp(ct2).

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion

NASA Astrophysics Data System (ADS)

Fukao, Takeshi; Kurima, Shunsuke; Yokota, Tomomi

2018-05-01

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as \\[ \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a growth condition for $\\beta$ even though the Stefan problem was excluded from examples of (P). This paper completely removes the growth condition for $\\beta$ by confirming Cauchy's criterion for solutions of the following approximate problem (P)$_{\\varepsilon}$ with approximate parameter $\\varepsilon>0$: \\[ \\frac{\\partial u_{\\varepsilon}}{\\partial t} + (-\\Delta+1)(\\varepsilon(-\\Delta+1)u_{\\varepsilon} + \\beta(u_{\\varepsilon}) + \\pi_{\\varepsilon}(u_{\\varepsilon})) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which is called the Cahn--Hilliard system, even if $\\Omega \\subset \\mathbb{R}^N$ ($N \\in \\mathbb{N}$) is an unbounded domain. Moreover, it can be seen that the Stefan problem is covered in the framework of this paper.

The Cauchy Problem for Ut = Delta u(m) When 0 m 1.

DTIC Science & Technology

1985-01-01

Ecuaciones Funcionales, Facultad de Matematicas, Universidad Complutense, Madrid 3, Spain. • * Department of Mathematics, University of Nancy I, B. P. 239...required on u° to provide even a local solution in time, namely * Dpto Ecuaciones Funcionales, Facultad de Matematicas, Universidad Complutense, Madrid 3

The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

NASA Astrophysics Data System (ADS)

Li, Chunxia; Li, Shi-Hao

2018-06-01

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Contact and crack problems for an elastic wedge. [stress concentration in elastic half spaces

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.

1974-01-01

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

A Truncated Cauchy Distribution

ERIC Educational Resources Information Center

Nadarajah, Saralees; Kotz, Samuel

2006-01-01

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

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…

Averaging of random walks and shift-invariant measures on a Hilbert space

NASA Astrophysics Data System (ADS)

Sakbaev, V. Zh.

2017-06-01

We study random walks in a Hilbert space H and representations using them of solutions of the Cauchy problem for differential equations whose initial conditions are numerical functions on H. We construct a finitely additive analogue of the Lebesgue measure: a nonnegative finitely additive measure λ that is defined on a minimal subset ring of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles with absolutely converging products of the side lengths and is invariant under shifts and rotations in H. We define the Hilbert space H of equivalence classes of complex-valued functions on H that are square integrable with respect to a shift-invariant measure λ. Using averaging of the shift operator in H over random vectors in H with a distribution given by a one-parameter semigroup (with respect to convolution) of Gaussian measures on H, we define a one-parameter semigroup of contracting self-adjoint transformations on H, whose generator is called the diffusion operator. We obtain a representation of solutions of the Cauchy problem for the Schrödinger equation whose Hamiltonian is the diffusion operator.

Well-posedness of the Cauchy problem for models of large amplitude internal waves

NASA Astrophysics Data System (ADS)

Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

2010-02-01

We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

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

Mitsuda, Eiji; Yoshino, Hirotaka; Tomimatsu, Akira

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from 'quasinormal' modes of the self-similar system as well as 'high-frequency' waves are clarified. We find a characteristic power-law time evolution of the outgoingmore » energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.« less

Global Well-Posedness of the NLS System for Infinitely Many Fermions

NASA Astrophysics Data System (ADS)

Chen, Thomas; Hong, Younghun; Pavlović, Nataša

2017-04-01

In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions d = 2, 3, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by Lewin and Sabin in [33,34], who addressed this problem for more regular pair interactions.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Inner cauchy horizon of axisymmetric and stationary black holes with surrounding matter in einstein-maxwell theory.

PubMed

Ansorg, Marcus; Hennig, Jörg

2009-06-05

We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8piJ);{2}+(4piQ;{2});{2}=A;{+}A;{-}, where A+ and A- denote the areas of event and Cauchy horizon, respectively.

KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2017-07-01

Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer) function is given in the case of a pure solitonic solution. Properties of this function are discussed in detail using the Kadomtsev-Petviashvili II equation as an example. This enables formulation of the Darboux transformations in terms of the Cauchy-Jost function and classification of these transformations. Action of Darboux transformations on Grassmanians—i.e. on the space of soliton parameters—is derived and the relation of the Darboux transformations with the property of total nonnegativity of elements of corresponding Grassmanians is discussed. To the memory of our friend and colleague Peter P Kulish

A relativistic generalisation of rigid motions

NASA Astrophysics Data System (ADS)

Llosa, J.; Molina, A.; Soler, D.

2012-07-01

A weaker substitute for the too restrictive class of Born-rigid motions is proposed, which we call radar-holonomic motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy problem are studied. We finally obtain an example of a radar-holonomic congruence containing a given worldline with a given value of the rotation on this line.

Decay of the compressible magneto-micropolar fluids

NASA Astrophysics Data System (ADS)

Zhang, Peixin

2018-02-01

This paper considers the large-time behavior of solutions to the Cauchy problem on the compressible magneto-micropolar fluid system under small perturbation in regular Sobolev space. Based on the time-weighted energy estimate, the asymptotic stability of the steady state with the strictly positive constant density, vanishing velocity, micro-rotational velocity, and magnetic field is established.

An Analytical Framework for Runtime of a Class of Continuous Evolutionary Algorithms.

PubMed

Zhang, Yushan; Hu, Guiwu

2015-01-01

Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based on Gaussian and Cauchy mutations, using an absorbing Markov chain. Given a constant variation, we calculate the runtime upper bound of special Gaussian mutation EP and Cauchy mutation EP. Our analysis reveals that the upper bounds are impacted by individual number, problem dimension number n, searching range, and the Lebesgue measure of the optimal neighborhood. Furthermore, we provide conditions whereby the average runtime of the considered EP can be no more than a polynomial of n. The condition is that the Lebesgue measure of the optimal neighborhood is larger than a combinatorial calculation of an exponential and the given polynomial of n.

On the Occurrence of Mass Inflation for the Einstein-Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law

NASA Astrophysics Data System (ADS)

Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond

2018-03-01

In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along the event horizon. More precisely, we construct open sets of characteristic data which, on the outgoing initial null hypersurface (taken to be the event horizon), converges exponentially to a reference Reissner-Nördstrom black hole at infinity. We prove the stability of the radius function at the Cauchy horizon, and show that, depending on the decay rate of the initial data, mass inflation may or may not occur. In the latter case, we find that the solution can be extended across the Cauchy horizon with continuous metric and Christoffel symbols in {L^2_{loc}} , thus violating the Christodoulou-Chruściel version of strong cosmic censorship.

The Cauchy-Schwarz Inequality and the Induced Metrics on Real Vector Spaces Mainly on the Real Line

ERIC Educational Resources Information Center

Ramasinghe, W.

2005-01-01

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

Multimodal Estimation of Distribution Algorithms.

PubMed

Yang, Qiang; Chen, Wei-Neng; Li, Yun; Chen, C L Philip; Xu, Xiang-Min; Zhang, Jun

2016-02-15

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima.

Empirical Analysis of Using Erasure Coding in Outsourcing Data Storage With Provable Security

DTIC Science & Technology

2016-06-01

the fastest encoding performance among the four tested schemes. We expected to observe that Cauchy Reed-Solomonwould be faster than Reed- Solomon for all...providing recoverability for POR. We survey MDS codes and select Reed- Solomon and Cauchy Reed- Solomon MDS codes to be implemented into a prototype POR...tools providing recoverability for POR. We survey MDS codes and select Reed- Solomon and Cauchy Reed- Solomon MDS codes to be implemented into a

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

To the theory of non-local non-isothermal filtration in porous medium

NASA Astrophysics Data System (ADS)

Meilanov, R. R.; Akhmedov, E. N.; Beybalaev, V. D.; Magomedov, R. A.; Ragimkhanov, G. B.; Aliverdiev, A. A.

2018-01-01

A new approach to the theory of non-local and non-isothermal filtration based on the mathematical apparatus of fractional order derivatives is developing. A solution of the Cauchy problem for the system of equations of non-local non-isothermal filtration in fractional calculus is obtained. Some applications of the solutions obtained to the problems of underground hydrodynamics (fracturing and explosion) are considered. A computational experiment was carried out to analyze the solutions obtained. Graphs of pressure and temperature dependences are plotted against time.

Mean estimation in highly skewed samples

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

Pederson, S P

The problem of inference for the mean of a highly asymmetric distribution is considered. Even with large sample sizes, usual asymptotics based on normal theory give poor answers, as the right-hand tail of the distribution is often under-sampled. This paper attempts to improve performance in two ways. First, modifications of the standard confidence interval procedure are examined. Second, diagnostics are proposed to indicate whether or not inferential procedures are likely to be valid. The problems are illustrated with data simulated from an absolute value Cauchy distribution. 4 refs., 2 figs., 1 tab.

Analysis of nonlinear internal waves observed by Landsat thematic mapper

NASA Astrophysics Data System (ADS)

Artale, V.; Levi, D.; Marullo, S.; Santoleri, R.

1990-09-01

In this work we test the compatibility between the theoretical parameters of a nonlinear wave model and the quantitative information that one can deduce from satellite-derived data. The theoretical parameters are obtained by applying an inverse problem to the solution of the Cauchy problem for the Korteweg-de Vries equation. Our results are applied to the case of internal wave patterns elaborated from two different satellite sensors at the south of Messina (the thematic mapper) and at the north of Messina (the synthetic aperture radar).

Representations for implicit constitutive relations describing non-dissipative response of isotropic materials

NASA Astrophysics Data System (ADS)

Gokulnath, C.; Saravanan, U.; Rajagopal, K. R.

2017-12-01

A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed. Using this methodology, a general constitutive representation for a subclass of implicit models relating the Cauchy stress and the Hencky strain is obtained for an isotropic material with no internal constraints. It is shown that even for this subclass, unlike classical Green elasticity, one has to specify three potentials to relate the Cauchy stress and the Hencky strain. Then, a procedure to obtain implicit constitutive representations for isotropic materials with internal constraints is presented. As an illustration, it is shown that for incompressible materials the Cauchy stress and the Hencky strain could be related through a single potential. Finally, constitutive approximations are obtained when the displacement gradient is small.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Oscillation Amplitude Growth for a Decelerating Object with Constant Pitch Damping

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Queen, Eric M.; Litton, Daniel

2006-01-01

The equations governing the deceleration and oscillation of a blunt body moving along a planar trajectory are re-expressed in the form of the Euler-Cauchy equation. An analytic solution of this equation describes the oscillation amplitude growth and frequency dilation with time for a statically stable decelerating body with constant pitch damping. The oscillation histories for several constant pitch damping values, predicted by the solution of the Euler-Cauchy equation are compared to POST six degree-of-freedom (6-DoF) trajectory simulations. The simulations use simplified aerodynamic coefficients matching the Euler-Cauchy approximations. Agreement between the model predictions and simulation results are excellent. Euler-Cauchy curves are also fit through nonlinear 6-DoF simulations and ballistic range data to identify static stability and pitch damping coefficients. The model os shown to closely fit through the data points and capture the behavior of the blunt body observed in simulation and experiment. The extracted coefficients are in reasonable agreement with higher fidelity, nonlinear parameter identification results. Finally, a nondimensional version of the Euler-Cauchy equation is presented and shown to be a simple and effective tool for designing dynamically scaled experiments for decelerating blunt capsule flight.

A Refined Cauchy-Schwarz Inequality

ERIC Educational Resources Information Center

Mercer, Peter R.

2007-01-01

The author presents a refinement of the Cauchy-Schwarz inequality. He shows his computations in which refinements of the triangle inequality and its reverse inequality are obtained for nonzero x and y in a normed linear space.

Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Ling, Eric

2018-06-01

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3 + 1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.

Inclusion of inhomogeneous deformation and strength characteristics in the problem on zonal disintegration of rocks

NASA Astrophysics Data System (ADS)

Chanyshev, AI; Belousova, OE

2018-03-01

The authors determine stress and deformation in a heterogeneous rock mass at the preset displacement and Cauchy stress vector at the boundary of an underground excavation. The influence of coordinates on Young’s modulus, shear modulus and ultimate strength is shown. It is found that regions of tension and compression alternate at the excavation boundary—i.e. zonal rock disintegration phenomenon is observed.

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

NASA Technical Reports Server (NTRS)

Banyukevich, A.; Ziolkovski, K.

1975-01-01

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Scattering for the 3D Gross-Pitaevskii Equation

NASA Astrophysics Data System (ADS)

Guo, Zihua; Hani, Zaher; Nakanishi, Kenji

2017-11-01

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gérard (Ann. Inst. H. Poincaré Anal. Non Linéaire 23(5):765-779, 2006). In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob; Englander, Arnold

2014-01-01

Trajectory optimization methods using MBH have become well developed during the past decade. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing RVs from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by Englander significantly improves MBH performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness, where efficiency is finding better solutions in less time, and robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive RWs originally developed in the field of statistical physics.

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

Chaotic dynamics of flexible Euler-Bernoulli beams

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

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

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

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

The Stack of Yang-Mills Fields on Lorentzian Manifolds

NASA Astrophysics Data System (ADS)

Benini, Marco; Schenkel, Alexander; Schreiber, Urs

2018-03-01

We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in Hollander (Isr. J. Math. 163:93-124, 2008), which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BG con.

Interaction between a crack and a soft inclusion

NASA Technical Reports Server (NTRS)

Xue-Hui, L.; Erdogan, F.

1985-01-01

With the application to weld defects in mind, the interaction problem between a planar-crack and a flat inclusion in an elastic solid is considered. The elastic inclusion is assumed to be sufficiently thin so that the thickness distribution of the stresses in the inclusion may be neglected. The problem is reduced to a system of four integral equations having Cauchy-type dominant kernels. The stress intensity factors are calculated and tabulated for various crack-inclusion geometries and the inclusion to matrix modulus ratios, and for general homogeneous loadiong conditions away from the crack-inclusion region.

Wave computation on the Poincaré dodecahedral space

NASA Astrophysics Data System (ADS)

Bachelot-Motet, Agnès

2013-12-01

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace-Beltrami operator.

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

Complicated asymptotic behavior of solutions for porous medium equation in unbounded space

NASA Astrophysics Data System (ADS)

Wang, Liangwei; Yin, Jingxue; Zhou, Yong

2018-05-01

In this paper, we find that the unbounded spaces Yσ (RN) (0 < σ <2/m-1 ) can provide the work spaces where complicated asymptotic behavior appears in the solutions of the Cauchy problem of the porous medium equation. To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions, we establish the propagation estimates, the growth estimates and the weighted L1-L∞ estimates for the solutions.

Optimization of the interplanetary trajectories of spacecraft with a solar electric propulsion power plant of minimal power

NASA Astrophysics Data System (ADS)

Ivanyukhin, A. V.; Petukhov, V. G.

2016-12-01

The problem of optimizing the interplanetary trajectories of a spacecraft (SC) with a solar electric propulsion system (SEPS) is examined. The problem of investigating the permissible power minimum of the solar electric propulsion power plant required for a successful flight is studied. Permissible ranges of thrust and exhaust velocity are analyzed for the given range of flight time and final mass of the spacecraft. The optimization is performed according to Portnyagin's maximum principle, and the continuation method is used for reducing the boundary problem of maximal principle to the Cauchy problem and to study the solution/ parameters dependence. Such a combination results in the robust algorithm that reduces the problem of trajectory optimization to the numerical integration of differential equations by the continuation method.

Adaptive grid based multi-objective Cauchy differential evolution for stochastic dynamic economic emission dispatch with wind power uncertainty

PubMed Central

Lei, Xiaohui; Wang, Chao; Yue, Dong; Xie, Xiangpeng

2017-01-01

Since wind power is integrated into the thermal power operation system, dynamic economic emission dispatch (DEED) has become a new challenge due to its uncertain characteristics. This paper proposes an adaptive grid based multi-objective Cauchy differential evolution (AGB-MOCDE) for solving stochastic DEED with wind power uncertainty. To properly deal with wind power uncertainty, some scenarios are generated to simulate those possible situations by dividing the uncertainty domain into different intervals, the probability of each interval can be calculated using the cumulative distribution function, and a stochastic DEED model can be formulated under different scenarios. For enhancing the optimization efficiency, Cauchy mutation operation is utilized to improve differential evolution by adjusting the population diversity during the population evolution process, and an adaptive grid is constructed for retaining diversity distribution of Pareto front. With consideration of large number of generated scenarios, the reduction mechanism is carried out to decrease the scenarios number with covariance relationships, which can greatly decrease the computational complexity. Moreover, the constraint-handling technique is also utilized to deal with the system load balance while considering transmission loss among thermal units and wind farms, all the constraint limits can be satisfied under the permitted accuracy. After the proposed method is simulated on three test systems, the obtained results reveal that in comparison with other alternatives, the proposed AGB-MOCDE can optimize the DEED problem while handling all constraint limits, and the optimal scheme of stochastic DEED can decrease the conservation of interval optimization, which can provide a more valuable optimal scheme for real-world applications. PMID:28961262

Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2018-05-01

In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.

Isentropic fluid dynamics in a curved pipe

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Holden, Helge

2016-10-01

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1].

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Englander, Arnold C.

2014-01-01

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems

NASA Astrophysics Data System (ADS)

Lastra, A.; Malek, S.

2015-11-01

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ɛ with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on (ɛ, t) near the origin in C2 and are bounded holomorphic on some horizontal strip in C w.r.t. the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t = 0 cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space, when the complex parameter ɛ belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood Ω of 0 in C*. These solutions are achieved by means of Laplace and Fourier inverse transforms of some common ɛ-depending function on C × R, analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second, when the perturbation parameter belongs to Ω. Moreover, these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w.r.t. ɛ. With the help of the classical Ramis-Sibuya theorem, we obtain the existence of a formal series (generally divergent) in ɛ which is the common Gevrey asymptotic expansion of the built up actual solutions considered above.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

Spectral Cauchy characteristic extraction of strain, news and gravitational radiation flux

NASA Astrophysics Data System (ADS)

Handmer, Casey J.; Szilágyi, Béla; Winicour, Jeffrey

2016-11-01

We present a new approach for the Cauchy-characteristic extraction (CCE) of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic symmetries. In CCE, a characteristic evolution code takes numerical data on an inner worldtube supplied by a Cauchy evolution code, and propagates it outwards to obtain the space-time metric in a neighborhood of null infinity. The metric is first determined in a scrambled form in terms of coordinates determined by the Cauchy formalism. In prior treatments, the waveform is first extracted from this metric and then transformed into an asymptotic inertial coordinate system. This procedure provides the physically proper description of the waveform and the radiated energy but it does not generalize to determine the flux of angular momentum or supermomentum. Here we formulate and implement a new approach which transforms the full metric into an asymptotic inertial frame and provides a uniform treatment of all the radiation fluxes associated with the asymptotic symmetries. Computations are performed and calibrated using the spectral Einstein code.

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Thermodynamics and Hawking radiation of five-dimensional rotating charged Goedel black holes

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

Wu Shuangqing; Peng Junjin; College of Science, Wuhan Textile University, Wuhan, Hubei 430074

2011-02-15

We study the thermodynamics of Goedel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed timelike curves and the absence of a globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, we extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and the effective action give the same Hawking fluxes as those from the Planckmore » distribution for blackbody radiation in the background of the charged rotating Goedel black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.« less

Temporal Quantum Correlations in Inelastic Light Scattering from Water.

PubMed

Kasperczyk, Mark; de Aguiar Júnior, Filomeno S; Rabelo, Cassiano; Saraiva, Andre; Santos, Marcelo F; Novotny, Lukas; Jorio, Ado

2016-12-09

Water is one of the most prevalent chemicals on our planet, an integral part of both our environment and our existence as a species. Yet it is also rich in anomalous behaviors. Here we reveal that water is a novel-yet ubiquitous-source for quantum correlated photon pairs at ambient conditions. The photon pairs are produced through Raman scattering, and the correlations arise from the shared quantum of a vibrational mode between the Stokes and anti-Stokes scattering events. We confirm the nonclassical nature of the produced photon pairs by showing that the cross-correlation and autocorrelations of the signals violate a Cauchy-Schwarz inequality by over 5 orders of magnitude. The unprecedented degree of violating the inequality in pure water, as well as the well-defined polarization properties of the photon pairs, points to its usefulness in quantum information.

Gauge invariant spectral Cauchy characteristic extraction

NASA Astrophysics Data System (ADS)

Handmer, Casey J.; Szilágyi, Béla; Winicour, Jeffrey

2015-12-01

We present gauge invariant spectral Cauchy characteristic extraction. We compare gravitational waveforms extracted from a head-on black hole merger simulated in two different gauges by two different codes. We show rapid convergence, demonstrating both gauge invariance of the extraction algorithm and consistency between the legacy Pitt null code and the much faster spectral Einstein code (SpEC).

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Ultrarelativistic bound states in the spherical well

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

Żaba, Mariusz; Garbaczewski, Piotr

2016-07-15

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ){sup 1/2}, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E{sub (k,l)} series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth seriesmore » eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E{sub (k,0)} are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E{sub (k,0)}(d = 3) = E{sub 2k}(d = 1). Likewise, the eigenfunctions ψ{sub (k,0)}(d = 3) and ψ{sub 2k}(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).« less

A preconditioned formulation of the Cauchy-Riemann equations

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

A preconditioning of the Cauchy-Riemann equations which results in a second-order system is described. This system is shown to have a unique solution if the boundary conditions are chosen carefully. This choice of boundary condition enables the solution of the first-order system to be retrieved. A numerical solution of the preconditioned equations is obtained by the multigrid method.

Common Misconceptions about the Dynamical Theory of Crystal Lattices: Cauchy Relations, Lattice Potentials and Infinite Crystals

ERIC Educational Resources Information Center

Elcoro, Luis; Etxebarria, Jesus

2011-01-01

The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

Determination of the refractive index of insoluble organic extracts from atmospheric aerosol over the visible wavelength range using optical tweezers

NASA Astrophysics Data System (ADS)

Shepherd, Rosalie H.; King, Martin D.; Marks, Amelia A.; Brough, Neil; Ward, Andrew D.

2018-04-01

Optical trapping combined with Mie spectroscopy is a new technique used to record the refractive index of insoluble organic material extracted from atmospheric aerosol samples over a wide wavelength range. The refractive index of the insoluble organic extracts was shown to follow a Cauchy equation between 460 and 700 nm for organic aerosol extracts collected from urban (London) and remote (Antarctica) locations. Cauchy coefficients for the remote sample were for the Austral summer and gave the Cauchy coefficients of A = 1.467 and B = 1000 nm2 with a real refractive index of 1.489 at a wavelength of 589 nm. Cauchy coefficients for the urban samples varied with season, with extracts collected during summer having Cauchy coefficients of A = 1.465 ± 0.005 and B = 4625 ± 1200 nm2 with a representative real refractive index of 1.478 at a wavelength of 589 nm, whilst samples extracted during autumn had larger Cauchy coefficients of A = 1.505 and B = 600 nm2 with a representative real refractive index of 1.522 at a wavelength of 589 nm. The refractive index of absorbing aerosol was also recorded. The absorption Ångström exponent was determined for woodsmoke and humic acid aerosol extract. Typical values of the Cauchy coefficient for the woodsmoke aerosol extract were A = 1.541 ± 0.03 and B = 14 800 ± 2900 nm2, resulting in a real refractive index of 1.584 ± 0.007 at a wavelength of 589 nm and an absorption Ångström exponent of 8.0. The measured values of refractive index compare well with previous monochromatic or very small wavelength range measurements of refractive index. In general, the real component of the refractive index increases from remote to urban to woodsmoke. A one-dimensional radiative-transfer calculation of the top-of-the-atmosphere albedo was applied to model an atmosphere containing a 3 km thick layer of aerosol comprising pure water, pure insoluble organic aerosol, or an aerosol consisting of an aqueous core with an insoluble organic shell. The calculation demonstrated that the top-of-the-atmosphere albedo increases by 0.01 to 0.04 for pure organic particles relative to water particles of the same size and that the top-of-the-atmosphere albedo increases by 0.03 for aqueous core-shell particles as volume fraction of the shell material increases to 25 %.

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

NASA Technical Reports Server (NTRS)

Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

2001-01-01

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

NASA Astrophysics Data System (ADS)

Van de Moortel, Maxime

2018-05-01

We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

NASA Astrophysics Data System (ADS)

Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

2017-06-01

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

A fictitious domain approach for the Stokes problem based on the extended finite element method

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel; Lozinski, Alexei

2014-01-01

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.

Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces

NASA Astrophysics Data System (ADS)

Guo, Zihua

We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation ∂u+|∂u+uu=0, u(x,0)=u(x), is locally well-posed in the Sobolev spaces H for s>1-α if 0⩽α⩽1. The new ingredient is that we generalize the methods of Ionescu, Kenig and Tataru (2008) [13] to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and Tzvetkov (2001) [21]. Moreover, as a bi-product we prove that if 0<α⩽1 the corresponding modified equation (with the nonlinearity ±uuu) is locally well-posed in H for s⩾1/2-α/4.

Processes of aggression described by kinetic method

NASA Astrophysics Data System (ADS)

Aristov, V. V.; Ilyin, O.

2014-12-01

In the last decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France and USSR based on the kinetic theory. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial initial conditions. The solution of the problem is given in the form of traveling wave. The propagation velocity of a frontline depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the frontline velocities are complied with the historical data.

A New Goodness of Fit Test for Normality with Mean and Variance Unknown.

DTIC Science & Technology

1981-12-01

be realized, since fewer random deviates may have to be generated in order to get consistent critical values at the desired a levels . Plotting... a - levels n * -straightforward .20 .15 .10 .05 .01 * =reflection ..... 10 * .5710 .5120 .4318 .3208 .1612 10 ** .3670 .2914 .2206 .1388 .0390 25...Population Is Cauchy Actual Population: Cauchy Statistic: Kolmogorov-Smirnov Calculation method Powers at a - levels n = straightforwar .20 .15 .10 .05

Mammogram registration using the Cauchy-Navier spline

NASA Astrophysics Data System (ADS)

Wirth, Michael A.; Choi, Christopher

2001-07-01

The process of comparative analysis involves inspecting mammograms for characteristic signs of potential cancer by comparing various analogous mammograms. Factors such as the deformable behavior of the breast, changes in breast positioning, and the amount/geometry of compression may contribute to spatial differences between corresponding structures in corresponding mammograms, thereby significantly complicating comparative analysis. Mammogram registration is a process whereby spatial differences between mammograms can be reduced. Presented in this paper is a nonrigid approach to matching corresponding mammograms based on a physical registration model. Many of the earliest approaches to mammogram registration used spatial transformations which were innately rigid or affine in nature. More recently algorithms have incorporated radial basis functions such as the Thin-Plate Spline to match mammograms. The approach presented here focuses on the use of the Cauchy-Navier Spline, a deformable registration model which offers approximate nonrigid registration. The utility of the Cauchy-Navier Spline is illustrated by matching both temporal and bilateral mammograms.

The Boundary Function Method. Fundamentals

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

A Novel Feature Level Fusion for Heart Rate Variability Classification Using Correntropy and Cauchy-Schwarz Divergence.

PubMed

Goshvarpour, Ateke; Goshvarpour, Atefeh

2018-04-30

Heart rate variability (HRV) analysis has become a widely used tool for monitoring pathological and psychological states in medical applications. In a typical classification problem, information fusion is a process whereby the effective combination of the data can achieve a more accurate system. The purpose of this article was to provide an accurate algorithm for classifying HRV signals in various psychological states. Therefore, a novel feature level fusion approach was proposed. First, using the theory of information, two similarity indicators of the signal were extracted, including correntropy and Cauchy-Schwarz divergence. Applying probabilistic neural network (PNN) and k-nearest neighbor (kNN), the performance of each index in the classification of meditators and non-meditators HRV signals was appraised. Then, three fusion rules, including division, product, and weighted sum rules were used to combine the information of both similarity measures. For the first time, we propose an algorithm to define the weights of each feature based on the statistical p-values. The performance of HRV classification using combined features was compared with the non-combined features. Totally, the accuracy of 100% was obtained for discriminating all states. The results showed the strong ability and proficiency of division and weighted sum rules in the improvement of the classifier accuracies.

The Correlated Jacobi and the Correlated Cauchy-Lorentz Ensembles

NASA Astrophysics Data System (ADS)

Wirtz, Tim; Waltner, Daniel; Kieburg, Mario; Kumar, Santosh

2016-01-01

We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for k=1 to derive a closed-form expression for the eigenvalue density. For real matrices we obtain the density in terms of a twofold integral that we evaluate numerically. For both expressions we find agreement when comparing with Monte Carlo simulations. Relations between these quantities for the Jacobi and the Cauchy-Lorentz ensemble are derived.

Decay of the 3D viscous liquid-gas two-phase flow model with damping

NASA Astrophysics Data System (ADS)

Zhang, Yinghui

2016-08-01

We establish the optimal Lp - L2(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, Lp - L2 estimates for the linearized equations, and delicate energy estimates.

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2009-05-01

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou’s result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator.

Qualitative analysis of a discrete thermostatted kinetic framework modeling complex adaptive systems

NASA Astrophysics Data System (ADS)

Bianca, Carlo; Mogno, Caterina

2018-01-01

This paper deals with the derivation of a new discrete thermostatted kinetic framework for the modeling of complex adaptive systems subjected to external force fields (nonequilibrium system). Specifically, in order to model nonequilibrium stationary states of the system, the external force field is coupled to a dissipative term (thermostat). The well-posedness of the related Cauchy problem is investigated thus allowing the new discrete thermostatted framework to be suitable for the derivation of specific models and the related computational analysis. Applications to crowd dynamics and future research directions are also discussed within the paper.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Analysis of an Interface Crack for a Functionally Graded Strip Sandwiched between Two Homogeneous Layers of Finite Thickness

NASA Technical Reports Server (NTRS)

Shbeeh, N. I.; Binienda, W. K.

1999-01-01

The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a non-homogeneous interface was formulated for singular integral equations with Cauchy kernels and integrated using the Lobatto-Chebyshev collocation technique. Mixed-mode Stress Intensity Factors and Strain Energy Release Rates were calculated. The Stress Intensity Factors were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various non-homogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.

Bi-material plane with interface crack for the model of semi-linear material

NASA Astrophysics Data System (ADS)

Domanskaya, T. O.; Malkov, V. M.; Malkova, Yu. V.

2018-05-01

The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. The plane is formed of two half-planes. Mechanical properties of half-planes are described by the model of semi-linear material. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. As an application of the problem of jumps, the problem of interface crack is solved. The values of nominal (Piola) and Cauchy stresses and displacements are founded. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. As a special case, the analytical solution of the problem of a crack in a homogeneous plane is obtained from the problem for bi-material plane with interface crack.

Effects of hindlimb unweighting on the mechanical and structure properties of the rat abdominal aorta

NASA Technical Reports Server (NTRS)

Papadopoulos, Anthony; Delp, Michael D.

2003-01-01

Previous studies have shown that hindlimb unweighting of rats, a model of microgravity, reduces evoked contractile tension of peripheral conduit arteries. It has been hypothesized that this diminished contractile tension is the result of alterations in the mechanical properties of these arteries (e.g., active and passive mechanics). Therefore, the purpose of this study was to determine whether the reduced contractile force of the abdominal aorta from 2-wk hindlimb-unweighted (HU) rats results from a mechanical function deficit resulting from structural vascular alterations or material property changes. Aortas were isolated from control (C) and HU rats, and vasoconstrictor responses to norepinephrine (10(-9)-10(-4) M) and AVP (10(-9)-10(-5) M) were tested in vitro. In a second series of tests, the active and passive Cauchy stress-stretch relations were determined by incrementally increasing the uniaxial displacement of the aortic rings. Maximal Cauchy stress in response to norepinephrine and AVP were less in aortic rings from HU rats. The active Cauchy stress-stretch response indicated that, although maximum stress was lower in aortas from HU rats (C, 8.1 +/- 0.2 kPa; HU, 7.0 +/- 0.4 kPa), it was achieved at a similar hoop stretch. There were also no differences in the passive Cauchy stress-stretch response or the gross vascular morphology (e.g., medial cross-sectional area: C, 0.30 +/- 0.02 mm(2); HU, 0.32 +/- 0.01 mm(2)) between groups and no differences in resting or basal vascular tone at the displacement that elicits peak developed tension between groups (resting tension: C, 1.71 +/- 0.06 g; HU, 1.78 +/- 0.14 g). These results indicate that HU does not alter the functional mechanical properties of conduit arteries. However, the significantly lower active Cauchy stress of aortas from HU rats demonstrates a true contractile deficit in these arteries.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News

NASA Astrophysics Data System (ADS)

Handmer, Casey; Szilagyi, Bela; Winicour, Jeff

2015-04-01

We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries.

Abbe's number and Cauchy's constant of iodine and selenium doped poly (methylmethacrylate) and polystyrene composites

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

Mehta, Sheetal, E-mail: smehta-29@yahoo.com; Das, Kallol, E-mail: smehta-29@yahoo.com; Keller, Jag Mohan, E-mail: smehta-29@yahoo.com

2014-04-24

Poly (methyl methacrylate) / Polystyrene and iodine / selenium hybrid matrixes have been prepared and characterized. Refractive index measurements were done at 390, 535, 590, 635 nm wavelengths. Abbe's number and Cauchy's constants of the iodine / selenium doped poly (methylmethacrylate) and polystyrene samples are being reported. The results also showed that the refractive index of the composite varies non-monotonically with the doping concentration at low iodine concentration or in the region of nanoparticles formation and is also dependent on thermal annealing.

Processes of aggression described by kinetic method

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

Aristov, V. V.; Ilyin, O.

In the last decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France and USSR based on the kinetic theory. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial initial conditions. The solution of the problem is given in the form of traveling wave. The propagation velocity of a frontline depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solutionmore » of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the frontline velocities are complied with the historical data.« less

Kinetic models for historical processes of fast invasion and aggression

NASA Astrophysics Data System (ADS)

Aristov, Vladimir V.; Ilyin, Oleg V.

2015-04-01

In the last few decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological, and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France, and the USSR based on kinetic theory. We simulate this process with the Cauchy boundary problem for two-element kinetic equations. The solution of the problem is given in the form of a traveling wave. The propagation velocity of a front line depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the front-line velocities agree with the historical data.

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

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

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

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1983-01-01

A cylindrical shell having a very stiff and plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flaw which may be modeled as a part through surface crack or a through crack. The effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter is studied. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the Mode 1 stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part through crack problem is treated by using a line spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equations of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Trigonometrical sums connected with the chiral Potts model, Verlinde dimension formula, two-dimensional resistor network, and number theory

NASA Astrophysics Data System (ADS)

Chair, Noureddine

2014-02-01

We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott's conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory.

Distinguishability of black hole microstates

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

Bao, Ning; Ooguri, Hirosi

We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will then compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.

Distinguishability of black hole microstates

DOE PAGES

Bao, Ning; Ooguri, Hirosi

2017-09-01

We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will then compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.

Comments on ;An improved Cauchy number approach for predicting the drag and reconfiguration of flexible vegetation; by Peter Whittaker, Catherine A.M.E. Wilson, and Jochen Aberle

NASA Astrophysics Data System (ADS)

Chen, Li; Chen, Xiaobing

2017-07-01

Whittaker et al. (2015) presented a modified Cauchy number approach for the estimate of flow resistance induced by flexible vegetation. The approach represents a noteworthy effort in quantifying vegetation resistance to streamflow. Here we briefly discuss some theoretical and practical issues of this approach, and show how it is related to the approach developed by Kouwen and others (Kouwen et al., 1969; Kouwen and Unny, 1973) and recently revised by Chen et al. (2014).

A new approach for solving the three-dimensional steady Euler equations. I - General theory

NASA Technical Reports Server (NTRS)

Chang, S.-C.; Adamczyk, J. J.

1986-01-01

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

The short pulse equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2017-07-01

We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation u_{xt}=u+{1/6}(u^3)_{xx} with zero boundary conditions (as |x|→ ∞). This approach is directly applied to a Lax pair for the SP equation. It allows us to give a parametric representation of the solution to the Cauchy problem. This representation is then used for studying the longtime behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the longtime behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.

A new approach for solving the three-dimensional steady Euler equations. I - General theory

NASA Astrophysics Data System (ADS)

Chang, S.-C.; Adamczyk, J. J.

1986-08-01

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

Decay of the 3D viscous liquid-gas two-phase flow model with damping

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

Zhang, Yinghui, E-mail: zhangyinghui0910@126.com

We establish the optimal L{sup p} − L{sup 2}(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, L{sup p} − L{sup 2} estimates for the linearized equations, and delicate energy estimates.

Non-cooperative Fisher-KPP systems: traveling waves and long-time behavior

NASA Astrophysics Data System (ADS)

Girardin, Léo

2018-01-01

This paper is concerned with non-cooperative parabolic reaction-diffusion systems which share structural similarities with the scalar Fisher-KPP equation. These similarities make it possible to prove, among other results, an extinction and persistence dichotomy and, when persistence occurs, the existence of a positive steady state, the existence of traveling waves with a half-line of possible speeds and a positive minimal speed and the equality between this minimal speed and the spreading speed for the Cauchy problem. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.

On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions

NASA Astrophysics Data System (ADS)

Punshon-Smith, Samuel; Smith, Scott

2018-02-01

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in {{L}1}.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

NASA Astrophysics Data System (ADS)

Hassani, A. R.; Faal, R. T.

2016-12-01

This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

Application of micropolar plasticity to post failure analysis in geomechanics

NASA Astrophysics Data System (ADS)

Manzari, Majid T.

2004-08-01

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy-Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

A Riemann-Hilbert Approach for the Novikov Equation

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2016-09-01

We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Ahmad, S.; Wang, H. C.

1989-01-01

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

Solving the Quantum Many-Body Problem via Correlations Measured with a Momentum Microscope

NASA Astrophysics Data System (ADS)

Hodgman, S. S.; Khakimov, R. I.; Lewis-Swan, R. J.; Truscott, A. G.; Kheruntsyan, K. V.

2017-06-01

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s -wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system—the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Global existence and incompressible limit in critical spaces for compressible flow of liquid crystals

NASA Astrophysics Data System (ADS)

Bie, Qunyi; Cui, Haibo; Wang, Qiru; Yao, Zheng-An

2017-10-01

The Cauchy problem for the compressible flow of nematic liquid crystals in the framework of critical spaces is considered. We first establish the existence and uniqueness of global solutions provided that the initial data are close to some equilibrium states. This result improves the work by Hu and Wu (SIAM J Math Anal 45(5):2678-2699, 2013) through relaxing the regularity requirement of the initial data in terms of the director field. Based on the global existence, we then consider the incompressible limit problem for ill prepared initial data. We prove that as the Mach number tends to zero, the global solution to the compressible flow of liquid crystals converges to the solution to the corresponding incompressible model in some function spaces. Moreover, the accurate converge rates are obtained.

On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer order m as a multi-order (1, 1,…, 1), the Gelfond-Leontiev generalized differentiation operators, many other integral and differential operators in Calculus that have been used in various topics, some of them not related to FC at all, others involved in differential and integral equations for treating fractional order models.

Characterization of exchange rate regimes based on scaling and correlation properties of volatility for ASEAN-5 countries

NASA Astrophysics Data System (ADS)

Muniandy, Sithi V.; Uning, Rosemary

2006-11-01

Foreign currency exchange rate policies of ASEAN member countries have undergone tremendous changes following the 1997 Asian financial crisis. In this paper, we study the fractal and long-memory characteristics in the volatility of five ASEAN founding members’ exchange rates with respect to US dollar. The impact of exchange rate policies implemented by the ASEAN-5 countries on the currency fluctuations during pre-, mid- and post-crisis are briefly discussed. The time series considered are daily price returns, absolute returns and aggregated absolute returns, each partitioned into three segments based on the crisis regimes. These time series are then modeled using fractional Gaussian noise, fractionally integrated ARFIMA (0,d,0) and generalized Cauchy process. The first two stationary models provide the description of long-range dependence through Hurst and fractional differencing parameter, respectively. Meanwhile, the generalized Cauchy process offers independent estimation of fractal dimension and long memory exponent. In comparison, among the three models we found that the generalized Cauchy process showed greater sensitivity to transition of exchange rate regimes that were implemented by ASEAN-5 countries.

Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole

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

Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sumsmore » are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.« less

Analysis of airfoil leading edge separation bubbles

NASA Technical Reports Server (NTRS)

Carter, J. E.; Vatsa, V. N.

1982-01-01

A local inviscid-viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles. In this analysis an inverse boundary layer finite difference analysis is solved iteratively with a Cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis. Favorable comparisons with data indicate the overall validity of the present localized interaction approach. In addition numerical tests were performed to test the sensitivity of the computed results to the mesh size, limits on the Cauchy integral, and the location of the transition region.

Limitless Analytic Elements

NASA Astrophysics Data System (ADS)

Strack, O. D. L.

2018-02-01

We present equations for new limitless analytic line elements. These elements possess a virtually unlimited number of degrees of freedom. We apply these new limitless analytic elements to head-specified boundaries and to problems with inhomogeneities in hydraulic conductivity. Applications of these new analytic elements to practical problems involving head-specified boundaries require the solution of a very large number of equations. To make the new elements useful in practice, an efficient iterative scheme is required. We present an improved version of the scheme presented by Bandilla et al. (2007), based on the application of Cauchy integrals. The limitless analytic elements are useful when modeling strings of elements, rivers for example, where local conditions are difficult to model, e.g., when a well is close to a river. The solution of such problems is facilitated by increasing the order of the elements to obtain a good solution. This makes it unnecessary to resort to dividing the element in question into many smaller elements to obtain a satisfactory solution.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

The crack problem in a reinforced cylindrical shell

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1986-01-01

In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

The crack problem in a reinforced cylindrical shell

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1986-01-01

A partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z = 0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Existence of evolutionary variational solutions via the calculus of variations

NASA Astrophysics Data System (ADS)

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo

In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that is ∫0T ∫Ω [uṡ∂tφ+f(x,Du)] dx dt⩽∫0T ∫Ω f(x,Du+Dφ) dx dt, whenever T>0 and φ∈C0∞(Ω×(0,T),RN). For the integrand f:Ω×R→[0,∞] we merely assume convexity with respect to the gradient variable and coercivity. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy-Dirichlet problems of parabolic systems of the type ∂tu-divDξf(x,Du)=0 in Ω×(0,∞).

An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

NASA Astrophysics Data System (ADS)

Shao, Zhongshi; Pi, Dechang; Shao, Weishi

2017-11-01

This article proposes an extended continuous estimation of distribution algorithm (ECEDA) to solve the permutation flow-shop scheduling problem (PFSP). In ECEDA, to make a continuous estimation of distribution algorithm (EDA) suitable for the PFSP, the largest order value rule is applied to convert continuous vectors to discrete job permutations. A probabilistic model based on a mixed Gaussian and Cauchy distribution is built to maintain the exploration ability of the EDA. Two effective local search methods, i.e. revolver-based variable neighbourhood search and Hénon chaotic-based local search, are designed and incorporated into the EDA to enhance the local exploitation. The parameters of the proposed ECEDA are calibrated by means of a design of experiments approach. Simulation results and comparisons based on some benchmark instances show the efficiency of the proposed algorithm for solving the PFSP.

Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

NASA Astrophysics Data System (ADS)

Wen, Huanyao; Zhu, Limei

2018-02-01

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in H2 (R3) are obtained by introducing a new linearized system with respect to (nγ -n˜γ , n - n ˜ , P - P ˜ , u , H) for constants n ˜ ≥ 0 and P ˜ > 0, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of (n - n ˜ ,nγ -n˜γ) in H2 (R3) norm.

Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions

NASA Astrophysics Data System (ADS)

Katayama, Soichiro

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In this paper, we will show that the global solution is asymptotically free in the energy sense, by obtaining the asymptotic pointwise behavior of the derivatives of the solution. Nonetheless we can also show that the pointwise behavior of the solution itself may be quite different from that of the free solution. In connection with the above results, a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions.

Decay Rates and Probability Estimatesfor Massive Dirac Particlesin the Kerr-Newman Black Hole Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L∞ {loc} at least at the rate t-5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Spectral approach to homogenization of hyperbolic equations with periodic coefficients

NASA Astrophysics Data System (ADS)

Dorodnyi, M. A.; Suslina, T. A.

2018-06-01

In L2 (Rd ;Cn), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x / ε, ε > 0. We study the behavior of the operators cos ⁡ (Aε1/2 τ) and Aε-1/2 sin ⁡ (Aε1/2 τ), τ ∈ R, for small ε. Approximations for these operators in the (Hs →L2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂τ2 vε = -Aεvε + F. General results are applied to the acoustics equation and the system of elasticity theory.

A difference-differential analogue of the burgers equation: Stability of the two-wave behavior

NASA Astrophysics Data System (ADS)

Henkin, G. M.; Polterovich, V. M.

1994-12-01

We study the Cauchy problem for the difference-differential equation (*) 332_2006_Article_BF02430643_TeX2GIFE1.gif {dF_n }/{dt} = \\varphi left( {F_n } right)left( {F_{n - 1} - F_n } right),n in mathbb{Z}, where ϕ is some positive function on [0, 1], ℤ is a set of integer numbers, and F n=Fn(t) are non-negative functions of time with values in [0, 1], F ∞(t)=0, F ∞(t)=1 for any fixed t. For non-increasing the non-constant ϕ it was shown [V. Polterovich and G. Henkin, Econom. Math. Methods, 24, 1988, pp. 1071 1083 (in Russian)] that the behavior of the trajectories of (*) is similar to the behavior of a solution for the famous Burgers equation; namely, any trajectory of (*) rapidly converging at the initial moment of time to zero as n → -8 and to 1 as n → ∞ converges with the time uniformly in n to a wave-train that moves with constant velocity. On the other hand, (*) is a variant of discretization for the shock-wave equation, and this variant differs from those previously examined by Lax and others. In this paper we study the asymptotic behavior of solutions of the Cauchy problem for the equation (*) with non-monotonic function ϕ of a special form, considering this investigation as a step toward elaboration of the general case. We show that under certain conditions, trajectories of (*) with time convergence to the sum of two wave-trains with different overfalls moving with different velocities. The velocity of the front wave is greater, so that the distance between wave-trains increases linearly. The investigation of (*) with non-monotonic ϕ may have important consequences for studying the Schumpeterian evolution of industries (G. Henkin and V. Polterovich, J. Math. Econom., 20, 1991, 551 590). In the framework of this economic problem, F n(t) is interpreted as the proportion of industrial capacities that have efficiency levels no greater than n at moment t.

Rupture Propagation for Stochastic Fault Models

NASA Astrophysics Data System (ADS)

Favreau, P.; Lavallee, D.; Archuleta, R.

2003-12-01

The inversion of strong motion data of large earhquakes give the spatial distribution of pre-stress on the ruptured faults and it can be partially reproduced by stochastic models, but a fundamental question remains: how rupture propagates, constrained by the presence of spatial heterogeneity? For this purpose we investigate how the underlying random variables, that control the pre-stress spatial variability, condition the propagation of the rupture. Two stochastic models of prestress distributions are considered, respectively based on Cauchy and Gaussian random variables. The parameters of the two stochastic models have values corresponding to the slip distribution of the 1979 Imperial Valley earthquake. We use a finite difference code to simulate the spontaneous propagation of shear rupture on a flat fault in a 3D continuum elastic body. The friction law is the slip dependent friction law. The simulations show that the propagation of the rupture front is more complex, incoherent or snake-like for a prestress distribution based on Cauchy random variables. This may be related to the presence of a higher number of asperities in this case. These simulations suggest that directivity is stronger in the Cauchy scenario, compared to the smoother rupture of the Gauss scenario.

Triangles with Integer Dimensions

ERIC Educational Resources Information Center

Gilbertson, Nicholas J.; Rogers, Kimberly Cervello

2016-01-01

Interesting and engaging mathematics problems can come from anywhere. Sometimes great problems arise from interesting contexts. At other times, interesting problems arise from asking "what if" questions while appreciating the structure and beauty of mathematics. The intriguing problem described in this article resulted from the second…

Image registration based on subpixel localization and Cauchy-Schwarz divergence

NASA Astrophysics Data System (ADS)

Ge, Yongxin; Yang, Dan; Zhang, Xiaohong; Lu, Jiwen

2010-07-01

We define a new matching metric-corner Cauchy-Schwarz divergence (CCSD) and present a new approach based on the proposed CCSD and subpixel localization for image registration. First, we detect the corners in an image by a multiscale Harris operator and take them as initial interest points. And then, a subpixel localization technique is applied to determine the locations of the corners and eliminate the false and unstable corners. After that, CCSD is defined to obtain the initial matching corners. Finally, we use random sample consensus to robustly estimate the parameters based on the initial matching. The experimental results demonstrate that the proposed algorithm has a good performance in terms of both accuracy and efficiency.

Yet another proof of Hawking and Ellis's Lemma 8.5.5

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2014-11-01

The fact that the null generators of a future Cauchy horizon are past-complete was first proved by Hawking and Ellis (1973 The Large Scale Structure of Spacetime (Cambridge: Cambridge University Press)). Then, Budzyński, Kondracki and Królak outlined a proof free from the error found in the original one (2000 New properties of Cauchy and event horizons arXiv:gr-qc/0011033). Now, Minguzzi has published his version of the proof (2014 J. Math. Phys. 55 082503), patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note, I present a simpler one.

Statistics of Gaussian packets on metric and decorated graphs.

PubMed

Chernyshev, V L; Shafarevich, A I

2014-01-28

We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth.

Decay of the 3D inviscid liquid-gas two-phase flow model

NASA Astrophysics Data System (ADS)

Zhang, Yinghui

2016-06-01

We establish the optimal {Lp-L2(1 ≤ p < 6/5)} time decay rates of the solution to the Cauchy problem for the 3D inviscid liquid-gas two-phase flow model and analyze the influences of the damping on the qualitative behaviors of solution. Compared with the viscous liquid-gas two-phase flow model (Zhang and Zhu in J Differ Equ 258:2315-2338, 2015), our results imply that the friction effect of the damping is stronger than the dissipation effect of the viscosities and enhances the decay rate of the velocity. Our proof is based on Hodge decomposition technique, the {Lp-L2} estimates for the linearized equations and an elaborate energy method.

Adaptive consensus of scale-free multi-agent system by randomly selecting links

NASA Astrophysics Data System (ADS)

Mou, Jinping; Ge, Huafeng

2016-06-01

This paper investigates an adaptive consensus problem for distributed scale-free multi-agent systems (SFMASs) by randomly selecting links, where the degree of each node follows a power-law distribution. The randomly selecting links are based on the assumption that every agent decides to select links among its neighbours according to the received data with a certain probability. Accordingly, a novel consensus protocol with the range of the received data is developed, and each node updates its state according to the protocol. By the iterative method and Cauchy inequality, the theoretical analysis shows that all errors among agents converge to zero, and in the meanwhile, several criteria of consensus are obtained. One numerical example shows the reliability of the proposed methods.

A computational procedure for multibody systems including flexible beam dynamics

NASA Technical Reports Server (NTRS)

Downer, J. D.; Park, K. C.; Chiou, J. C.

1990-01-01

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. The flexible beams are modeled using a fully nonlinear theory which accounts for both finite rotations and large deformations. The present formulation incorporates physical measures of conjugate Cauchy stress and covariant strain increments. As a consequence, the beam model can easily be interfaced with real-time strain measurements and feedback control systems. A distinct feature of the present work is the computational preservation of total energy for undamped systems; this is obtained via an objective strain increment/stress update procedure combined with an energy-conserving time integration algorithm which contains an accurate update of angular orientations. The procedure is demonstrated via several example problems.

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

The Problems of Diagnosis and Remediation of Dyscalculia.

ERIC Educational Resources Information Center

Price, Nigel; Youe, Simon

2000-01-01

Focuses on the problems of diagnosis and remediation of dyscalculia. Explores whether there is justification for believing that specific difficulty with mathematics arises jointly with a specific language problem, or whether a specific difficulty with mathematics can arise independently of problems with language. Uses a case study to illuminate…

Signatures of extra dimensions in gravitational waves from black hole quasinormal modes

NASA Astrophysics Data System (ADS)

Chakraborty, Sumanta; Chakravarti, Kabir; Bose, Sukanta; SenGupta, Soumitra

2018-05-01

In this work, we have derived the evolution equation for gravitational perturbation in four-dimensional spacetime in the presence of a spatial extra dimension. The evolution equation is derived by perturbing the effective gravitational field equations on the four-dimensional spacetime, which inherits nontrivial higher-dimensional effects. Note that this is different from the perturbation of the five-dimensional gravitational field equations that exist in the literature and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four-dimensional part and another piece that depends on extra dimensions. The four-dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasinormal mode frequencies, signaling the higher-dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience damping much smaller than that of the massless modes in general relativity and may even dominate over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem, as well. In this context, we have shown that, except for minute details, the overall features of the gravitational perturbations are captured both in the Cauchy evolution as well as in the analysis of quasinormal modes. The implications on observations of black holes with LIGO and proposed space missions such as LISA are also discussed.

Modulated elliptic wave and asymptotic solitons in a shock problem to the modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Kotlyarov, Vladimir; Minakov, Alexander

2015-07-01

We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg—de Vries equation with an initial function of the step type. This function rapidly tends to zero as x\\to +∞ and to some positive constant c as x\\to -∞ . In 1989 Khruslov and Kotlyarov have found (Khruslov and Kotlyarov 1989 Inverse Problems 5 1075-88) that for a large time the solution breaks up into a train of asymptotic solitons located in the domain 4{c}2t-{C}N{ln}t\\lt x≤slant 4{c}2t ({C}N is a constant). The number N of these solitons grows unboundedly as t\\to ∞ . In 2010 Kotlyarov and Minakov have studied temporary asymptotics of the solution of the Cauchy problem on the whole line (Kotlyarov and Minakov 2010 J. Math. Phys. 51 093506) and have found that in the domain -6{c}2t\\lt x\\lt 4{c}2t this solution is described by a modulated elliptic wave. We consider here the modulated elliptic wave in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. Our main result shows that the modulated elliptic wave also breaks up into solitons, which are similar to the asymptotic solitons in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88), but differ from them in phase. It means that the modulated elliptic wave does not represent the asymptotics of the solution in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. The correct asymptotic behavior of the solution is given by the train of asymptotic solitons given in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88). However, in the asymptotic regime as t\\to ∞ in the region 4{c}2t-\\displaystyle \\frac{N+1/4}{c}{ln}t\\lt x\\lt 4{c}2t-\\displaystyle \\frac{N-3/4}{c}{ln}t we can watch precisely a pair of solitons with numbers N. One of them is the asymptotic soliton while the other soliton is generated from the elliptic wave. Their phases become closer to each other for a large N, i.e. these solitons are also close to each other. This result gives the answer on a very important question about matching of the asymptotic formulas in the mentioned region where the both formulas are well-defined. Thus we have here a new and previously unknown mechanism (5.35) of matching of the asymptotics of the solution in the adjacent regions.

Guidance and control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Hibey, Joseph L.

1989-01-01

The optimal control problem arising in coplanar orbital transfer employing aeroassist technology and the fuel-optimal control problem arising in orbital transfer vehicles employing aeroassist technology are addressed.

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir Hossein; Goldbert, Alan; Bagasol, Leonard Neil; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Two dimensional fully nonlinear numerical wave tank based on the BEM

NASA Astrophysics Data System (ADS)

Sun, Zhe; Pang, Yongjie; Li, Hongwei

2012-12-01

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

Effect of Ply Orientation and Crack Location on SIFs in Finite Multilayers with Aligned Cracks

NASA Astrophysics Data System (ADS)

Chen, Linfeng; Pindera, Marek-Jerzy

2008-02-01

An exact elasticity solution is presented for arbitrarily laminated finite multilayers in a state of generalized plane deformation under horizontally pinned end constraints that are weakened by aligned cracks. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to Cauchy-type singular integral equations in the unknown displacement discontinuities. Solution to these equations is obtained using the approach developed by Erdogan and co-workers. Numerical results quantify the thus-far undocumented geometric and material effects on Mode I, II and III stress intensity factors in composite multilayers with interacting cracks under uniform vertical displacement. These effects include finite dimensions, crack location, material anisotropy due to a unidirectional fiber-reinforced layer/s orientation, and orientational grading.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

NASA Astrophysics Data System (ADS)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation

NASA Astrophysics Data System (ADS)

Yu, Shengqi

2018-05-01

This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.

Hamiltonian formulation of Palatini f(R) theories a la Brans-Dicke theory

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

Olmo, Gonzalo J.; Sanchis-Alepuz, Helios; Institut fuer Physik, Karl-Franzens-Universitaet Graz

2011-05-15

We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the {omega}=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the {omega}=-3/2 and {omega}{ne}-3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the {omega}=-3/2 case is well formulated andmore » there is no reason to believe that it is not well posed in general.« less

Inequalities, Assessment and Computer Algebra

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2015-01-01

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

An experimental study of wall adaptation and interference assessment using Cauchy integral formula

NASA Technical Reports Server (NTRS)

Murthy, A. V.

1991-01-01

This paper summarizes the results of an experimental study of combined wall adaptation and residual interference assessment using the Cauchy integral formula. The experiments were conducted on a supercritical airfoil model in the Langley 0.3-m Transonic Cryogenic Tunnel solid flexible wall test section. The ratio of model chord to test section height was about 0.7. The method worked satisfactorily in reducing the blockage interference and demonstrated the primary requirement for correcting for the blockage effects at high model incidences to correctly determine high lift characteristics. The studies show that the method has potential for reducing the residual interference to considerably low levels. However, corrections to blockage and upwash velocities gradients may still be required for the final adapted wall shapes.

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

Esfahani, M. Nasr; Yilmaz, M.; Sonne, M. R.

The trend towards nanomechanical resonator sensors with increasing sensitivity raises the need to address challenges encountered in the modeling of their mechanical behavior. Selecting the best approach in mechanical response modeling amongst the various potential computational solid mechanics methods is subject to controversy. A guideline for the selection of the appropriate approach for a specific set of geometry and mechanical properties is needed. In this study, geometrical limitations in frequency response modeling of flexural nanomechanical resonators are investigated. Deviation of Euler and Timoshenko beam theories from numerical techniques including finite element modeling and Surface Cauchy-Born technique are studied. The resultsmore » provide a limit beyond which surface energy contribution dominates the mechanical behavior. Using the Surface Cauchy-Born technique as the reference, a maximum error on the order of 50 % is reported for high-aspect ratio resonators.« less

Solving the Cauchy-Riemann equations on parallel computers

NASA Technical Reports Server (NTRS)

Fatoohi, Raad A.; Grosch, Chester E.

1987-01-01

Discussed is the implementation of a single algorithm on three parallel-vector computers. The algorithm is a relaxation scheme for the solution of the Cauchy-Riemann equations; a set of coupled first order partial differential equations. The computers were chosen so as to encompass a variety of architectures. They are: the MPP, and SIMD machine with 16K bit serial processors; FLEX/32, an MIMD machine with 20 processors; and CRAY/2, an MIMD machine with four vector processors. The machine architectures are briefly described. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Conclusions are presented.

Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas

NASA Astrophysics Data System (ADS)

Zhu, Jian-Zhou

2018-03-01

The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.

Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2002-04-01

The nonlinear vortex stretching in incompressible Navier-Stokes turbulence is compared with a linear stretching process of passive vectors (PVs). In particular, we pay special attention to the difference of these processes under long and short time evolutions. For finite time evolution, we confirm our previous finding that the stretching effect of vorticity is weaker than that of general passive vectors for a majority of the initial conditions with the same energy spectra. The above difference can be explained qualitatively by examining the Biot-Savart formula. In order to see to what extent infinitesimal time development explains the above difference, we examine the probability density functions (PDFs) of the stretching rates of the passive vectors in the vicinity of a solution of Navier-Stokes equations. It is found that the PDFs are found to have a Gaussian distribution, suggesting that there are equally many PVs that stretched less and more than the vorticity. This suggests the importance of the vorticity-strain correlation built up over finite time in turbulence. We also discuss the case of Euler equations, where the dynamics of the Jacobian matrix relating the physical and material coordinates is examined numerically. A kind of alignment problem associated with the Cauchy-Green tensor is proposed and studied using the results of numerical simulations. It is found that vorticity tends to align itself with the most compressing eigenvector of the Cauchy-Green tensor. A two-dimensional counterpart of active-passive comparison is briefly studied. There is no essential difference between stretching of vorticity gradients and that of passive scalar gradients and a physical interpretation is given to it.

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

The propagator W ( t 0 , t 1 )( g , h ) for the wave equation in a given space-time takes initial data ( g ( x ), h ( x )) on a Cauchy surface {( t , x ) :  t = t 0 } and evaluates the solution ( u ( t 1 , x ),∂ t u ( t 1 , x )) at other times t 1 . The Friedmann-Robertson-Walker space-times are defined for t 0 , t 1 >0, whereas for t 0 →0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K =0 and K =-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0< t 0 < t the limit, [Formula: see text] exists, it is independent of h ( x ), and for all reasonable initial data g ( x ), it gives rise to a well-defined solution for all t >0 emanating from the space-time singularity at t =0. Under reflection t →- t , the Friedmann-Robertson-Walker metric gives a space-time metric for t <0 with a singular future at t =0, and the same solution formulae hold. We thus have constructed solutions u ( t , x ) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t =0 of space-time, taking on specified data u (0,⋅)= g (⋅) at the singular time.

The Cauchy Problem in Local Spaces for the Complex Ginzburg-Landau EquationII. Contraction Methods

NASA Astrophysics Data System (ADS)

Ginibre, J.; Velo, G.

We continue the study of the initial value problem for the complex Ginzburg-Landau equation (with a > 0, b > 0, g>= 0) in initiated in a previous paper [I]. We treat the case where the initial data and the solutions belong to local uniform spaces, more precisely to spaces of functions satisfying local regularity conditions and uniform bounds in local norms, but no decay conditions (or arbitrarily weak decay conditions) at infinity in . In [I] we used compactness methods and an extended version of recent local estimates [3] and proved in particular the existence of solutions globally defined in time with local regularity of the initial data corresponding to the spaces Lr for r>= 2 or H1. Here we treat the same problem by contraction methods. This allows us in particular to prove that the solutions obtained in [I] are unique under suitable subcriticality conditions, and to obtain for them additional regularity properties and uniform bounds. The method extends some of those previously applied to the nonlinear heat equation in global spaces to the framework of local uniform spaces.

Derivation of the out-of-plane behaviour of an English bond masonry wall through homogenization strategies

NASA Astrophysics Data System (ADS)

Silva, Luís Carlos; Milani, Gabriele; Lourenço, Paulo B.

2017-11-01

Two finite element homogenized-based strategies are presented for the out-of-plane behaviour characterization of an English bond masonry wall. A finite element micro-modelling approach using Cauchy stresses and first order movements are assumed for both strategies. The material nonlinearity is lumped on joints interfaces and bricks are considered elastic. Nevertheless, the first model is based on a Plane-stress assumption, in which the out-of-plane quantities are derived through on-thickness wall integration considering a Kirchhoff-plate theory. The second model is a tridimensional one, in which the homogenized out-of-plane quantities can be directly derived after solving the boundary value problem. The comparison is conducted by assessing the obtained out-of-plane bending- and torsion-curvature diagrams. A good agreement is found for the present study case.

Ill-posedness of the 3D incompressible hyperdissipative Navier–Stokes system in critical Fourier-Herz spaces

NASA Astrophysics Data System (ADS)

Nie, Yao; Zheng, Xiaoxin

2018-07-01

We study the Cauchy problem for the 3D incompressible hyperdissipative Navier–Stokes equations and consider the well-posedness and ill-posedness in critical Fourier-Herz spaces . We prove that if and , the system is locally well-posed for large initial data as well as globally well-posed for small initial data. Also, we obtain the same result for and . More importantly, we show that the system is ill-posed in the sense of norm inflation for and q  >  2. The proof relies heavily on particular structure of initial data u 0 that we construct, which makes the first iteration of solution inflate. Specifically, the special structure of u 0 transforms an infinite sum into a finite sum in ‘remainder term’, which permits us to control the remainder.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

NASA Astrophysics Data System (ADS)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Internal Structure of Charged Particles in a GRT Gravitational Model

NASA Astrophysics Data System (ADS)

Khlestkov, Yu. A.; Sukhanova, L. A.

2018-05-01

With the help of an exact solution of the Einstein and Maxwell equations, the internal structure of a multiply connected space of wormhole type with two unclosed static throats leading out of it into two parallel vacuum spaces or into one space is investigated in GRT for a free electric field and dust-like matter. The given geometry is considered as a particle-antiparticle pair with fundamental constants arising in the form of first integrals in the solution of the Cauchy problem - electric charges ±e of opposite sign in the throats and rest mass m0 - the total gravitational mass of the inner world of the particle in the throat. With the help of the energy conservation law, the unremovable rotation of the internal structure is included and the projection of the angular momentum of which onto the rotation axis is identified with the z-projection of the spin of the charged particle. The radius of 2-Gaussian curvature of the throat R* is identified with the charge radius of the particle, and the z-projection of the magnetic moment and the g-factor are found. The feasibility of the given gravitational model is confirmed by the found condition of independence of the spin quantum number of the electron and the proton s = 1/2 of the charge radius R* and the relativistic rest mass m* of the rotating throat, which is reliably confirmed experimentally, and also by the coincidence with high accuracy of the proton radius calculated in the model R*p = 0.8412·10-13 cm with the value of the proton charge radius obtained experimentally by measuring the Lamb shift on muonic hydrogen. The electron in the given model also turns out to be a structured particle with radius R*e = 3.8617·10-11 cm.

Flexible Polyhedral Surfaces.

ERIC Educational Resources Information Center

Alexandrov, V. A.

1998-01-01

Discusses some questions connected with Cauchy's theorem which states that two convex closed polyhedral surfaces whose corresponding faces are congruent and whose faces adjoin each other in the same way are congruent. Describes how to construct a flexible polyhedron. (ASK)

EPR-dosimetry of ionizing radiation

NASA Astrophysics Data System (ADS)

Popova, Mariia; Vakhnin, Dmitrii; Tyshchenko, Igor

2017-09-01

This article discusses the problems that arise during the radiation sterilization of medical products. It is propose the solution based on alanine EPR-dosimetry. The parameters of spectrometer and methods of absorbed dose calculation are given. In addition, the problems that arise during heavy particles irradiation are investigated.

Constraining the physical state by symmetries

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

Fatibene, L., E-mail: lorenzo.fatibene@unito.it; INFN - Sezione Torino - IS QGSKY; Ferraris, M.

After reviewing the hole argument and its relations with initial value problem and general covariance, we shall discuss how much freedom one has to define the physical state in a generally covariant field theory (with or without internal gauge symmetries). Our analysis relies on Cauchy problems, thus it is restricted to globally hyperbolic spacetimes. We shall show that in generally covariant theories on a compact space (as well as for internal gauge symmetries on any spacetime) one has no freedom and one is forced to declare as physically equivalent two configurations which differ by a global spacetime diffeomorphism (or bymore » an internal gauge transformation) as it is usually prescribed. On the contrary, when space is not compact, the result does not hold true and one may have different options to define physically equivalent configurations, still preserving determinism. - Highlights: • Investigate the relation between the hole argument, covariance, determinism and physical state. • Show that if space is compact then any diffeomorphism is a gauge symmetry. • Show that if space is not compact then there may be more freedom in choosing gauge group.« less

Generalized large-scale semigeostrophic approximations for the f-plane primitive equations

NASA Astrophysics Data System (ADS)

Oliver, Marcel; Vasylkevych, Sergiy

2016-05-01

We derive a family of balance models for rotating stratified flow in the primitive equation (PE) setting. By construction, the models possess conservation laws for energy and potential vorticity and are formally of the same order of accuracy as Hoskins’ semigeostrophic equations. Our construction is based on choosing a new coordinate frame for the PE variational principle in such a way that the consistently truncated Lagrangian degenerates. We show that the balance relations so obtained are elliptic when the fluid is stably stratified and certain smallness assumptions are satisfied. Moreover, the potential temperature can be recovered from the potential vorticity via inversion of a non-standard Monge-Ampère problem which is subject to the same ellipticity condition. While the present work is entirely formal, we conjecture, based on a careful rewriting of the equations of motion and a straightforward derivative count, that the Cauchy problem for the balance models is well posed subject to conditions on the initial data. Our family of models includes, in particular, the stratified analog of the L 1 balance model of Salmon.

Data dependence for the amplitude equation of surface waves

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2016-04-01

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1985-01-01

In this paper a cylindrical shell having a very stiff end plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flow which may be modeled as a part-through surface crack or through crack. The primary objective is to study the effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the mode I stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built-in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part-through crack problem is treated by using a line-spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equation of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem. Even though the problem is formulated for a general surface crack profile and arbitrary crack surface tractions, the numerical results are obtained only for a semielliptic part-through axial crack located at the inside or outside surface of the cylinder and for internal pressure acting on the cylinder. The stress intensity factors are calculated and presented for a relatively wide range of dimensionless length parameters of the problem.

On New Proofs of Fundamental Inequalities with Applications

ERIC Educational Resources Information Center

Ray, Partha

2010-01-01

By using the Cauchy-Schwarz inequality a new proof of several standard inequalities is given. A new proof of Young's inequality is given by using Holder's inequality. A new application of the above inequalities is included.

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Boulware, David G.

1992-11-01

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

NASA Astrophysics Data System (ADS)

Wrochna, Michał; Zahn, Jochen

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the ‘subsidiary condition’ approach of Hack and Schenkel in the case of Maxwell, Yang-Mills, and Rarita-Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang-Mills case is concluded from known results in the subsidiary condition (or Gupta-Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang-Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

An improved Cauchy number approach for predicting the drag and reconfiguration of flexible vegetation

NASA Astrophysics Data System (ADS)

Whittaker, Peter; Wilson, Catherine A. M. E.; Aberle, Jochen

2015-09-01

An improved model to describe the drag and reconfiguration of flexible riparian vegetation is proposed. The key improvement over previous models is the use of a refined 'vegetative' Cauchy number to explicitly determine the magnitude and rate of the vegetation's reconfiguration. After being derived from dimensional consideration, the model is applied to two experimental data sets. The first contains high-resolution drag force and physical property measurements for twenty-one foliated and defoliated full-scale trees, including specimens of Alnus glutinosa, Populus nigra and Salix alba. The second data set is independent and of a different scale, consisting of drag force and physical property measurements for natural and artificial branches of willow and poplar, under partially and fully submerged flow conditions. Good agreement between the measured and predicted drag forces is observed for both data sets, especially when compared to a more typical 'rigid' approximation, where the effects of reconfiguration are neglected.

Medical image diagnoses by artificial neural networks with image correlation, wavelet transform, simulated annealing

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1993-09-01

Classical artificial neural networks (ANN) and neurocomputing are reviewed for implementing a real time medical image diagnosis. An algorithm known as the self-reference matched filter that emulates the spatio-temporal integration ability of the human visual system might be utilized for multi-frame processing of medical imaging data. A Cauchy machine, implementing a fast simulated annealing schedule, can determine the degree of abnormality by the degree of orthogonality between the patient imagery and the class of features of healthy persons. An automatic inspection process based on multiple modality image sequences is simulated by incorporating the following new developments: (1) 1-D space-filling Peano curves to preserve the 2-D neighborhood pixels' relationship; (2) fast simulated Cauchy annealing for the global optimization of self-feature extraction; and (3) a mini-max energy function for the intra-inter cluster-segregation respectively useful for top-down ANN designs.

Cauchy integral method for two-dimensional solidification interface shapes

NASA Astrophysics Data System (ADS)

Siegel, R.; Sosoka, D. J.

1982-07-01

A method is developed to determine the shape of steady state solidification interfaces formed when liquid above its freezing point circulates over a cold surface. The solidification interface, which is at uniform temperature, will form in a shape such that the non-uniform energy convected to it is locally balanced by conduction into the solid. The interface shape is of interest relative to the crystal structure formed during solidification; regulating the crystal structure has application in casting naturally strengthened metallic composites. The results also pertain to phase-change energy storage devices, where the solidified configuration and overall heat transfer are needed. The analysis uses a conformal mapping technique to relate the desired interface coordinates to the components of the temperature gradient at the interface. These components are unknown because the interface shape is unknown. A Cauchy integral formulation provides a second relation involving the components, and a simultaneous solution yields the interface shape.

The limit space of a Cauchy sequence of globally hyperbolic spacetimes

NASA Astrophysics Data System (ADS)

Noldus, Johan

2004-02-01

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the limit space is unique up to isometry. I also show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case. The difference in philosophy between Lorentzian and Riemannian geometry is one of relativism versus absolutism. In the latter every point distinguishes itself while in the former in general two elements get distinguished by a third, different, one.

Interior of a charged distorted black hole

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

Abdolrahimi, Shohreh; Frolov, Valeri P.; Shoom, Andrey A.

We study the interior of a charged, nonrotating distorted black hole. We consider static and axisymmetric black holes, and focus on a special case when an electrically charged distorted solution is obtained by the Harrison-Ernst transformation from an uncharged one. We demonstrate that the Cauchy horizon of such a black hole remains regular, provided the distortion is regular at the event horizon. The shape and the inner geometry of both the outer and inner (Cauchy) horizons are studied. We demonstrate that there exists a duality between the properties of the horizons. Proper time of a free fall of a testmore » particle moving in the interior of the distorted black hole along the symmetry axis is calculated. We also study the property of the curvature in the inner domain between the horizons. Simple relations between the 4D curvature invariants and the Gaussian curvature of the outer and inner horizon surfaces are found.« less

Examining the patterns and dynamics of species abundance distributions in succession of forest communities by model selection.

PubMed

Yin, Zuo-Yun; Zeng, Lu; Luo, Shao-Ming; Chen, Ping; He, Xiao; Guo, Wei; Li, Bailian

2018-01-01

There are a few common species and many rare species in a biological community or a multi-species collection in given space and time. This hollow distribution curve is called species abundance distribution (SAD). Few studies have examined the patterns and dynamics of SADs during the succession of forest communities by model selection. This study explored whether the communities in different successional stages followed different SAD models and whether there existed a best SAD model to reveal their intrinsic quantitative features of structure and dynamics in succession. The abundance (the number of individuals) of each vascular plant was surveyed by quadrat sampling method from the tree, shrub and herb layers in two typical communities (i.e., the evergreen needle- and broad-leaved mixed forest and the monsoon evergreen broad-leaved forest) in southern subtropical Dinghushan Biosphere Reserve, South China. The sites of two forest communities in different successional stages are both 1 ha in area. We collected seven widely representative SAD models with obviously different function forms and transformed them into the same octave (log2) scale. These models are simultaneously confronted with eight datasets from four layers of two communities, and their goodness-of-fits to the data were evaluated by the chi-squared test, the adjusted coefficient of determination and the information criteria. The results indicated that: (1) the logCauchy model followed all the datasets and was the best among seven models; (2) the fitness of each model to the data was not directly related to the successional stage of forest community; (3) according to the SAD curves predicted by the best model (i.e., the logCauchy), the proportion of rare species decreased but that of common ones increased in the upper layers with succession, while the reverse was true in the lower layers; and (4) the difference of the SADs increased between the upper and the lower layers with succession. We concluded that the logCauchy model had the widest applicability in describing the SADs, and could best mirror the SAD patterns and dynamics of communities and their different layers in the succession of forests. The logCauchy-modeled SADs can quantitatively guide the construction of ecological forests and the restoration of degraded vegetation.

Examining the patterns and dynamics of species abundance distributions in succession of forest communities by model selection

PubMed Central

Luo, Shao-Ming; Chen, Ping; He, Xiao; Guo, Wei; Li, Bailian

2018-01-01

There are a few common species and many rare species in a biological community or a multi-species collection in given space and time. This hollow distribution curve is called species abundance distribution (SAD). Few studies have examined the patterns and dynamics of SADs during the succession of forest communities by model selection. This study explored whether the communities in different successional stages followed different SAD models and whether there existed a best SAD model to reveal their intrinsic quantitative features of structure and dynamics in succession. The abundance (the number of individuals) of each vascular plant was surveyed by quadrat sampling method from the tree, shrub and herb layers in two typical communities (i.e., the evergreen needle- and broad-leaved mixed forest and the monsoon evergreen broad-leaved forest) in southern subtropical Dinghushan Biosphere Reserve, South China. The sites of two forest communities in different successional stages are both 1 ha in area. We collected seven widely representative SAD models with obviously different function forms and transformed them into the same octave (log2) scale. These models are simultaneously confronted with eight datasets from four layers of two communities, and their goodness-of-fits to the data were evaluated by the chi-squared test, the adjusted coefficient of determination and the information criteria. The results indicated that: (1) the logCauchy model followed all the datasets and was the best among seven models; (2) the fitness of each model to the data was not directly related to the successional stage of forest community; (3) according to the SAD curves predicted by the best model (i.e., the logCauchy), the proportion of rare species decreased but that of common ones increased in the upper layers with succession, while the reverse was true in the lower layers; and (4) the difference of the SADs increased between the upper and the lower layers with succession. We concluded that the logCauchy model had the widest applicability in describing the SADs, and could best mirror the SAD patterns and dynamics of communities and their different layers in the succession of forests. The logCauchy-modeled SADs can quantitatively guide the construction of ecological forests and the restoration of degraded vegetation. PMID:29746516

Proof of a new area law in general relativity

NASA Astrophysics Data System (ADS)

Bousso, Raphael; Engelhardt, Netta

2015-08-01

A future holographic screen is a hypersurface of indefinite signature, foliated by marginally trapped surfaces with area A (r ). We prove that A (r ) grows strictly monotonically. Future holographic screens arise in gravitational collapse. Past holographic screens exist in our own Universe; they obey an analogous area law. Both exist more broadly than event horizons or dynamical horizons. Working within classical general relativity, we assume the null curvature condition and certain generiticity conditions. We establish several nontrivial intermediate results. If a surface σ divides a Cauchy surface into two disjoint regions, then a null hypersurface N that contains σ splits the entire spacetime into two disjoint portions: the future-and-interior, K+; and the past-and-exterior, K-. If a family of surfaces σ (r ) foliate a hypersurface, while flowing everywhere to the past or exterior, then the future-and-interior K+(r ) grows monotonically under inclusion. If the surfaces σ (r ) are marginally trapped, we prove that the evolution must be everywhere to the past or exterior, and the area theorem follows. A thermodynamic interpretation as a second law is suggested by the Bousso bound, which relates A (r ) to the entropy on the null slices N (r ) foliating the spacetime. In a companion letter, we summarize the proof and discuss further implications.

Flow of “stress power-law” fluids between parallel rotating discs with distinct axes

DOE PAGES

Srinivasan, Shriram; Karra, Satish

2015-04-16

The problem of flow between parallel rotating discs with distinct axes corresponds to the case of flow in an orthogonal rheometer and has been studied extensively for different fluids since the instrument's inception. All the prior studies presume a constitutive prescription of the fluid stress in terms of the kinematical variables. In this paper, we approach the problem from a different perspective, i.e., a constitutive specification of the symmetric part of the velocity gradient in terms of the Cauchy stress. Such an approach ensures that the boundary conditions can be incorporated in a manner quite faithful to real world experimentsmore » with the instrument. Interestingly, the choice of the boundary condition is critical to the solvability of the problem for the case of creeping/Stokes flow. Furthermore, when the no-slip condition is enforced at the boundaries, depending on the model parameters and axes offset, the fluid response can show non-uniqueness or unsolvability, features which are absent in a conventional constitutive specification. In case of creeping/Stokes flow with prescribed values of the stress, the fluid response is indeterminate. We also record the response of a particular case of the given “stress power-law” fluid; one that cannot be attained by the conventional power-law fluids.« less

A time reversal algorithm in acoustic media with Dirac measure approximations

NASA Astrophysics Data System (ADS)

Bretin, Élie; Lucas, Carine; Privat, Yannick

2018-04-01

This article is devoted to the study of a photoacoustic tomography model, where one is led to consider the solution of the acoustic wave equation with a source term writing as a separated variables function in time and space, whose temporal component is in some sense close to the derivative of the Dirac distribution at t  =  0. This models a continuous wave laser illumination performed during a short interval of time. We introduce an algorithm for reconstructing the space component of the source term from the measure of the solution recorded by sensors during a time T all along the boundary of a connected bounded domain. It is based at the same time on the introduction of an auxiliary equivalent Cauchy problem allowing to derive explicit reconstruction formula and then to use of a deconvolution procedure. Numerical simulations illustrate our approach. Finally, this algorithm is also extended to elasticity wave systems.

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Mathematical analysis of an age-structured population model with space-limited recruitment.

PubMed

Kamioka, Katumi

2005-11-01

In this paper, we investigate structured population model of marine invertebrate whose life stage is composed of sessile adults and pelagic larvae, such as barnacles contained in a local habitat. First we formulate the basic model as an Cauchy problem on a Banach space to discuss the existence and uniqueness of non-negative solution. Next we define the basic reproduction number R0 to formulate the invasion condition under which the larvae can successfully settle down in the completely vacant habitat. Subsequently we examine existence and stability of steady states. We show that the trivial steady state is globally asymptotically stable if R0 < or = 1, whereas it is unstable if R0 > 1. Furthermore, we show that a positive (non-trivial) steady state uniquely exists if R0 > 1 and it is locally asymptotically stable as far as absolute value of R0 - 1 is small enough.

Efficient fractal-based mutation in evolutionary algorithms from iterated function systems

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.; Aybar-Ruíz, A.; Camacho-Gómez, C.; Pereira, E.

2018-03-01

In this paper we present a new mutation procedure for Evolutionary Programming (EP) approaches, based on Iterated Function Systems (IFSs). The new mutation procedure proposed consists of considering a set of IFS which are able to generate fractal structures in a two-dimensional phase space, and use them to modify a current individual of the EP algorithm, instead of using random numbers from different probability density functions. We test this new proposal in a set of benchmark functions for continuous optimization problems. In this case, we compare the proposed mutation against classical Evolutionary Programming approaches, with mutations based on Gaussian, Cauchy and chaotic maps. We also include a discussion on the IFS-based mutation in a real application of Tuned Mass Dumper (TMD) location and optimization for vibration cancellation in buildings. In both practical cases, the proposed EP with the IFS-based mutation obtained extremely competitive results compared to alternative classical mutation operators.

Initial conditions and degrees of freedom of non-local gravity

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe

2018-05-01

We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.

Longtime Well-posedness for the 2D Groma-Balogh Model

NASA Astrophysics Data System (ADS)

Wan, Renhui; Chen, Jiecheng

2016-12-01

In this paper, we consider the cauchy problem for the 2D Groma-Balogh model (Acta Mater 47:3647-3654, 1999). From the works Cannone et al. (Arch Ration Mech Anal 196:71-96, 2010) and El Hajj (Ann Inst Henri Poincaré Anal Nonlinéaire 27:21-35, 2010), one can see global well-posedness for this model is an open question. However, we can prove longtime well-posedness. In particular, we show that this model admits a unique solution with the lifespan T^star satisfying T^star log ^2(1+T^star )≳ ɛ ^{-2} if the initial data is of size ɛ . To achieve this, we first establish some new decay estimates concerning the operator e^{-{R}_{12}^2t}. Then, we prove the longtime well-posedness by utilizing the weak dissipation to deal with the nonlinear terms.

A new hyper-elastic model for predicting multi-axial behaviour of rubber-like materials: formulation and computational aspects

NASA Astrophysics Data System (ADS)

Yaya, Kamel; Bechir, Hocine

2018-05-01

We propose a new hyper-elastic model that is based on the standard invariants of Green-Cauchy. Experimental data reported by Treloar (Trans. Faraday Soc. 40:59, 1944) are used to identify the model parameters. To this end, the data of uni-axial tension and equi-bi-axial tension are used simultaneously. The new model has four material parameters, their identification leads to linear optimisation problem and it is able to predict multi-axial behaviour of rubber-like materials. We show that the response quality of the new model is equivalent to that of the well-known Ogden six parameters model. Thereafter, the new model is implemented in FE code. Then, we investigate the inflation of a rubber balloon with the new model and Ogden models. We compare both the analytic and numerical solutions derived from these models.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Cauchy problem in spacetimes with closed timelike curves

NASA Astrophysics Data System (ADS)

Friedman, John; Morris, Michael S.; Novikov, Igor D.; Echeverria, Fernando; Klinkhammer, Gunnar; Thorne, Kip S.; Yurtsever, Ulvi

1990-09-01

The laws of physics might permit the existence, in the real Universe, of closed timelike curves (CTC's). Macroscopic CTC's might be a semiclassical consequence of Planck-scale, quantum gravitational, Lorentzian foam, if such foam exists. If CTC's are permitted, then the semiclassical laws of physics (the laws with gravity classical and other fields quantized or classical) should be augmented by a principle of self-consistency, which states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime. The consequences of this principle are explored for the Cauchy problem of the evolution of a classical, massless scalar field Φ (satisfying □Φ=0) in several model spacetimes with CTC's. In general, self-consistency constrains the initial data for the field Φ. For a family of spacetimes with traversible wormholes, which initially possess no CTC's and then evolve them to the future of a stable Cauchy horizon scrH, self-consistency seems to place no constraints on initial data for Φ that are posed on past null infinity, and none on data posed on spacelike slices which precede scrH. By contrast, initial data posed in the future of scrH, where the CTC's reside, are constrained; but the constraints appear to be mild in the sense that in some neighborhood of every event one is free to specify initial data arbitrarily, with the initial data elsewhere being adjusted to guarantee self-consistent evolution. A spacetime whose self-consistency constraints have this property is defined to be ``benign with respect to the scalar field Φ.'' The question is posed as to whether benign spacetimes in some sense form a generic subset of all spacetimes with CTC's. It is shown that in the set of flat, spatially and temporally closed, 2-dimensional spacetimes the benign ones are not generic. However, it seems likely that every 4-dimensional, asymptotically flat space-time that is stable and has a topology of the form R×(S-one point), where S is a closed 3-manifold, is benign. Wormhole spacetimes are of this type, with S=S1×S2. We suspect that these types of self-consistency behavior of the scalar field Φ are typical for noninteracting (linearly superposing), classical fields. However, interacting classical systems can behave quite differently, as is demonstrated by a study of the motion of a hard-sphere billiard ball in a wormhole spacetime with closed timelike curves: If the ball is classical, then some choices of initial data (some values of the ball's initial position and velocity) give rise to unique, self-consistent motions of the ball; other choices produce two different self-consistent motions; and others might (but we are not yet sure) produce no self-consistent motions whatsoever. By contrast, in a path-integral formulation of the nonrelativistic quantum mechanics of such a billiard ball, there appears to be a unique, self-consistent set of probabilities for the outcomes of all measurements. This paper's conclusion, that CTC's may not be as nasty as people have assumed, is reinforced by the fact that they do not affect Gauss's theorem and thus do not affect the derivation of global conservation laws from differential ones. The standard conservation laws remain valid globally, and in asymptotically flat, wormhole spacetimes they retain a natural, quasilocal interpretation.

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.

ST-intuitionistic fuzzy metric space with properties

NASA Astrophysics Data System (ADS)

Arora, Sahil; Kumar, Tanuj

2017-07-01

In this paper, we define ST-intuitionistic fuzzy metric space and the notion of convergence and completeness properties of cauchy sequences is studied. Further, we prove some properties of ST-intuitionistic fuzzy metric space. Finally, we introduce the concept of symmetric ST Intuitionistic Fuzzy metric space.

Grid Frequency Extreme Event Analysis and Modeling: Preprint

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

Florita, Anthony R; Clark, Kara; Gevorgian, Vahan

Sudden losses of generation or load can lead to instantaneous changes in electric grid frequency and voltage. Extreme frequency events pose a major threat to grid stability. As renewable energy sources supply power to grids in increasing proportions, it becomes increasingly important to examine when and why extreme events occur to prevent destabilization of the grid. To better understand frequency events, including extrema, historic data were analyzed to fit probability distribution functions to various frequency metrics. Results showed that a standard Cauchy distribution fit the difference between the frequency nadir and prefault frequency (f_(C-A)) metric well, a standard Cauchy distributionmore » fit the settling frequency (f_B) metric well, and a standard normal distribution fit the difference between the settling frequency and frequency nadir (f_(B-C)) metric very well. Results were inconclusive for the frequency nadir (f_C) metric, meaning it likely has a more complex distribution than those tested. This probabilistic modeling should facilitate more realistic modeling of grid faults.« less

Quantum field theory in spaces with closed time-like curves

NASA Astrophysics Data System (ADS)

Boulware, D. G.

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Charged black holes in string-inspired gravity II. Mass inflation and dependence on parameters and potentials

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

Hansen, Jakob; Yeom, Dong-han, E-mail: hansen@kisti.re.kr, E-mail: innocent.yeom@gmail.com

2015-09-01

We investigate the relation between the existence of mass inflation and model parameters of string-inspired gravity models. In order to cover various models, we investigate a Brans-Dicke theory that is coupled to a U(1) gauge field. By tuning a model parameter that decides the coupling between the Brans-Dicke field and the electromagnetic field, we can make both of models such that the Brans-Dicke field is biased toward strong or weak coupling directions after gravitational collapses. We observe that as long as the Brans-Dicke field is biased toward any (strong or weak) directions, there is no Cauchy horizon and no massmore » inflation. Therefore, we conclude that to induce a Cauchy horizon and mass inflation inside a charged black hole, either there is no bias of the Brans-Dicke field as well as no Brans-Dicke hair outside the horizon or such a biased Brans-Dicke field should be well trapped and controlled by a potential.« less

Charged black holes in string-inspired gravity II. Mass inflation and dependence on parameters and potentials

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

Hansen, Jakob; Yeom, Dong-han

2015-09-07

We investigate the relation between the existence of mass inflation and model parameters of string-inspired gravity models. In order to cover various models, we investigate a Brans-Dicke theory that is coupled to a U(1) gauge field. By tuning a model parameter that decides the coupling between the Brans-Dicke field and the electromagnetic field, we can make both of models such that the Brans-Dicke field is biased toward strong or weak coupling directions after gravitational collapses. We observe that as long as the Brans-Dicke field is biased toward any (strong or weak) directions, there is no Cauchy horizon and no massmore » inflation. Therefore, we conclude that to induce a Cauchy horizon and mass inflation inside a charged black hole, either there is no bias of the Brans-Dicke field as well as no Brans-Dicke hair outside the horizon or such a biased Brans-Dicke field should be well trapped and controlled by a potential.« less

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

NASA Astrophysics Data System (ADS)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Thermal issues at the SSC

NASA Technical Reports Server (NTRS)

Ranganathan, Raj P.; Dao, Bui V.

1992-01-01

A variety of heat transfer problems arise in the design of the Superconducting Super Collider (SSC). One class of problems is to minimize heat leak from the ambient to the SSC rings, since the rings contain superconducting magnets maintained at a temperature of 4 K. Another arises from the need to dump the beam of protrons (traveling around the SSC rings) on to absorbers during an abort of the collider. Yet another category of problems is the cooling of equipment to dissipate the heat generated during operation. An overview of these problems and sample heat transfer results are given in this paper.

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

NASA Astrophysics Data System (ADS)

Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

2018-06-01

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow

NASA Astrophysics Data System (ADS)

Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro

2010-03-01

For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full Eulerian finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the Eulerian frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present Eulerian approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.

Lévy targeting and the principle of detailed balance.

PubMed

Garbaczewski, Piotr; Stephanovich, Vladimir

2011-07-01

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) solution of the master equation. Here, an asymptotic behavior of different μ-motion scenarios ceases to depend on μ. That is exemplified by considering Gaussian and Cauchy family target PDFs. A complementary problem of the reverse engineering is analyzed: given a priori a semigroup potential, quantify how sensitive upon the choice of the μ driver is an asymptotic behavior of solutions of the associated master equation and thus an invariant PDF itself. This task is accomplished for so-called μ family of Lévy oscillators.

Non-Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics

NASA Astrophysics Data System (ADS)

Korsunsky, Alexander M.

2010-03-01

One of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two-dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two-dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non-singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces

NASA Astrophysics Data System (ADS)

Akagi, Goro; Ôtani, Mitsuharu

The existence of strong solutions of Cauchy problem for the following evolution equation du(t)/dt+∂ϕ1(u(t))-∂ϕ2(u(t))∋f(t) is considered in a real reflexive Banach space V, where ∂ϕ1 and ∂ϕ2 are subdifferential operators from V into its dual V*. The study for this type of problems has been done by several authors in the Hilbert space setting. The scope of our study is extended to the V- V* setting. The main tool employed here is a certain approximation argument in a Hilbert space and for this purpose we need to assume that there exists a Hilbert space H such that V⊂H≡H*⊂V* with densely defined continuous injections. The applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation: ut(x,t)-Δpu(x,t)-|u|u(x,t)=f(x,t), x∈Ω, t>0, u|=0, where Ω is a bounded domain in RN. In particular, the existence of local (in time) weak solution is shown under the subcritical growth condition q

Considerations in cross-validation type density smoothing with a look at some data

NASA Technical Reports Server (NTRS)

Schuster, E. F.

1982-01-01

Experience gained in applying nonparametric maximum likelihood techniques of density estimation to judge the comparative quality of various estimators is reported. Two invariate data sets of one hundered samples (one Cauchy, one natural normal) are considered as well as studies in the multivariate case.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

Hadamard Property of the in and out States for Klein-Gordon Fields on Asymptotically Static Spacetimes

NASA Astrophysics Data System (ADS)

Gérard, Christian; Wrochna, Michał

2017-08-01

We consider the massive Klein-Gordon equation on a class of asymptotically static spacetimes (in the long range sense) with Cauchy surface of bounded geometry. We prove the existence and Hadamard property of the in and out states constructed by scattering theory methods.

Violation of Bell's inequalities in quantum optics

NASA Technical Reports Server (NTRS)

Reid, M. D.; Walls, D. F.

1984-01-01

An optical field produced by intracavity four-wave mixing is shown to exhibit the following nonclassical features: photon antibunching, squeezing, and violation of Cauchy-Schwarz and Bell's inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P function.

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Attention problems and pathological gaming: resolving the 'chicken and egg' in a prospective analysis.

PubMed

Ferguson, Christopher J; Ceranoglu, T Atilla

2014-03-01

Pathological gaming (PG) behaviors are behaviors which interfere with other life responsibilities. Continued debate exists regarding whether symptoms of PG behaviors are a unique phenomenon or arise from other mental health problems, including attention problems. Development of attention problems and occurrence of pathological gaming in 144 adolescents were followed during a 1-year prospective analysis. Teens and their parents reported on pathological gaming behaviors, attention problems, and current grade point average, as well as several social variables. Results were analyzed using regression and path analysis. Attention problems tended to precede pathological gaming behaviors, but the inverse was not true. Attention problems but not pathological gaming predicted lower GPA 1 year later. Current results suggest that pathological gaming arises from attention problems, but not the inverse. These results suggest that pathological gaming behaviors are symptomatic of underlying attention related mental health issues, rather than a unique phenomenon.

Coherent exciton transport in dendrimers and continuous-time quantum walks

NASA Astrophysics Data System (ADS)

Mülken, Oliver; Bierbaum, Veronika; Blumen, Alexander

2006-03-01

We model coherent exciton transport in dendrimers by continuous-time quantum walks. For dendrimers up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site, we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes shows characteristic patterns and allows us to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or to be again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.

Rayleigh Scattering in Planetary Atmospheres: Corrected Tables Through Accurate Computation of X and Y Functions

NASA Astrophysics Data System (ADS)

Natraj, Vijay; Li, King-Fai; Yung, Yuk L.

2009-02-01

Tables that have been used as a reference for nearly 50 years for the intensity and polarization of reflected and transmitted light in Rayleigh scattering atmospheres have been found to be inaccurate, even to four decimal places. We convert the integral equations describing the X and Y functions into a pair of coupled integro-differential equations that can be efficiently solved numerically. Special care has been taken in evaluating Cauchy principal value integrals and their derivatives that appear in the solution of the Rayleigh scattering problem. The new approach gives results accurate to eight decimal places for the entire range of tabulation (optical thicknesses 0.02-1.0, surface reflectances 0-0.8, solar and viewing zenith angles 0°-88.85°, and relative azimuth angles 0°-180°), including the most difficult case of direct transmission in the direction of the sun. Revised tables have been created and stored electronically for easy reference by the planetary science and astrophysics community.

Coherent Structure Detection using Persistent Homology and other Topological Tools

NASA Astrophysics Data System (ADS)

Smith, Spencer; Roberts, Eric; Sindi, Suzanne; Mitchell, Kevin

2017-11-01

For non-autonomous, aperiodic fluid flows, coherent structures help organize the dynamics, much as invariant manifolds and periodic orbits do for autonomous or periodic systems. The prevalence of such flows in nature and industry has motivated many successful techniques for defining and detecting coherent structures. However, often these approaches require very fine trajectory data to reconstruct velocity fields and compute Cauchy-Green-tensor-related quantities. We use topological techniques to help detect coherent trajectory sets in relatively sparse 2D advection problems. More specifically, we have developed a homotopy-based algorithm, the ensemble-based topological entropy calculation (E-tec), which assigns to each edge in an initial triangulation of advected points a topologically forced lower bound on its future stretching rate. The triangulation and its weighted edges allow us to analyze flows using persistent homology. This topological data analysis tool detects clusters and loops in the triangulation that are robust in the presence of noise and in this case correspond to coherent trajectory sets.

Automated Approach to Very High-Order Aeroacoustic Computations. Revision

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2001-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

On the Rigid-Lid Approximation for Two Shallow Layers of Immiscible Fluids with Small Density Contrast

NASA Astrophysics Data System (ADS)

Duchêne, Vincent

2014-08-01

The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface displacements. In this paper, we offer a rigorous justification of this approximation in the case of two shallow layers of immiscible fluids with constant and quasi-equal mass density. More precisely, we control the difference between the solutions of the Cauchy problem predicted by the shallow-water (Saint-Venant) system in the rigid-lid and free-surface configuration. We show that in the limit of a small density contrast, the flow may be accurately described as the superposition of a baroclinic (or slow) mode, which is well predicted by the rigid-lid approximation, and a barotropic (or fast) mode, whose initial smallness persists for large time. We also describe explicitly the first-order behavior of the deformation of the surface and discuss the case of a nonsmall initial barotropic mode.

Vector intensity reconstruction using the data completion method.

PubMed

Langrenne, Christophe; Garcia, Alexandre

2013-04-01

This paper presents an application of the data completion method (DCM) for vector intensity reconstructions. A mobile array of 36 pressure-pressure probes (72 microphones) is used to perform measurements near a planar surface. Nevertheless, since the proposed method is based on integral formulations, DCM can be applied with any kind of geometry. This method requires the knowledge of Cauchy data (pressure and velocity) on a part of the boundary of an empty domain in order to evaluate pressure and velocity on the remaining part of the boundary. Intensity vectors are calculated in the interior domain surrounded by the measurement array. This inverse acoustic problem requires the use of a regularization method to obtain a realistic solution. An experiment in a closed wooden car trunk mock-up excited by a shaker and two loudspeakers is presented. In this case, where the volume of the mock-up is small (0.61 m(3)), standing-waves and fluid structure interactions appear and show that DCM is a powerful tool to identify sources in a confined space.

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2000-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Quenching rate for a nonlocal problem arising in the micro-electro mechanical system

NASA Astrophysics Data System (ADS)

Guo, Jong-Shenq; Hu, Bei

2018-03-01

In this paper, we study the quenching rate of the solution for a nonlocal parabolic problem which arises in the study of the micro-electro mechanical system. This question is equivalent to the stabilization of the solution to the transformed problem in self-similar variables. First, some a priori estimates are provided. In order to construct a Lyapunov function, due to the lack of time monotonicity property, we then derive some very useful and challenging estimates by a delicate analysis. Finally, with this Lyapunov function, we prove that the quenching rate is self-similar which is the same as the problem without the nonlocal term, except the constant limit depends on the solution itself.

UNIFORM ESTIMATES FOR SOLUTIONS OF THE \\overline{\\partial}-EQUATION IN PSEUDOCONVEX POLYHEDRA

NASA Astrophysics Data System (ADS)

Sergeev, A. G.; Henkin, G. M.

1981-04-01

It is proved that the nonhomogeneous Cauchy-Riemann equation on an analytic submanifold "in general position" in a Cartesian product of strictly convex domains admits a solution with a uniform estimate. The possibility of weakening the requirement of general position in this result is investigated. Bibliography: 46 titles.

A Characterization of Banach Spaces Containing l1

PubMed Central

Rosenthal, Haskell P.

1974-01-01

It is proved that a Banach space contains a subspace isomorphic to l1 if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent. PMID:16592162

8. Asymptotically Flat and Regular Cauchy Data

NASA Astrophysics Data System (ADS)

Dain, Sergio

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

High-throughput exploration of thermoelectric and mechanical properties of amorphous NbO2 with transition metal additions

NASA Astrophysics Data System (ADS)

Music, Denis; Geyer, Richard W.; Hans, Marcus

2016-07-01

To increase the thermoelectric efficiency and reduce the thermal fatigue upon cyclic heat loading, alloying of amorphous NbO2 with all 3d and 5d transition metals has systematically been investigated using density functional theory. It was found that Ta fulfills the key design criteria, namely, enhancement of the Seebeck coefficient and positive Cauchy pressure (ductility gauge). These quantum mechanical predictions were validated by assessing the thermoelectric and elastic properties on combinatorial thin films, which is a high-throughput approach. The maximum power factor is 2813 μW m-1 K-2 for the Ta/Nb ratio of 0.25, which is a hundredfold increment compared to pure NbO2 and exceeds many oxide thermoelectrics. Based on the elasticity measurements, the consistency between theory and experiment for the Cauchy pressure was attained within 2%. On the basis of the electronic structure analysis, these configurations can be perceived as metallic, which is consistent with low electrical resistivity and ductile behavior. Furthermore, a pronounced quantum confinement effect occurs, which is identified as the physical origin for the Seebeck coefficient enhancement.

A local quasicontinuum method for 3D multilattice crystalline materials: Application to shape-memory alloys

NASA Astrophysics Data System (ADS)

Sorkin, V.; Elliott, R. S.; Tadmor, E. B.

2014-07-01

The quasicontinuum (QC) method, in its local (continuum) limit, is applied to materials with a multilattice crystal structure. Cauchy-Born (CB) kinematics, which accounts for the shifts of the crystal motif, is used to relate atomic motions to continuum deformation gradients. To avoid failures of CB kinematics, QC is augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required periodic cell size. This approach is referred to as Cascading Cauchy-Born kinematics (CCB). In this paper, the method is described and developed. It is then used, along with an effective interaction potential (EIP) model for shape-memory alloys, to simulate the shape-memory effect and pseudoelasticity in a finite specimen. The results of these simulations show that (i) the CCB methodology is an essential tool that is required in order for QC-type simulations to correctly capture the first-order phase transitions responsible for these material behaviors, and (ii) that the EIP model adopted in this work coupled with the QC/CCB methodology is capable of predicting the characteristic behavior found in shape-memory alloys.

How to use retarded Green's functions in de Sitter spacetime

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

Higuchi, Atsushi; Cheong, Lee Yen

2008-10-15

We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetismmore » in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the 'North and South Poles' which is nonsingular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green's function with corresponding gauge parameters.« less

Golden Ratio in a Coupled-Oscillator Problem

ERIC Educational Resources Information Center

Moorman, Crystal M.; Goff, John Eric

2007-01-01

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem

NASA Astrophysics Data System (ADS)

Kostin, A. B.; Sherstyukov, V. B.

2017-12-01

For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Kramers problem: Numerical Wiener-Hopf-like model characteristics

NASA Astrophysics Data System (ADS)

Ezin, A. N.; Samgin, A. L.

2010-11-01

Since the Kramers problem cannot be, in general, solved in terms of elementary functions, various numerical techniques or approximate methods must be employed. We present a study of characteristics for a particle in a damped well, which can be considered as a discretized version of the Melnikov [Phys. Rev. E 48, 3271 (1993)]10.1103/PhysRevE.48.3271 turnover theory. The main goal is to justify the direct computational scheme to the basic Wiener-Hopf model. In contrast to the Melnikov approach, which implements factorization through a Cauchy-theorem-based formulation, we employ the Wiener-Levy theorem to reduce the Kramers problem to a Wiener-Hopf sum equation written in terms of Toeplitz matrices. This latter can provide a stringent test for the reliability of analytic approximations for energy distribution functions occurring in the Kramers problems at arbitrary damping. For certain conditions, the simulated characteristics are compared well with those determined using the conventional Fourier-integral formulas, but sometimes may differ slightly depending on the value of a dissipation parameter. Another important feature is that, with our method, we can avoid some complications inherent to the Melnikov method. The calculational technique reported in the present paper may gain particular importance in situations where the energy losses of the particle to the bath are a complex-shaped function of the particle energy and analytic solutions of desired accuracy are not at hand. In order to appreciate more readily the significance and scope of the present numerical approach, we also discuss concrete aspects relating to the field of superionic conductors.

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

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

Lusanna, Luca

2004-08-19

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are gauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the Dirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of causality dictates the choice of retarded solutions at the classical level. However both the problems of themore » classical theory of the electron, leading to the choice of (1/2) (retarded + advanced) solutions, and the regularization of quantum field theory, leading to the Feynman propagator, introduce anticipatory aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.Talk and 'best contribution' at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16, 2003.« less

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Common Methodological Problems in Research on the Addictions.

ERIC Educational Resources Information Center

Nathan, Peter E.; Lansky, David

1978-01-01

Identifies common problems in research on the addictions and offers suggestions for remediating these methodological problems. The addictions considered include alcoholism and drug dependencies. Problems considered are those arising from inadequate, incomplete, or biased reviews of relevant literatures and methodological shortcomings of subject…

Low thrust propulsion system effects on communication satellites.

NASA Technical Reports Server (NTRS)

Hall, D. F.; Lyon, W. C.

1972-01-01

Choice of type and placement of thrusters on spacecraft (s/c) should include consideration of their effects on other subsystems. Models are presented of the exhaust plumes of mercury, cesium, colloid, hydrazine, ammonia, and Teflon rockets. Effects arising from plume impingement on s/c surfaces, radio frequency interference, optical interference, and earth environmental contamination are discussed. Some constraints arise in the placement of mercury, cesium, and Teflon thrusters. Few problems exist with other thruster types, nor is earth contamination a problem.

The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1989-01-01

The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code.

Evolution of Degenerate Space-Time from Non-Degenerate Initial Value in Ashtekar's Formalism

NASA Astrophysics Data System (ADS)

Ma, Yongge; Liang, Canbin

1998-09-01

The possibility of evolving a degenerate space-time from non-degenerate initial value in Ashtekar's formalism is considered in a constructed example. It is found that this possibility could be realized in the time evolution given by Ashtekar's equations, but the topology change of space makes it fail to be a Cauchy evolution.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

Milne, a routine for the numerical solution of Milne's problem

NASA Astrophysics Data System (ADS)

Rawat, Ajay; Mohankumar, N.

2010-11-01

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_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.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.

The Riemann-Hilbert problem for nonsymmetric systems

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.; Paveri-Fontana, S.

1991-12-01

A comparison of the Riemann-Hilbert problem and the Wiener-Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.

A Comparison of Solver Performance for Complex Gastric Electrophysiology Models

PubMed Central

Sathar, Shameer; Cheng, Leo K.; Trew, Mark L.

2016-01-01

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543

Problem-Solving during Shared Reading at Kindergarten

ERIC Educational Resources Information Center

Gosen, Myrte N.; Berenst, Jan; de Glopper, Kees

2015-01-01

This paper reports on a conversation analytic study of problem-solving interactions during shared reading at three kindergartens in the Netherlands. It illustrates how teachers and pupils discuss book characters' problems that arise in the events in the picture books. A close analysis of the data demonstrates that problem-solving interactions do…

Transnational Environmental Problems--The United States, Canada, Mexico.

ERIC Educational Resources Information Center

Wilcher, Marshall E.

1983-01-01

Examines problems associated with transboundary environmental pollution, focusing on problems arising between the United States and Mexico and between the United States and Canada. Also discusses new organizational forms developed to bring transboundary issues to a higher policy-making level. (JN)

Fair Inference on Outcomes

PubMed Central

Nabi, Razieh; Shpitser, Ilya

2017-01-01

In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The issue of fairness arises in such problems where some covariates or treatments are “sensitive,” in the sense of having potential of creating discrimination. In this paper, we argue that the presence of discrimination can be formalized in a sensible way as the presence of an effect of a sensitive covariate on the outcome along certain causal pathways, a view which generalizes (Pearl 2009). A fair outcome model can then be learned by solving a constrained optimization problem. We discuss a number of complications that arise in classical statistical inference due to this view and provide workarounds based on recent work in causal and semi-parametric inference.

Distinctions between fraud, bias, errors, misunderstanding, and incompetence.

PubMed

DeMets, D L

1997-12-01

Randomized clinical trials are challenging not only in their design and analysis, but in their conduct as well. Despite the best intentions and efforts, problems often arise in the conduct of trials, including errors, misunderstandings, and bias. In some instances, key players in a trial may discover that they are not able or competent to meet requirements of the study. In a few cases, fraudulent activity occurs. While none of these problems is desirable, randomized clinical trials are usually found sufficiently robust by many key individuals to produce valid results. Other problems are not tolerable. Confusion may arise among scientists, scientific and lay press, and the public about the distinctions between these areas and their implications. We shall try to define these problems and illustrate their impact through a series of examples.

A non-local free boundary problem arising in a theory of financial bubbles

PubMed Central

Berestycki, Henri; Monneau, Regis; Scheinkman, José A.

2014-01-01

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero. PMID:25288815

A Summary of Some Discrete-Event System Control Problems

NASA Astrophysics Data System (ADS)

Rudie, Karen

A summary of the area of control of discrete-event systems is given. In this research area, automata and formal language theory is used as a tool to model physical problems that arise in technological and industrial systems. The key ingredients to discrete-event control problems are a process that can be modeled by an automaton, events in that process that cannot be disabled or prevented from occurring, and a controlling agent that manipulates the events that can be disabled to guarantee that the process under control either generates all the strings in some prescribed language or as many strings as possible in some prescribed language. When multiple controlling agents act on a process, decentralized control problems arise. In decentralized discrete-event systems, it is presumed that the agents effecting control cannot each see all event occurrences. Partial observation leads to some problems that cannot be solved in polynomial time and some others that are not even decidable.

The Visual Effects of Intraocular Colored Filters

PubMed Central

Hammond, Billy R.

2012-01-01

Modern life is associated with a myriad of visual problems, most notably refractive conditions such as myopia. Human ingenuity has addressed such problems using strategies such as spectacle lenses or surgical correction. There are other visual problems, however, that have been present throughout our evolutionary history and are not as easily solved by simply correcting refractive error. These problems include issues like glare disability and discomfort arising from intraocular scatter, photostress with the associated transient loss in vision that arises from short intense light exposures, or the ability to see objects in the distance through a veil of atmospheric haze. One likely biological solution to these more long-standing problems has been the use of colored intraocular filters. Many species, especially diurnal, incorporate chromophores from numerous sources (e.g., often plant pigments called carotenoids) into ocular tissues to improve visual performance outdoors. This review summarizes information on the utility of such filters focusing on chromatic filtering by humans. PMID:24278692

Some Geometric Inequalities Relating to an Interior Point in Triangle

ERIC Educational Resources Information Center

Wu, Yu-Dong; Zhang, Zhi-Hua; Liang, Chun-Lei

2010-01-01

In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

Material Characterization using Passive Multispectral Polarimetric Imagery

DTIC Science & Technology

2013-03-01

least intuitive RS technique is undoubtedly polarimetry . Polarization is a property of all TEM waves, so its applications are not limited to any...Shaw. “Review of passive imaging polarimetry for remote sensing applications”. Applied Optics, 45(22):5453–5469, 2006. [48] Vanderbilt, V.C. and...refractive index; polarimetry ; multispectral; polarization; polarisation; polarimetric imagery; dispersion; Drude model; Cauchy equation; remote

Inequalities for frequency-moment sum rules of electron liquids

NASA Technical Reports Server (NTRS)

Iwamoto, N.

1986-01-01

The relations between the various frequency-moment sum rules of electron liquids, which include even-power moments, are systematically examined by using the Cauchy-Schwarz and Hoelder inequalities. A relation involving the isothermal sound velocity and the kinetic and potential energies is obtained from one of the inequalities in the long-wavelength limit, and is generalized to arbitrary spatial dimensions.

Charge-transfer potentials for ionic crystals: Cauchy violation, LO-TO splitting, and the necessity of an ionic reference state.

PubMed

Sukhomlinov, Sergey V; Müser, Martin H

2015-12-14

In this work, we study how including charge transfer into force fields affects the predicted elastic and vibrational Γ-point properties of ionic crystals, in particular those of rock salt. In both analytical and numerical calculations, we find that charge transfer generally leads to a negative contribution to the Cauchy pressure, P(C) ≡ C12 - C66, where C12 and C66 are elements of the elastic tensor. This contribution increases in magnitude with pressure for different charge-transfer approaches in agreement with results obtained with density functional theory (DFT). However, details of the charge-transfer models determine the pressure dependence of the longitudinal optical-transverse optical splitting and that for partial charges. These last two quantities increase with density as long as the chemical hardness depends at most weakly on the environment while experiments and DFT find a decrease. In order to reflect the correct trends, the charge-transfer expansion has to be made around ions and the chemical (bond) hardness has to increase roughly exponentially with inverse density or bond lengths. Finally, the adjustable force-field parameters only turn out meaningful, when the expansion is made around ions.

Charge-transfer potentials for ionic crystals: Cauchy violation, LO-TO splitting, and the necessity of an ionic reference state

NASA Astrophysics Data System (ADS)

Sukhomlinov, Sergey V.; Müser, Martin H.

2015-12-01

In this work, we study how including charge transfer into force fields affects the predicted elastic and vibrational Γ-point properties of ionic crystals, in particular those of rock salt. In both analytical and numerical calculations, we find that charge transfer generally leads to a negative contribution to the Cauchy pressure, PC ≡ C12 - C66, where C12 and C66 are elements of the elastic tensor. This contribution increases in magnitude with pressure for different charge-transfer approaches in agreement with results obtained with density functional theory (DFT). However, details of the charge-transfer models determine the pressure dependence of the longitudinal optical-transverse optical splitting and that for partial charges. These last two quantities increase with density as long as the chemical hardness depends at most weakly on the environment while experiments and DFT find a decrease. In order to reflect the correct trends, the charge-transfer expansion has to be made around ions and the chemical (bond) hardness has to increase roughly exponentially with inverse density or bond lengths. Finally, the adjustable force-field parameters only turn out meaningful, when the expansion is made around ions.

Implementation of compressive sensing for preclinical cine-MRI

NASA Astrophysics Data System (ADS)

Tan, Elliot; Yang, Ming; Ma, Lixin; Zheng, Yahong Rosa

2014-03-01

This paper presents a practical implementation of Compressive Sensing (CS) for a preclinical MRI machine to acquire randomly undersampled k-space data in cardiac function imaging applications. First, random undersampling masks were generated based on Gaussian, Cauchy, wrapped Cauchy and von Mises probability distribution functions by the inverse transform method. The best masks for undersampling ratios of 0.3, 0.4 and 0.5 were chosen for animal experimentation, and were programmed into a Bruker Avance III BioSpec 7.0T MRI system through method programming in ParaVision. Three undersampled mouse heart datasets were obtained using a fast low angle shot (FLASH) sequence, along with a control undersampled phantom dataset. ECG and respiratory gating was used to obtain high quality images. After CS reconstructions were applied to all acquired data, resulting images were quantitatively analyzed using the performance metrics of reconstruction error and Structural Similarity Index (SSIM). The comparative analysis indicated that CS reconstructed images from MRI machine undersampled data were indeed comparable to CS reconstructed images from retrospective undersampled data, and that CS techniques are practical in a preclinical setting. The implementation achieved 2 to 4 times acceleration for image acquisition and satisfactory quality of image reconstruction.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Stress Formulation in Three-Dimensional Elasticity

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2001-01-01

The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation: differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function. This Completed Beltrami-Michell Formulation (CBMF) can be specialized to derive the traditional methods, but the reverse is not possible. Elasticity solutions must be verified for the compliance of the new equation because the boundary compatibility conditions expressed in terms of displacement are not trivially satisfied. This paper presents the variational derivation of the stress formulation, illustrates the method, examines attributes and benefits, and outlines the future course of research.

High-throughput exploration of thermoelectric and mechanical properties of amorphous NbO{sub 2} with transition metal additions

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

Music, Denis, E-mail: music@mch.rwth-aachen.de; Geyer, Richard W.; Hans, Marcus

2016-07-28

To increase the thermoelectric efficiency and reduce the thermal fatigue upon cyclic heat loading, alloying of amorphous NbO{sub 2} with all 3d and 5d transition metals has systematically been investigated using density functional theory. It was found that Ta fulfills the key design criteria, namely, enhancement of the Seebeck coefficient and positive Cauchy pressure (ductility gauge). These quantum mechanical predictions were validated by assessing the thermoelectric and elastic properties on combinatorial thin films, which is a high-throughput approach. The maximum power factor is 2813 μW m{sup −1} K{sup −2} for the Ta/Nb ratio of 0.25, which is a hundredfold increment compared to puremore » NbO{sub 2} and exceeds many oxide thermoelectrics. Based on the elasticity measurements, the consistency between theory and experiment for the Cauchy pressure was attained within 2%. On the basis of the electronic structure analysis, these configurations can be perceived as metallic, which is consistent with low electrical resistivity and ductile behavior. Furthermore, a pronounced quantum confinement effect occurs, which is identified as the physical origin for the Seebeck coefficient enhancement.« less

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems.

DTIC Science & Technology

1980-10-01

faster than previous algorithms. Indeed, with only minor modifications, the standard multigrid programs solve the LCP with essentially the same efficiency... Lemna 2.2. Let Uk be the solution of the LCP (2.3), and let uk > 0 be an approximate solu- tion obtained after one or more Gk projected sweeps. Let...in Figure 3.2, Ivu IIG decreased from .293 10 to .110 10 with the expenditure of (99.039-94.400) = 4.639 work units. While minor variations do arise, a

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

Contextualized Mathematics Problems and Transfer of Knowledge: Establishing Problem Spaces and Boundaries

ERIC Educational Resources Information Center

McGraw, Rebecca; Patterson, Cody L.

2017-01-01

In this study, we examine how inservice secondary mathematics teachers working together on a contextualized problem negotiate issues arising from the ill-structured nature of the problem such as what assumptions one may make, what real-world considerations should be taken into account, and what constitutes a satisfactory solution. We conceptualize…

From the Golden Rectangle and Fibonacci to Pedagogy and Problem Posing

ERIC Educational Resources Information Center

Brown, Stephen I.

1976-01-01

Beginning with an analysis of the golden rectangle, the author shows how a series of problems for student investigation arise from queries concerning changes in conditions and analogous situations. (SD)

Problems in Recording the Electrocardiogram.

ERIC Educational Resources Information Center

Webster, John G.

The unwanted signals that arise in electrocardiography are discussed. A technical background of electrocardiography is given, along with teaching techniques that educate students of medical instrumentation to solve the problems caused by these signals. (MJH)

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Exploiting Symmetry on Parallel Architectures.

NASA Astrophysics Data System (ADS)

Stiller, Lewis Benjamin

1995-01-01

This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.

Parallel block schemes for large scale least squares computations

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

Golub, G.H.; Plemmons, R.J.; Sameh, A.

1986-04-01

Large scale least squares computations arise in a variety of scientific and engineering problems, including geodetic adjustments and surveys, medical image analysis, molecular structures, partial differential equations and substructuring methods in structural engineering. In each of these problems, matrices often arise which possess a block structure which reflects the local connection nature of the underlying physical problem. For example, such super-large nonlinear least squares computations arise in geodesy. Here the coordinates of positions are calculated by iteratively solving overdetermined systems of nonlinear equations by the Gauss-Newton method. The US National Geodetic Survey will complete this year (1986) the readjustment ofmore » the North American Datum, a problem which involves over 540 thousand unknowns and over 6.5 million observations (equations). The observation matrix for these least squares computations has a block angular form with 161 diagnonal blocks, each containing 3 to 4 thousand unknowns. In this paper parallel schemes are suggested for the orthogonal factorization of matrices in block angular form and for the associated backsubstitution phase of the least squares computations. In addition, a parallel scheme for the calculation of certain elements of the covariance matrix for such problems is described. It is shown that these algorithms are ideally suited for multiprocessors with three levels of parallelism such as the Cedar system at the University of Illinois. 20 refs., 7 figs.« less

Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

NASA Astrophysics Data System (ADS)

Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

2018-03-01

We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

Using geologic structures to constrain constitutive laws not accessible in the laboratory

USGS Publications Warehouse

Nevitt, Johanna; Warren, Jessica M.; Kumamoto, Kathryn M.; Pollard, David D.

2018-01-01

In this essay, we explore a central problem of structural geology today, and in the foreseeable future, which is the determination of constitutive laws governing rock deformation to produce geologic structures. Although laboratory experiments provide much needed data and insights about constitutive laws, these experiments cannot cover the range of conditions and compositions relevant to the formation of geologic structures. We advocate that structural geologists address this limitation by interpreting natural experiments, documented with field and microstructural data, using continuum mechanical models that enable the deduction of constitutive laws. To put this procedure into a historical context, we review the founding of structural geology by James Hutton in the late 18th century, and the seminal contributions to continuum mechanics from Newton to Cauchy that provide the tools to model geologic structures. The procedure is illustrated with two examples drawn from recent and on-going field investigations of crustal and mantle lithologies. We conclude by pointing to future research opportunities that will engage structural geologists in the pursuit of constitutive laws during the 21st century.

Bridging the Gap Between Stationary Homogeneous Isotropic Turbulence and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

A statistical theory of stationary isotropic turbulence is presented with eddies possessing Gaussian velocity distribution, Maxwell-Boltzmann speed distribution in harmony with perceptions of Heisenberg, and Planck energy distribution in harmony with perceptions of Chandrasekhar and in agreement with experimental observations of Van Atta and Chen. Defining the action S = - mΦ in terms of velocity potential of atomic motion, scale-invariant Schrödinger equation is derivedfrom invariant Bernoulli equation. Thus, the gap between the problems of turbulence and quantum mechanics is closed through connections between Cauchy-Euler-Bernoulli equations of hydrodynamics, Hamilton-Jacobi equation of classical mechanics, and finally Schrödinger equation of quantum mechanics. Transitions of particle (molecular cluster cji) from a small rapidly-oscillating eddy ej (high-energy level-j) to a large slowly-oscillating eddy ei (low energy-level-i) leads to emission of a sub-particle (molecule mji) that carries away the excess energy ɛji = h (νj -νi) in harmony with Bohr theory of atomic spectra. ∖ ∖ NASA Grant No. NAG3-1863.

Complex plane integration in the modelling of electromagnetic fields in layered media: part 1. Application to a very large loop

NASA Astrophysics Data System (ADS)

Silva, Valdelírio da Silva e.; Régis, Cícero; Howard, Allen Q., Jr.

2014-02-01

This paper analyses the details of a procedure for the numerical integration of Hankel transforms in the calculation of the electromagnetic fields generated by a large horizontal loop over a 1D earth. The method performs the integration by deforming the integration path into the complex plane and applying Cauchy's theorem on a modified version of the integrand. The modification is the replacement of the Bessel functions J0 and J1 by the Hankel functions H_0^{(1)} and H_1^{(1)} respectively. The integration in the complex plane takes advantage of the exponentially decaying behaviour of the Hankel functions, allowing calculation on very small segments, instead of the infinite line of the original improper integrals. A crucial point in this problem is the location of the poles. The companion paper shows two methods to estimate the pole locations. We have used this method to calculate the fields of very large loops. Our results show that this method allows the estimation of the integrals with fewer evaluations of the integrand functions than other methods.

Financial derivative pricing under probability operator via Esscher transfomation

NASA Astrophysics Data System (ADS)

Achi, Godswill U.

2014-10-01

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing9 where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φx(u) of Xt we recuperate the Black-Scholes formula for financial derivative prices.

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

NASA Astrophysics Data System (ADS)

Lusanna, Luca

Clock synchronization leads to the definition of instantaneous 3-spaces (to be used as Cauchy surfaces) in non-inertial frames, the only ones allowed by the equivalence principle. ADM canonical tetrad gravity in asymptotically Minkowskian space-times can be described in this framework. This allows to find the York canonical basis in which the inertial (gauge) and tidal (physical) degrees of freedom of the gravitational field can be identified. A Post-Minkowskian linearization with respect to the asymptotic Minkowski metric (asymptotic background) allows to solve the Dirac constraints in non-harmonic 3-orthogonal gauges and to find non-harmonic TT gravitational waves. The inertial gauge variable York time (the trace of the extrinsic curvature of the 3-space) describes the general relativistic freedom in clock synchronization. After a digression on the gauge problem in general relativity, it is shown that dark matter, whose experimental signatures are the rotation curves and the mass of galaxies, may be described (at least partially) as an inertial relativistic effect (absent in Newton gravity) connected with the York time.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Institutional Resource Requirements, Management, and Accountability.

ERIC Educational Resources Information Center

Matlock, John; Humphries, Frederick S.

A detailed resource management study was conducted at Tennessee State University, and resource management problems at other higher education institutions were identified through the exchange of data and studies. Resource requirements and management problems unique to black institutions were examined, as were the problems that arise from regional…

Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, C. K. W. (Editor); Hardin, J. C. (Editor)

1997-01-01

The proceedings of the Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems held at Florida State University are the subject of this report. For this workshop, problems arising in typical industrial applications of CAA were chosen. Comparisons between numerical solutions and exact solutions are presented where possible.

A New Approach to Isolating External Magnetic Field Components in Spacecraft Measurements of the Earth's Magnetic Field Using Global Positioning System observables

NASA Technical Reports Server (NTRS)

Raymond, C.; Hajj, G.

1994-01-01

We review the problem of separating components of the magnetic field arising from sources in the Earth's core and lithosphere, from those contributions arising external to the Earth, namely ionospheric and magnetospheric fields, in spacecraft measurements of the Earth's magnetic field.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Direct calculation of wall interferences and wall adaptation for two-dimensional flow in wind tunnels with closed walls

NASA Technical Reports Server (NTRS)

Amecke, Juergen

1986-01-01

A method for the direct calculation of the wall induced interference velocity in two dimensional flow based on Cauchy's integral formula was derived. This one-step method allows the calculation of the residual corrections and the required wall adaptation for interference-free flow starting from the wall pressure distribution without any model representation. Demonstrated applications are given.

Advective Mixing in a Nondivergent Barotropic Hurricane Model

DTIC Science & Technology

2010-01-20

voted to the mixing of fluid from different regions of a hurri- cane, which is considered as a fundamental mechanism that is intimately related to...range is governed by the Cauchy-Riemann deformation tensor , 1(x0,t0)= ( dx0φ t0+T t0 (x0) )∗( dx0φ t0+T t0 (x0) ) , and becomes maximal when ξ0 is

Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. II. KIDs for the Kerr-(A)(de Sitter) family

NASA Astrophysics Data System (ADS)

Paetz, Tim-Torben

2017-04-01

We characterize Cauchy data sets leading to vacuum space-times with vanishing Mars-Simon tensor. This approach provides an algorithmic procedure to check whether a given initial data set (Σ ,hi j,Ki j) evolves into a space-time which is locally isometric to a member of the Kerr-(A)(dS) family.

Identities associated with Milne-Thomson type polynomials and special numbers.

PubMed

Simsek, Yilmaz; Cakic, Nenad

2018-01-01

The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

Positive Discipline A to Z: 1001 Solutions to Everyday Parenting Problems.

ERIC Educational Resources Information Center

Nelsen, Jane; And Others

This book is a parenting reference work that offers background on common disciplinary problems and parenting issues, advice on how to handle problems and issues as they arise, and insight into how to avoid disciplinary problems in the future. The book is divided into three sections: Basic Positive Discipline Parenting Tools, Positive Discipline…

Cognitive Abilities Adjustment and Parenting Practices in Preschoolers with Disruption Conduct Problems

ERIC Educational Resources Information Center

Fernandez-Parra, A.; Lopez-Rubio, S.; Mata, S.; Calero, M. D.; Vives, M. C.; Carles, R.; Navarro, E.

2013-01-01

Introduction: Conduct problems arising in infancy are one of the main reasons for which parents seek psychological assistance. Although these problems usually begin when the child has started school, in recent years a group of children has been identified who begin to manifest such problems from their earliest infancy and whose prognosis seems to…

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Responding to Adolescent Suicide.

ERIC Educational Resources Information Center

Phi Delta Kappa Educational Foundation, Bloomington, IN.

This publication is designed to help educators deal with the problems that arise after an adolescent's suicide. It recommends that teachers should be able to detect differences in students' responses to emotional problems. Following a preface and a brief review of the extent of the problem, the first chapter discusses which adolescents are…

Introducing the Hero Complex and the Mythic Iconic Pathway of Problem Gambling

ERIC Educational Resources Information Center

Nixon, Gary; Solowoniuk, Jason

2009-01-01

Early research into the motivations behind problem gambling reflected separate paradigms of thought splitting our understanding of the gambler into divergent categories. However, over the past 25 years, problem gambling is now best understood to arise from biological, environmental, social, and psychological processes, and is now encapsulated…

Esperanto and International Language Problems: A Research Bibliography.

ERIC Educational Resources Information Center

Tonkin, Humphrey R.

This bibliography is intended both for the researcher and for the occasional student of international language problems, particularly as these relate to the international language Esperanto. The book is divided into two main sections: Part One deals with problems arising from communication across national boundaries and the search for a solution…

Correct numerical simulation of a two-phase coolant

NASA Astrophysics Data System (ADS)

Kroshilin, A. E.; Kroshilin, V. E.

2016-02-01

Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models' ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

Constraining the physical state by symmetries

NASA Astrophysics Data System (ADS)

Fatibene, L.; Ferraris, M.; Magnano, G.

2017-03-01

After reviewing the hole argument and its relations with initial value problem and general covariance, we shall discuss how much freedom one has to define the physical state in a generally covariant field theory (with or without internal gauge symmetries). Our analysis relies on Cauchy problems, thus it is restricted to globally hyperbolic spacetimes. We shall show that in generally covariant theories on a compact space (as well as for internal gauge symmetries on any spacetime) one has no freedom and one is forced to declare as physically equivalent two configurations which differ by a global spacetime diffeomorphism (or by an internal gauge transformation) as it is usually prescribed. On the contrary, when space is not compact, the result does not hold true and one may have different options to define physically equivalent configurations, still preserving determinism. For this scenario to be effective, the group G of formal transformations needs to be a subgroup of dynamical symmetries (otherwise field equations, which are written in terms of configurations would not induce equations for the physical state classes) and it must contain the group D generated by Cauchy transformations (otherwise the equations induced on physical state classes would not be well posed, either). We argue that it is exactly because of this double inclusion that the hole argument in its initial problem formulation is more powerful than in its boundary formulation. In the boundary formulation of the hole argument one still has that the group G of formal transformations is a subgroup of dynamical symmetries, but there is no evidence for it to contain a particular non-trivial subgroup.In this paper we shall show that this scenario is exactly implemented in generally covariant theories. In the last section we shall show it to be implemented in gauge theories as well.Norton also argued (see [1]) that the definition of physical state is something to be discussed in physics and it is not something which can be settled by a purely mathematical argument. This position is certainly plausible and agreeable. However, we shall here argue that some constraints to the definition of physical state can be in fact put on a mathematical stance (the ones which go back to Einstein-Hilbert about well-posedness of Cauchy problems).A physical state is hence defined as an equivalence class of configurations, for which dynamics is well-posed, i.e. its evolution is deterministically singled out by initial conditions. It also defines what the physical observables are, i.e., by definition, the quantities which depend on the equivalence classes, but not on the specific representative configurations. Equivalently, physical observables are defined as quantities which are invariant with respect to formal transformations.A detailed analysis of these issues shows an unexpected structure of cases which is not clarified in general, yet. What is clear is that assuming, as usually done, that the physical state of a generally covariant theory is to be identified with equivalence classes of configurations modulo spacetime diffeomorphisms is a fair assumption, still a choice which is sometimes forced by mathematics (in particular by determinism in the form of Cauchy theorem on globally hyperbolic spacetimes with a compact space) but sometimes it is one of many possible choices which, in those cases, we agree should be addressed from a physical stance.We shall argue that sometimes one can find subclasses of diffeomorphisms (i.e. the group generated by Cauchy-compatible transformations, below denoted by D →) which play a distinctive role in the discussion and which, to the best of our knowledge, has not properly been taken into account in standard frameworks.Let us start, for the sake of simplicity, by restricting to generally covariant theories. Gauge theories will be briefly discussed in the conclusions since most of what we shall do easily applies to those cases, as well; see [20] for general framework and notation.In a generally covariant theory one has a huge group of symmetries S containing the (lift to the configuration bundle of the) spacetime diffeomorphisms. The group of spacetime diffeomorphisms will be denoted by Diff(M) . In particular, the subgroup of spacetime diffeomorphisms which can be connected by a flow with the identity idM will be denoted by Diffe(M) . Any element Φ ∈Diffe(M) can be obtained by evaluating a 1-parameter subgroup Φs at s = 1, i.e. Φ =Φ1. The 1-parameter subgroup Φs is also called a flow of diffeomorphisms.The standard attitude is to assume that in a generally covariant theory any two configurations of fields differing by any spacetime diffeomorphism represent the same physical state. In other words, if σ is a section of the configuration bundle and Φ∗ σ =σ‧ is its image through a diffeomorphism (in Diffe(M) or in Diff(M) depending on the case) then both σ and σ‧ represent the same physical state of the system.Let us call formal transformations the group G of transformations which fix the physical state, or, equivalently, define the physical states of the orbits of the group G. As a matter of fact defining the group of formal transformations is equivalent to defining the physical state. Either one defines the physical state as the orbits of the action of formal transformations or defines formal transformations as the transformations acting on configurations by mapping one representative of the physical state into another representative of the same physical state, i.e. fixing the physical states.In order for this to make sense one needs a formal transformation Φ to be a symmetry of the system (as it is in generally covariant theories) since if σ is a solution, of course also σ‧ must be a solution as well. In other words any formal transformation (acting on configurations but leaving the physical state unchanged) must be a symmetry and the symmetry group is an upper bound to the group of formal transformations, i.e. one must have G ⊂ S.We shall show that there is a lower bound (which will be denoted by D → and which is generated by Cauchy transformations) for the group G of formal transformations as well, i.e. one must have D → ⊂ G ⊂ S.We shall argue that when D → ⊊ S =Diffe(M) one has a certain freedom in setting G between its lower and upper bounds. In these cases one has different options to set the group D → ⊂ G ⊂ S and each different assumption about what G is, in fact defines a different theory with the same dynamics but different interpretation of what is the physical state and what can be in principle observed; see [21]. We shall also discuss topological conditions on M for which this freedom is nullified and one is forced to set G =Diffe(M) as usually done in the literature. On the other hand, we can discuss the motion of particles in spacetime on a physical stance and show that it is reasonable to assume that the physical state is described by worldline trajectories and parameterisations are irrelevant. The two viewpoints come (quite independently) to the same conclusion, which is a good thing. We shall also show a counter example, showing a globally hyperbolic spacetime M = R × R with a non-compact space Σ ≡ R in which the situation is different from the compact space case. As a consequence, the usual assumption of identifying configurations which differ by a diffeomorphism is a legitimate though in general unmotivated choice. When describing a system one should be aware of which assumptions come from mathematical constraints and which assumptions are done on a physical stance.When setting up a general covariant theory one should first study whether the group D → is a strict subgroup of Diffe(M) . If it is, one should characterise possible subgroups D → ⊂ G ⊂ S. Then one should declare which one of such groups G is elected as the group of formal transformations. Different choices lead to different theories with an equivalent dynamics but different observables.

Errors, Error, and Text in Multidialect Setting.

ERIC Educational Resources Information Center

Candler, W. J.

1979-01-01

This article discusses the various dialects of English spoken in Liberia and analyzes the problems of Liberian students in writing compositions in English. Errors arise mainly from differences in culture and cognition, not from superficial linguistic problems. (CFM)

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

PubMed Central

Hemmelmayr, Vera C.; Cordeau, Jean-François; Crainic, Teodor Gabriel

2012-01-01

In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP. PMID:23483764

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics.

PubMed

Hemmelmayr, Vera C; Cordeau, Jean-François; Crainic, Teodor Gabriel

2012-12-01

In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP.

Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

ERIC Educational Resources Information Center

Khotimah, Rita Pramujiyanti; Masduki

2016-01-01

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed proofs of the main results in a self-contained book of reasonable length. Instead, the author concentrates on providing key definitions together with their motivations and explaining the main results, tools and difficulties for each topic. There is a section at the end of each chapter which points the reader to appropriate literature for further details. In this way, Rendall manages to describe the central issues concerning many subjects. Each of the twelve chapters (except for one on functional analysis) contains an important application to general relativity. For example, the chapter on ODEs discusses Bianchi spacetimes and the Einstein constraint equations are discussed in the chapter on elliptic equations. In the chapter on hyperbolic equations, the Einstein dust system is considered in the context of Leray hyperbolicity and Gowdy spacetimes are analysed in the section on Fuchsian methods. The book concludes with four chapters purely on applications to general relativity, namely The Cauchy problem for the Einstein equations, Global results, The Einstein-Vlasov system and The Einstein-scalar field systems. On reading this book, someone with a basic understanding of relativity could rapidly develop a picture, painted in broad brush strokes, of the main problems and tools in the area. It would be particularly useful for someone, such as a graduate student, just entering the field, or for someone who wants a general idea of the main issues. For those who want to go further, a lot more reading will be necessary but the author has sign-posted appropriate entry points to the literature throughout the book. Ultimately, this is a very technical subject and this book can only provide an overview. I believe that Alan Rendall's book is a valuable contribution to the field of mathematical relativity.

Chemistry and the Internal Combustion Engine II: Pollution Problems.

ERIC Educational Resources Information Center

Hunt, C. B.

1979-01-01

Discusses pollution problems which arise from the use of internal combustion (IC) engines in the United Kingdom (UK). The IC engine exhaust emissions, controlling IC engine pollution in the UK, and some future developments are also included. (HM)

On new physics searches with multidimensional differential shapes

NASA Astrophysics Data System (ADS)

Ferreira, Felipe; Fichet, Sylvain; Sanz, Veronica

2018-03-01

In the context of upcoming new physics searches at the LHC, we investigate the impact of multidimensional differential rates in typical LHC analyses. We discuss the properties of shape information, and argue that multidimensional rates bring limited information in the scope of a discovery, but can have a large impact on model discrimination. We also point out subtleties about systematic uncertainties cancellations and the Cauchy-Schwarz bound on interference terms.

Estimation and Control for Linear Systems with Additive Cauchy Noise

DTIC Science & Technology

2013-12-17

man & Hall, New York, 1994. [11] J. L. Speyer and W. H. Chung, Stochastic Processes, Estimation, and Control, SIAM, 2008. [12] Nassim N. Taleb ...Gaussian control algorithms. 18 4 References [1] N. N. Taleb . The Black Swan: The Impact of the Highly Improbable...the multivariable system. The estimator was then evaluated numerically for a third-order example. REFERENCES [1] N. N. Taleb , The Black Swan: The

Nonlinear Thermoelastic Effects in Surface Mechanics.

DTIC Science & Technology

1980-01-01

remaining quartic polynomial generated by det(A) .0 is presumed to not yield real roots (real characteristics) associated with elastic waves because...0253 UNCLASSIFIED NL NONINEAR THEMLOEIASTIC EFF’ECTS IN SUFC MECHANICS D T ICX2 ) J.1. PFirin General Electric Company. JUN 1 8 8 Schenectady, New York...f - Generalized analytic functions Ei Lagrangian strain components lk - Generalized Cauchy kernels, Eq. (1I) E - Young’s modulus, Pa ulk

An Orthotropic Model for Composite Materials in EPIC

DTIC Science & Technology

2014-06-06

directions, and fails the material by eliminating the deviatoric stresses when any of the plastic strain components reaches its user-supplied critical...the directions of the fibers, especially in comparison to the non-linear stress -strain curves obtained from off-axis tensile tests. A somewhat...increment in Cauchy stress ; and is the tensor of elastic moduli. In EPIC, this equation is implemented via central differences because the velocity

Optical properties and refractive indices of Gd3Al2Ga3O12:Ce3+ crystals

NASA Astrophysics Data System (ADS)

Kozlova, N. S.; Busanov, O. A.; Zabelina, E. V.; Kozlova, A. P.; Kasimova, V. M.

2016-05-01

Crystals of cerium-doped gadolinium-gallium-aluminum garnet have been grown by the Czochralski method. The transmission and reflection spectra of these crystals in the wavelength range of 250-800 nm have been obtained by optical spectroscopy. Refractive indices are calculated based on the measured Brewster angles, the experimental results are approximated using the Cauchy equation, and a dispersion dependence is obtained.

The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results

PubMed Central

Seppecher, P.

2015-01-01

In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces. PMID:26730215

"Que vienen los lobos!" (Breve nota sobre el plural de los apellidos) ("May The Wolves Come:" [A Brief Note on the Plural of Surnames])

ERIC Educational Resources Information Center

Vivaldi, Gonzalo Martin

1975-01-01

This article discusses the problems that arise with the formation of plural forms of surnames in Spanish, problems both with morphology and with ambiguity. Suggestions as to how to lessen problems are made. (Text is in Spanish.) (CLK)

Synovial sarcoma of the neck associated with previous head and neck radiation therapy

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

Mischler, N.E.; Chuprevich, T.; Tormey, D.C.

1978-08-01

Synovial sarcoma is a rare neoplasm that uncommonly arises in the neck. Fourteen years after facial and neck radiation therapy for acne, synovial sarcoma of the neck developed in a young man. Possible radiation-induced benign and malignant neoplasms that arise in the head and neck region, either of thyroid or extrathyroid origin, remain a continuing medical problem.

Obesity: a problem of darwinian proportions?

PubMed

Watnick, Suzanne

2006-10-01

Obesity has been described as an abnormality arising from the evolution of man, who becomes fat during the time of perpetual plenty. From the perspective of "Darwinian Medicine," if famine is avoided, obesity will prevail. Problems regarding obesity arise within many disciplines, including socioeconomic environments, the educational system, science, law, and government. This article will discuss various ethical aspects of several disciplines regarding obesity, with a focus on scientific inquiry. We will discuss this within the categories: (1) chronic kidney disease predialysis, (2) dialysis, and (3) renal transplantation. This article aims to help nephrologists and their patients navigate through the ethical aspects of obesity and chronic kidney disease.

Aspects of black holes and the information paradox

NASA Astrophysics Data System (ADS)

Levi, Thomas S.

In this thesis we explore various aspects of string theory and the black hole information paradox. The thesis is divided into two parts. In the first part, we examine black holes in the context of the AdS/CFT correspondence and holography. We show how the correspondence is formulated in a time dependent background when multiple vacua exist. We explain how particle production and Hawking radiation is expressed in the dual field theory. We then investigate the rotating BTZ black hole using AdS/CFT. We show how to compute field theory correlation functions in two ways. The first involves integration over the region up to and including the inner (Cauchy) horizon. The second integrates over only the region outside the outer (event) horizon, but over a contour in the complex time plane. We then show that the inner horizon is unstable to generic perturbations and how this instability can be detected in the dual field theory. We conjecture that signatures in the complex time plane might encode information behind the horizon in the dual field theory. In the second part of the thesis we turn to the "fuzzball" conjecture where black holes are seen as emergent phenomena that arise from a coarse-graining over many smooth microstates. We present a solution generating technique for general three-charge spacetimes that are candidate microstates for finite area black holes and rings. We show these microstates have the same asymptotic behavior as black holes or black rings, but in the interior are characterized by an intricate geometry of 2-cycles we call spacetime foam.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

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

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Closed solutions to a differential-difference equation and an associated plate solidification problem.

PubMed

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

POEMS in Newton's Aerodynamic Frustum

ERIC Educational Resources Information Center

Sampedro, Jaime Cruz; Tetlalmatzi-Montiel, Margarita

2010-01-01

The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article we present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton's aerodynamical problem for the frustum of a cone. Then, we exhibit a parallel…

How Do They Solve It? An Insight into the Learner's Approach to the Mechanism of Physics Problem Solving

ERIC Educational Resources Information Center

Hegde, Balasubrahmanya; Meera, B. N.

2012-01-01

A perceived difficulty is associated with physics problem solving from a learner's viewpoint, arising out of a multitude of reasons. In this paper, we have examined the microstructure of students' thought processes during physics problem solving by combining the analysis of responses to multiple-choice questions and semistructured student…

Corrosion control and disinfection studies in spacecraft water systems. [considering Saturn 5 orbital workshop

NASA Technical Reports Server (NTRS)

Shea, T. G.

1974-01-01

Disinfection and corrosion control in the water systems of the Saturn 5 Orbital Workshop Program are considered. Within this framework, the problem areas of concern are classified into four general areas: disinfection; corrosion; membrane-associated problems of disinfectant uptake and diffusion; and taste and odor problems arising from membrane-disinfectant interaction.

Psychotherapy with Older Dying Persons.

ERIC Educational Resources Information Center

Dye, Carol J.

Psychotherapy with older dying patients can lead to problems of countertransference for the clinician. Working with dying patients requires flexibility to adapt basic therapeutics to the institutional setting. Goals of psychotherapy must be reconceptualized for dying clients. The problems of countertransference arise because clinicians themselves…

Spelling: A Visual Skill.

ERIC Educational Resources Information Center

Hendrickson, Homer

1988-01-01

Spelling problems arise due to problems with form discrimination and inadequate visualization. A child's sequence of visual development involves learning motor control and coordination, with vision directing and monitoring the movements; learning visual comparison of size, shape, directionality, and solidity; developing visual memory or recall;…

Inequalities, assessment and computer algebra

NASA Astrophysics Data System (ADS)

Sangwin, Christopher J.

2015-01-01

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

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

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

Complexity seems to open a way towards a new Aristotelian-Thomistic ontology.

PubMed

Strumia, Alberto

2007-01-01

Today's sciences seem to converge all towards very similar foundational questions. Such claims, both of epistemological and ontological nature, seem to rediscover, in a new fashion some of the most relevant topics of ancient Greek and Mediaeval philosophy of nature, logic and metaphysics, such as the problem of the relationship between the whole and its parts (non redictionism), the problems of the paradoxes arising from the attempt to conceive the entity like an univocal concept (analogy and analogia entis), the problem of the mind-body relationship and that of an adequate cognitive theory (abstraction and immaterial nature of the mind), the complexity of some physical, chemical and biological systems and global properties arising from information (matter-form theory), etc. Medicine too is involved in some of such relevant questions and cannot avoid to take them into a special account.

On Pfaffian Random Point Fields

NASA Astrophysics Data System (ADS)

Kargin, V.

2014-02-01

We study Pfaffian random point fields by using the Moore-Dyson quaternion determinants. First, we give sufficient conditions that ensure that a self-dual quaternion kernel defines a valid random point field, and then we prove a CLT for Pfaffian point fields. The proofs are based on a new quaternion extension of the Cauchy-Binet determinantal identity. In addition, we derive the Fredholm determinantal formulas for the Pfaffian point fields which use the quaternion determinant.

Identifying Unique Ethical Challenges of Indigenous Field-Workers: A Commentary on Alexander and Richman's "Ethical Dilemmas in Evaluations Using Indigenous Research Workers"

ERIC Educational Resources Information Center

Smith, Nick L.

2008-01-01

In contrast with nonindigenous workers, to what extent do unique ethical problems arise when indigenous field-workers participate in field studies? Three aspects of study design and operation are considered: data integrity issues, risk issues, and protection issues. Although many of the data quality issues that arise with the use of indigenous…

A Computer Program for Solving a Set of Conditional Maximum Likelihood Equations Arising in the Rasch Model for Questionnaires.

ERIC Educational Resources Information Center

Andersen, Erling B.

A computer program for solving the conditional likelihood equations arising in the Rasch model for questionnaires is described. The estimation method and the computational problems involved are described in a previous research report by Andersen, but a summary of those results are given in two sections of this paper. A working example is also…

Solving LP Relaxations of Large-Scale Precedence Constrained Problems

NASA Astrophysics Data System (ADS)

Bienstock, Daniel; Zuckerberg, Mark

We describe new algorithms for solving linear programming relaxations of very large precedence constrained production scheduling problems. We present theory that motivates a new set of algorithmic ideas that can be employed on a wide range of problems; on data sets arising in the mining industry our algorithms prove effective on problems with many millions of variables and constraints, obtaining provably optimal solutions in a few minutes of computation.

NASA Aviation Safety Reporting System

NASA Technical Reports Server (NTRS)

1980-01-01

Problems in briefing of relief by air traffic controllers are discussed, including problems that arise when duty positions are changed by controllers. Altimeter reading and setting errors as factors in aviation safety are discussed, including problems associated with altitude-including instruments. A sample of reports from pilots and controllers is included, covering the topics of ATIS broadcasts an clearance readback problems. A selection of Alert Bulletins, with their responses, is included.

Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics

NASA Astrophysics Data System (ADS)

Arsenault, Louis-François; Neuberg, Richard; Hannah, Lauren A.; Millis, Andrew J.

2017-11-01

We present a supervised machine learning approach to the inversion of Fredholm integrals of the first kind as they arise, for example, in the analytic continuation problem of quantum many-body physics. The approach provides a natural regularization for the ill-conditioned inverse of the Fredholm kernel, as well as an efficient and stable treatment of constraints. The key observation is that the stability of the forward problem permits the construction of a large database of outputs for physically meaningful inputs. Applying machine learning to this database generates a regression function of controlled complexity, which returns approximate solutions for previously unseen inputs; the approximate solutions are then projected onto the subspace of functions satisfying relevant constraints. Under standard error metrics the method performs as well or better than the Maximum Entropy method for low input noise and is substantially more robust to increased input noise. We suggest that the methodology will be similarly effective for other problems involving a formally ill-conditioned inversion of an integral operator, provided that the forward problem can be efficiently solved.

How Seductive Are Decorative Elements in Learning Materials?

ERIC Educational Resources Information Center

Rey, Gunter Daniel

2012-01-01

The seductive detail effect arises when people learn more deeply from a multimedia presentation when interesting but irrelevant adjuncts are excluded. However, previous studies about this effect are rather inconclusive and contained various methodical problems. The recent experiment attempted to overcome these methodical problems. Undergraduate…

Phantom Effects in Multilevel Compositional Analysis: Problems and Solutions

ERIC Educational Resources Information Center

Pokropek, Artur

2015-01-01

This article combines statistical and applied research perspective showing problems that might arise when measurement error in multilevel compositional effects analysis is ignored. This article focuses on data where independent variables are constructed measures. Simulation studies are conducted evaluating methods that could overcome the…

The method of lines in analyzing solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.

1990-01-01

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

A general multiscale framework for the emergent effective elastodynamics of metamaterials

NASA Astrophysics Data System (ADS)

Sridhar, A.; Kouznetsova, V. G.; Geers, M. G. D.

2018-02-01

This paper presents a general multiscale framework towards the computation of the emergent effective elastodynamics of heterogeneous materials, to be applied for the analysis of acoustic metamaterials and phononic crystals. The generality of the framework is exemplified by two key characteristics. First, the underlying formalism relies on the Floquet-Bloch theorem to derive a robust definition of scales and scale separation. Second, unlike most homogenization approaches that rely on a classical volume average, a generalized homogenization operator is defined with respect to a family of particular projection functions. This yields a generalized macro-scale continuum, instead of the classical Cauchy continuum. This enables (in a micromorphic sense) to homogenize the rich dispersive behavior resulting from both Bragg scattering and local resonance. For an arbitrary unit cell, the homogenization projection functions are constructed using the Floquet-Bloch eigenvectors obtained in the desired frequency regime at select high symmetry points, which effectively resolves the emergent phenomena dominating that regime. Furthermore, a generalized Hill-Mandel condition is proposed that ensures power consistency between the homogenized and full-scale model. A high-order spatio-temporal gradient expansion is used to localize the multiscale problem leading to a series of recursive unit cell problems giving the appropriate micro-mechanical corrections. The developed multiscale method is validated against standard numerical Bloch analysis of the dispersion spectra of example unit cells encompassing multiple high-order branches generated by local resonance and/or Bragg scattering.

Transformational leadership can improve workforce competencies.

PubMed

Thompson, Juliana

2012-03-01

Staffing problems can arise because of poor delegation skills or a failure by leaders to respond appropriately to economic factors and patient demographics. Training dilemmas, meanwhile, can arise because of managers' confusion about what constitutes 'training' and what constitutes 'education', and where responsibility of provision lies, with the consequence that they neglect these activities. This article uses Kouzes and Posner's (2009) transformational leadership model to show how managers can respond. Leaders who challenge budgets, consider new ways of working and engage effectively with the workforce can improve productivity and care, while those who invest in appropriate learning will have a highly trained workforce. The author explains how integration of leadership roles and management functions can lead to innovative problem solving.

Euthanasia from the perspective of hospice care.

PubMed

Gillett, G

1994-01-01

The hospice believes in the concept of a gentle and harmonious death. In most hospice settings there is also a rejection of active euthanasia. This set of two apparently conflicting principles can be defended on the basis of two arguments. The first is that doctors should not foster the intent to kill as part of their moral and clinical character. This allows proper sensitivity to the complex and difficult situation that arises in many of the most difficult terminal care situations. The second argument turns on the seduction of technological solutions to human problems and the slippery slope that may arise in the presence of a quick and convenient way of dealing with problems of death and dying.

Solving Integer Programs from Dependence and Synchronization Problems

DTIC Science & Technology

1993-03-01

DEFF.NSNE Solving Integer Programs from Dependence and Synchronization Problems Jaspal Subhlok March 1993 CMU-CS-93-130 School of Computer ScienceT IC...method Is an exact and efficient way of solving integer programming problems arising in dependence and synchronization analysis of parallel programs...7/;- p Keywords: Exact dependence tesing, integer programming. parallelilzng compilers, parallel program analysis, synchronization analysis Solving

The King and Prisoner Puzzle: A Way of Introducing the Components of Logical Structures

ERIC Educational Resources Information Center

Roh, Kyeong Hah; Lee, Yong Hah; Tanner, Austin

2016-01-01

The purpose of this paper is to provide issues related to student understanding of logical components that arise when solving word problems. We designed a logic problem called the King and Prisoner Puzzle--a linguistically simple, yet logically challenging problem. In this paper, we describe various student solutions to the puzzle and discuss the…

The application of NASTRAN at Sperry Univac Holland. [analysis of engineering, modelling, and use of program system

NASA Technical Reports Server (NTRS)

Koopmans, G.

1973-01-01

Very divergent problems arising with different calculations indicate that NASTRAN is not always accessible for common use. Problems with engineering, modelling, and use of the program system are analysed and a way of solution is outlined. Related to this, some supplementary modifications are made at Sperry Univac Holland to facilitate the program for the less skilled user. The implementation of a new element also gives an insight into the use of NASTRAN at Sperry Univac Holland. As the users of Univac computers are from very different kinds of industries like shipbuilders, petrochemical industries, and building industries, the variety of problems coming from these users is very large. This variety results in experience not with one special kind of calculation nor one special kind of construction, but with a wide area of problems arising in the use of NASTRAN. These problems can roughly be divided into three different groups: (1) recognition of what is to be calculated and how, (2) construction of a model, and (3) handling the NASTRAN program. These are the basic problems for every less skilled user of NASTRAN and the Application/Research Department of Sperry Univac has to give reasonable answers to these questions.

[Errors in wound management].

PubMed

Filipović, Marinko; Novinscak, Tomislav

2014-10-01

Chronic ulcers have adverse effects on the patient quality of life and productivity, thus posing financial burden upon the healthcare system. Chronic wound healing is a complex process resulting from the interaction of the patient general health status, wound related factors, medical personnel skill and competence, and therapy related products. In clinical practice, considerable improvement has been made in the treatment of chronic wounds, which is evident in the reduced rate of the severe forms of chronic wounds in outpatient clinics. However, in spite of all the modern approaches, efforts invested by medical personnel and agents available for wound care, numerous problems are still encountered in daily practice. Most frequently, the problems arise from inappropriate education, of young personnel in particular, absence of multidisciplinary approach, and inadequate communication among the personnel directly involved in wound treatment. To perceive them more clearly, the potential problems or complications in the management of chronic wounds can be classified into the following groups: problems mostly related to the use of wound coverage and other etiology related specificities of wound treatment; problems related to incompatibility of the agents used in wound treatment; and problems arising from failure to ensure aseptic and antiseptic performance conditions.

A temps nouveaux, solutions nouvelles: quelques propositions (New Times, New Solutions: Some Proposals).

ERIC Educational Resources Information Center

Capelle, Guy

1983-01-01

Serious problems in education in Latin America arising from political, economic, and social change periodically put in question the status, objectives, and manner of French second-language instruction. A number of solutions to general and specific pedagogical problems are proposed. (MSE)

Understanding Gender-Based Wage Discrimination: Legal Interpretation and Trends of Pay Equity in Higher Education.

ERIC Educational Resources Information Center

Luna, Gaye

1990-01-01

Traces the history of laws and litigation concerning pay equity issues, also referred to as wage equity and comparable worth. Suggests that universities and colleges identify possible problems and take voluntary corrective measures before pay-equity problems arise. (MLF)

Reflective Questions, Self-Questioning and Managing Professionally Situated Practice

ERIC Educational Resources Information Center

Malthouse, Richard; Watts, Mike; Roffey-Barentsen, Jodi

2015-01-01

Reflective self-questioning arises within the workplace when people are confronted with professional problems and situations. This paper focuses on reflective and "situated reflective" questions in terms of self-questioning and professional workplace problem solving. In our view, the situational context, entailed by the setting, social…

Financial derivative pricing under probability operator via Esscher transfomation

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

Achi, Godswill U., E-mail: achigods@yahoo.com

2014-10-24

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula usingmore » the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.« less

Bifurcation of elastic solids with sliding interfaces

NASA Astrophysics Data System (ADS)

Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.

2018-01-01

Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.

Not Normal: the uncertainties of scientific measurements

NASA Astrophysics Data System (ADS)

Bailey, David C.

2017-01-01

Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties were studied by analysing 41 000 measurements of 3200 quantities from medicine, nuclear and particle physics, and interlaboratory comparisons ranging from chemistry to toxicology. Outliers are common, with 5σ disagreements up to five orders of magnitude more frequent than naively expected. Uncertainty-normalized differences between multiple measurements of the same quantity are consistent with heavy-tailed Student's t-distributions that are often almost Cauchy, far from a Gaussian Normal bell curve. Medical research uncertainties are generally as well evaluated as those in physics, but physics uncertainty improves more rapidly, making feasible simple significance criteria such as the 5σ discovery convention in particle physics. Contributions to measurement uncertainty from mistakes and unknown problems are not completely unpredictable. Such errors appear to have power-law distributions consistent with how designed complex systems fail, and how unknown systematic errors are constrained by researchers. This better understanding may help improve analysis and meta-analysis of data, and help scientists and the public have more realistic expectations of what scientific results imply.

Not Normal: the uncertainties of scientific measurements

PubMed Central

2017-01-01

Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties were studied by analysing 41 000 measurements of 3200 quantities from medicine, nuclear and particle physics, and interlaboratory comparisons ranging from chemistry to toxicology. Outliers are common, with 5σ disagreements up to five orders of magnitude more frequent than naively expected. Uncertainty-normalized differences between multiple measurements of the same quantity are consistent with heavy-tailed Student’s t-distributions that are often almost Cauchy, far from a Gaussian Normal bell curve. Medical research uncertainties are generally as well evaluated as those in physics, but physics uncertainty improves more rapidly, making feasible simple significance criteria such as the 5σ discovery convention in particle physics. Contributions to measurement uncertainty from mistakes and unknown problems are not completely unpredictable. Such errors appear to have power-law distributions consistent with how designed complex systems fail, and how unknown systematic errors are constrained by researchers. This better understanding may help improve analysis and meta-analysis of data, and help scientists and the public have more realistic expectations of what scientific results imply. PMID:28280557

Hyperbolicity of the Nonlinear Models of Maxwell's Equations

NASA Astrophysics Data System (ADS)

Serre, Denis

. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Sensitivity Analysis for Probabilistic Neural Network Structure Reduction.

PubMed

Kowalski, Piotr A; Kusy, Maciej

2018-05-01

In this paper, we propose the use of local sensitivity analysis (LSA) for the structure simplification of the probabilistic neural network (PNN). Three algorithms are introduced. The first algorithm applies LSA to the PNN input layer reduction by selecting significant features of input patterns. The second algorithm utilizes LSA to remove redundant pattern neurons of the network. The third algorithm combines the proposed two and constitutes the solution of how they can work together. PNN with a product kernel estimator is used, where each multiplicand computes a one-dimensional Cauchy function. Therefore, the smoothing parameter is separately calculated for each dimension by means of the plug-in method. The classification qualities of the reduced and full structure PNN are compared. Furthermore, we evaluate the performance of PNN, for which global sensitivity analysis (GSA) and the common reduction methods are applied, both in the input layer and the pattern layer. The models are tested on the classification problems of eight repository data sets. A 10-fold cross validation procedure is used to determine the prediction ability of the networks. Based on the obtained results, it is shown that the LSA can be used as an alternative PNN reduction approach.

Canonical Gravity, Non-Inertial Frames, Relativistic Metrology and Dark Matter

NASA Astrophysics Data System (ADS)

Lusanna, Luca

Clock synchronization leads to the definition of instantaneous 3-spaces (to be used as Cauchy surfaces) in non-inertial frames, the only ones allowed by the equivalence principle. ADM canonical tetrad gravity in asymptotically Minkowskian space-times can be described in this framework. This allows to find the York canonical basis in which the inertial (gauge) and tidal (physical) degrees of freedom of the gravitational field can be identified. A Post-Minkowskian linearization with respect to the asymptotic Minkowski metric (asymptotic background) allows to solve the Dirac constraints in non-harmonic 3-orthogonal gauges and to find non-harmonic TT gravitational waves. The inertial gauge variable York time (the trace of the extrinsic curvature of the 3-space) describes the general relativistic freedom in clock synchronization. After a digression on the gauge problem in general relativity and its connection with relativistic metrology, it is shown that dark matter, whose experimental signatures are the rotation curves and the mass of galaxies, may be described (at least partially) as an inertial relativistic effect (absent in Newtonian gravity) connected with the York time, namely with the non-Euclidean nature of 3-spaces as 3-sub-manifolds of space-time.

Expanding the scope of health information systems. Challenges and developments.

PubMed

Kuhn, K A; Wurst, S H R; Bott, O J; Giuse, D A

2006-01-01

To identify current challenges and developments in health information systems. Reports on HIS, eHealth and process support were analyzed, core problems and challenges were identified. Health information systems are extending their scope towards regional networks and health IT infrastructures. Integration, interoperability and interaction design are still today's core problems. Additional problems arise through the integration of genetic information into the health care process. There are noticeable trends towards solutions for these problems.

Can ethnography save the life of medical ethics?

PubMed

Hoffmaster, B

1992-12-01

Since its inception contemporary medical ethics has been regarded by many of its practitioners as 'applied ethics', that is, the application of philosophical theories to the moral problems that arise in health care. This 'applied ethics' model of medical ethics is, however, beset with internal and external difficulties. The internal difficulties point out that the model is intrinsically flawed. The external difficulties arise because the model does not fit work in the field. Indeed, the strengths of that work are its highly nuanced, particularized analyses of cases and issues and its appreciation of the circumstances and contexts that generate and structure these cases and issues. A shift away from a theory-driven 'applied ethics' to a more situational, contextual approach to medical ethics opens the way for ethnographic studies of moral problems in health care as well as a conception of moral theory that is more responsive to the empirical dimensions of those problems.

Communicating Scientific Findings to Lawyers, Policy-Makers, and the Public (Invited)

NASA Astrophysics Data System (ADS)

Thompson, W.; Velsko, S. P.

2013-12-01

This presentation will summarize the authors' collaborative research on inferential errors, bias and communication difficulties that have arisen in the area of WMD forensics. This research involves analysis of problems that have arisen in past national security investigations, interviews with scientists from various disciplines whose work has been used in WMD investigations, interviews with policy-makers, and psychological studies of lay understanding of forensic evidence. Implications of this research for scientists involved in nuclear explosion monitoring will be discussed. Among the issues covered will be: - Potential incompatibilities between the questions policy makers pose and the answers that experts can provide. - Common misunderstandings of scientific and statistical data. - Advantages and disadvantages of various methods for describing and characterizing the strength of scientific findings. - Problems that can arise from excessive hedging or, alternatively, insufficient qualification of scientific conclusions. - Problems that can arise from melding scientific and non-scientific evidence in forensic assessments.

Black holes in loop quantum gravity: the complete space-time.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2008-10-17

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Nonlinear modeling of crystal system transition of black phosphorus using continuum-DFT model.

PubMed

Setoodeh, A R; Farahmand, H

2018-01-24

In this paper, the nonlinear behavior of black phosphorus crystals is investigated in tandem with dispersion-corrected density functional theory (DFT-D) analysis under uniaxial loadings. From the identified anisotropic behavior of black phosphorus due to its morphological anisotropy, a hyperelastic anisotropic (HA) model named continuum-DFT is established to predict the nonlinear behavior of the material. In this respect, uniaxial Cauchy stresses are employed on both the DFT-D and HA models along the zig-zag and armchair directions. Simultaneously, the transition of the crystal system is recognized at about 4.5 GPa of the applied uniaxial tensile stress along the zig-zag direction on the DFT-D simulation in the nonlinear region. In order to develop the nonlinear continuum model, unknown constants are surveyed with the optimized least square technique. In this regard, the continuum model is obtained to reproduce the Cauchy stress-stretch and density of strain-stretch results of the DFT-D simulation. Consequently, the modified HA model is introduced to characterize the nonlinear behavior of black phosphorus along the zig-zag direction. More importantly, the specific transition of the crystal system is successfully predicted in the new modified continuum-DFT model. The results reveal that the multiscale continuum-DFT model is well defined to replicate the nonlinear behavior of black phosphorus along the zig-zag and armchair directions.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

NASA Astrophysics Data System (ADS)

Miyata, Y.; Suzuki, T.; Takechi, M.; Urano, H.; Ide, S.

2015-07-01

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2010-01-01

This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.

Ab-initio study of C15-type Laves phase superconductor LaRu2

NASA Astrophysics Data System (ADS)

Kholil, Md. Ibrahim; Islam, Md. Shahinur; Rahman, Md. Atikur

2017-01-01

Structural, elastic, electronic, optical, thermodynamic, and superconducting properties of the Laves phase superconductor LaRu2 with Tc 1.63 K were investigated using the first-principles calculations for the first time. The corresponding evaluated structural parameters are in good agreement with the available theoretical values. The different elastic properties like as, elastic constants, bulk modulus B, shear modulus G, Young's modulus E, and Poisson ratio ν were calculated using the Voigt-Reuss-Hill approximation. The ductility nature appears in both values of Cauchy pressure and Pugh's ratio. The band structure and Cauchy pressure shows that the material behaves metallic nature. The calculated total density of state is 6.80 (electrons/eV) of LaRu2. The optical properties such as reflectivity, absorption spectrum, refractive index, dielectric function, conductivity, and energy loss spectrum are also calculated. The photoconductivity reveals the metallic nature of LaRu2 and absorption coefficient is good in the infrared region. The evaluated density and Debye temperature are 9.55 gm/cm3 and 110.51 K, respectively. In addition, the study of thermodynamic properties like as minimum thermal conductivity, melting temperature, and Dulong-Petit limit are 0.26 (Wm-1 K-1), 1,471.65 K, and 74.80 (J/mole K), respectively. Finally, the investigated electron-phonon coupling constant is 0.66 of LaRu2 superconductor.

[Current problems arising from not having biosafety level 4 laboratories in Japan--qualitative study of infectious disease experts].

PubMed

Yamamoto, Yuko; Horiguchi, Itsuko; Marui, Eiji

2009-09-01

No public consensus exists yet on handling Biosafety Level 4 agents and no laboratory is operational at BSL4 in Japan. A discussion that includes neighboring residents and experts should be initiated to communicate risks. In this article, we present the current situation and prioritize problems we presently face. A three-stage Delphi survey was conducted. The subjects were twenty-two persons with extensive experience and knowledge of infectious diseases. Seven projections and issues were made with regard to the problems arising from the lack of an operational BSL4 laboratory. These were tabulated by the KJ method. The top seven projections were scored, such that the top received 7 points and the last received 1 point. A total of 51 projections were obtained for the first part of the survey, 39 for the second, and 29 for the last. The projection with the highest score was that it is impossible to cope with newly emerging infectious diseases. The second was that complete diagnoses are impossible without a BSL4 laboratory. All projections and issues were divided into the following four main groups: issues for researchers and laboratory staff, clinical practice and research on BSL4 agents, domestic and global security, and Japan's international position. We clarified possible problem arising from not having BSL4 laboratories in Japan. The identification of projections by the Delphi survey in this study should be considered as one of many attempts to develop effective risk communication strategies.

Addressing Cultural Diversity: Effects of a Problem-Based Intercultural Learning Unit

ERIC Educational Resources Information Center

Busse, Vera; Krause, Ulrike-Marie

2015-01-01

This article explores to what extent a problem-based learning unit in combination with cooperative learning and affectively oriented teaching methods facilitates intercultural learning. As part of the study, students reflected on critical incidents, which display misunderstandings or conflicts that arise as a result of cultural differences. In…

A Separate Reality: The Problem of Uncooperative Experiments.

ERIC Educational Resources Information Center

Lersten, Ken

The problem of the uncooperative experiment arises with the use of human subjects. Evidence shows that typical volunteer subjects have the following characteristics: better education, higher paying jobs, greater need for approval, lower authoritarianism, higher I.Q. score, and better adjustment to personal questions than nonvolunteers. Data also…

Introducing Mathematics to Information Problem-Solving Tasks: Surface or Substance?

ERIC Educational Resources Information Center

Erickson, Ander

2017-01-01

This study employs a cross-case analysis in order to explore the demands and opportunities that arise when information problem-solving tasks are introduced into college mathematics classes. Professors at three universities collaborated with me to develop statistics-related activities that required students to engage in research outside the…

Classroom Crisis Intervention through Contracting: A Moral Development Model.

ERIC Educational Resources Information Center

Smaby, Marlowe H.; Tamminen, Armas W.

1981-01-01

A counselor can arbitrate problem situations using a systematic approach to classroom intervention which includes meetings with the teacher and students. This crisis intervention model based on moral development can be more effective than reliance on guidance activities disconnected from the actual classroom settings where the problems arise.…

Lexical Frames and Reported Speech

ERIC Educational Resources Information Center

Williams, Howard

2004-01-01

This paper addresses a problem of lexical choice that arises for ESL/EFL learners in the writing of research papers, critiques, interview reports, or any other sort of discourse that requires source attribution. The problem falls naturally into two parts. One part concerns the general lack of linguistic resources typically available (for various…

RACIAL IMBALANCE AND EDUCATIONAL PLANNING.

ERIC Educational Resources Information Center

CONROY, VINCENT F.

HARVARD'S ADMINISTRATIVE CAREER PROGRAM FACED THE GROWING PROBLEM OF NEGRO ENROLLMENT IN THE PUBLIC SCHOOLS. NOTING THE FREQUENCY AND INTENSITY WITH WHICH THE PROBLEM WAS ARISING AT THE NATIONAL LEVEL, A GROUP OF LAWYERS AND EDUCATORS CONVENED TO WORK OUT THE LEGAL ASPECTS OF SCHOOL INTEGRATION. FUNDS FROM THE FORD FOUNDATION INITIATED THE…

Polyomino Problems to Confuse Computers

ERIC Educational Resources Information Center

Coffin, Stewart

2009-01-01

Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…

Digital Maps, Matrices and Computer Algebra

ERIC Educational Resources Information Center

Knight, D. G.

2005-01-01

The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

Development of a process control computer device for the adaptation of flexible wind tunnel walls

NASA Technical Reports Server (NTRS)

Barg, J.

1982-01-01

In wind tunnel tests, the problems arise of determining the wall pressure distribution, calculating the wall contour, and controlling adjustment of the walls. This report shows how these problems have been solved for the high speed wind tunnel of the Technical University of Berlin.

CONGRESS ON SCIENCE TEACHING AND ECONOMIC GROWTH.

ERIC Educational Resources Information Center

Inter-Union Commission on the Teaching of Science, Paris (France).

REPORTED ARE THE ACTIVITIES OF THE CONGRESS ORGANIZED BY THE INTER-UNION COMMISSION ON SCIENCE TEACHING (CEIS) OF THE INTERNATIONAL COUNCIL OF SCIENTIFIC UNIONS (ICSU). STUDIED WERE PROBLEMS ARISING IN SEVERAL BRANCHES OF KNOWLEDGE DUE TO BOTH INCREASED NUMBERS OF STUDENTS AND SHORTAGE OF TEACHERS. OF PARTICULAR INTEREST WERE THE PROBLEMS OF…

IMPACTS OF MATERIAL SUBSTITUTION IN AUTOMOBILE MANUFACTURE ON RESOURCE RECOVERY. VOLUME II. APPENDICES A-E

EPA Science Inventory

Probable changes in the mix of materials used to manufacture automobiles were examined to determine if economic or technical problems in recycling could arise such that the 'abandoned automobile problem' would be resurrected. Future trends in materials composition of the automobi...

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

Ethical considerations in revision rhinoplasty.

PubMed

Wayne, Ivan

2012-08-01

The problems that arise when reviewing another surgeon's work, the financial aspects of revision surgery, and the controversies that present in marketing and advertising will be explored. The technological advances of computer imaging and the Internet have introduced new problems that require our additional consideration. Copyright © 2012 by Thieme Medical Publishers, Inc.

The legacy of Charles Marlatt and efforts to limit plant pest invasions

Treesearch

Andrew M. Liebhold; Robert L. Griffin

2016-01-01

The problem of invasions by non-native plant pests has come to dominate the field of applied entomology. Most of the damaging insect pests of agriculture and forestry are non-native (Sailer 1978, Aukema et al. 2010) and this is a problem being faced around the world. This problem did not arise overnight; instead, there has been a steady accumulation of non-native...

Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

NASA Technical Reports Server (NTRS)

Mook, D. J.; Lew, Jiann-Shiun

1991-01-01

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

Program Aids Visualization Of Data

NASA Technical Reports Server (NTRS)

Truong, L. V.

1995-01-01

Living Color Frame System (LCFS) computer program developed to solve some problems that arise in connection with generation of real-time graphical displays of numerical data and of statuses of systems. Need for program like LCFS arises because computer graphics often applied for better understanding and interpretation of data under observation and these graphics become more complicated when animation required during run time. Eliminates need for custom graphical-display software for application programs. Written in Turbo C++.

Environmental Hazards of Nuclear Wastes

ERIC Educational Resources Information Center

Micklin, Philip P.

1974-01-01

Present methods for storage of radioactive wastes produced at nuclear power facilities are described. Problems arising from present waste management are discussed and potential solutions explored. (JP)

Stochastic species abundance models involving special copulas

NASA Astrophysics Data System (ADS)

Huillet, Thierry E.

2018-01-01

Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall-Olkin copula arises in a species extinction model with catastrophe. In a second one, a quasi-copula problem arises in a flagged species abundance model. In a third model, we study completely random species abundance models in the hypercube as those, not of product type, with uniform margins and singular. These can be understood from a singular copula supported by an inflated simplex. An exchangeable singular Dirichlet copula is also introduced, together with its induced completely random species abundance vector.

[Specific problems posed by carbohydrate utilization in the rainbow trout].

PubMed

Bergot, F

1979-01-01

Carbohydrate incorporation in trout diets arises problems both at digestive and metabolic levels. Digestive utilization of carbohydrate closely depends on their molecular weight. In addition, in the case of complex carbohydrates (starches), different factors such as the level of incorporation, the amount consumed and the physical state of starch influence the digestibility. The measurement of digestibility in itself is confronted with methodological difficulties. The way the feces are collected can affect the digestion coefficient. Dietary carbohydrates actually serve as a source of energy. Nevertheless, above a certain level in the diet, intolerance phenomena may appear. The question that arises now is to establish the optimal part that carbohydrates can take in the metabolizable energy of a given diet.

Optimization-based mesh correction with volume and convexity constraints

DOE PAGES

D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...

2016-02-24

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimizationmore » problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less

Anomalous Dynamical Behavior of Freestanding Graphene Membranes

NASA Astrophysics Data System (ADS)

Ackerman, M. L.; Kumar, P.; Neek-Amal, M.; Thibado, P. M.; Peeters, F. M.; Singh, Surendra

2016-09-01

We report subnanometer, high-bandwidth measurements of the out-of-plane (vertical) motion of atoms in freestanding graphene using scanning tunneling microscopy. By tracking the vertical position over a long time period, a 1000-fold increase in the ability to measure space-time dynamics of atomically thin membranes is achieved over the current state-of-the-art imaging technologies. We observe that the vertical motion of a graphene membrane exhibits rare long-scale excursions characterized by both anomalous mean-squared displacements and Cauchy-Lorentz power law jump distributions.

The shear modulus of metastable amorphous solids with strong central and bond-bending interactions

NASA Astrophysics Data System (ADS)

Zaccone, Alessio

2009-07-01

We derive expressions for the shear modulus of deeply quenched, glassy solids, in terms of a Cauchy-Born free energy expansion around a rigid (quenched) reference state, following the approach due to Alexander (1998 Phys. Rep. 296 65). Continuum-limit explicit expressions of the shear modulus are derived starting from the microscopic Hamiltonians of central and bond-bending interactions. The applicability of the expressions to dense covalent glasses as well as colloidal glasses involving strongly attractive or adhesive bonds is discussed.

Rotating Black Holes and the Kerr Metric

NASA Astrophysics Data System (ADS)

Kerr, Roy Patrick

2008-10-01

Since it was first discovered in 1963 the Kerr metric has been used by relativists as a test-bed for conjectures on worm-holes, time travel, closed time-like loops, and the existence or otherwise of global Cauchy surfaces. More importantly, it has also used by astrophysicists to investigate the effects of collapsed objects on their local environments. These two groups of applications should not be confused. Astrophysical Black Holes are not the same as the Kruskal solution and its generalisations.

The use of Lyapunov differential inequalities for estimating the transients of mechanical systems

NASA Astrophysics Data System (ADS)

Alyshev, A. S.; Dudarenko, N. A.; Melnikov, V. G.; Melnikov, G. I.

2018-05-01

In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities.

Quantal Response: Nonparametric Modeling

DTIC Science & Technology

2017-01-01

DATES COVERED (From ‐ To) 4. TITLE AND SUBTITLE    5a. CONTRACT NUMBER  5b. GRANT NUMBER  5c. PROGRAM  ELEMENT  NUMBER 6. AUTHOR(S)    5d...creasing function as P(x) = G ( f (x) ) , where G is a monotone function such as the standard logistic, normal, or Cauchy CDF. Finite -dimensional...examples with dimension k = 5 where various colors distinguish the basis elements . Figure 3 shows logistic response estimates for these 3 basis sets

In Silico Investigation of Intracranial Blast Mitigation with Relevance to Military Traumatic Brain Injury

DTIC Science & Technology

2010-09-01

how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat...analyzing stress wave propagation, which is the main dynamic effect loading the brain tissue during a blast event. We consider two key metrics of stress ...Cauchy stress tensor, and sij ¼ σij − 13σkkδij are the compo- nents of the deviatoric stress tensor (24). Fig. 1 shows snapshots of the pressure

On several aspects and applications of the multigrid method for solving partial differential equations

NASA Technical Reports Server (NTRS)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Quantum electron levels in the field of a charged black hole

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

Dokuchaev, V. I.; Eroshenko, Yu. N., E-mail: eroshenko@ms2.inr.ac.ru

2015-12-15

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.

Another short and elementary proof of strong subadditivity of quantum entropy

NASA Astrophysics Data System (ADS)

Ruskai, Mary Beth

2007-08-01

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allows an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.

An improved method for determination of refractive index of absorbing films: A simulation study

NASA Astrophysics Data System (ADS)

Özcan, Seçkin; Coşkun, Emre; Kocahan, Özlem; Özder, Serhat

2017-02-01

In this work an improved version of the method presented by Gandhi was presented for determination of refractive index of absorbing films. In this method local maxima of consecutive interference order in transmittance spectrum are used. The method is based on the minimizing procedure leading to the determination of interference order accurately by using reasonable Cauchy parameters. It was tested on theoretically generated transmittance spectrum of absorbing film and the details of the minimization procedure were discussed.

Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Thicke, Kyle

2017-12-01

We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in χ0 by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.

The Determination of Birefringence Dispersion in Nematic Liquid Crystals by Using the S-Transform

NASA Astrophysics Data System (ADS)

Coşkun, E.; Özder, S.; Kocahan, Ö.; Köysal, O.

2007-04-01

Transmittance spectra of 5CB and ZLI-6000 coded nematic liquid crystals were acquired in the 12600-22200 cm-1 region at room temperature. The S-transform was applied to analyze the transmittance signal. Dispersion curves of the birefringence were obtained for 5CB and ZLI-6000 by this analysis and data were fitted to the Cauchy formula whereby the dispersion parameters were extracted. Results are found to be in favorable accordance with the published values.

New Old Inflation

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

Dvali, Gia

2003-10-03

We propose a new class of inflationary solutions to the standard cosmological problems (horizon, flatness, monopole,...), based on a modification of old inflation. These models do not require a potential which satisfies the normal inflationary slow-roll conditions. Our universe arises from a single tunneling event as the inflaton leaves the false vacuum. Subsequent dynamics (arising from either the oscillations of the inflaton field or thermal effects) keep a second field trapped in a false minimum, resulting in an evanescent period of inflation (with roughly 50 e-foldings) inside the bubble. This easily allows the bubble to grow sufficiently large to containmore » our present horizon volume. Reheating is accomplished when the inflaton driving the last stage of inflation rolls down to the true vacuum, and adiabatic density perturbations arise from moduli-dependent Yukawa couplings of the inflaton to matter fields. Our scenario has several robust predictions, including virtual absence of gravity waves, a possible absence of tilt in scalar perturbations, and a higher degree of non-Gaussianity than other models. It also naturally incorporates a solution to the cosmological moduli problem.« less

Quality Problem-Based Learning Experiences for Students: Design Deliberations among Teachers from Diverse Disciplines.

ERIC Educational Resources Information Center

Butler, Susan McAleenan

This qualitative study, investigating the claims, concerns, and issues arising within the design stages of problem-based learning (PBL) curriculum units, was conducted during two masters-level classes during the summer of 1999. A hermeneutic dialectic discourse among veteran teachers (who were novice PBL curriculum designers) was facilitated by…

Peculiarities of Students of Pedagogical Specialties Training in Preventive Work with Juveniles Delinquents

ERIC Educational Resources Information Center

Moskalenko, Maxim R.; Dorozhkin, Evgenij M.; Ozhiganova, Maria V.; Murzinova, Yana A.; Syssa, Daria O.

2016-01-01

The relevance of the problem under investigation is due to the high significance of preventive work with juvenile delinquents to society. The article aims to study the problems arising while developing students' competencies in professional activities for the prevention of the infringing behavior of juvenile delinquents, as well as the…

A Solution to the Mysteries of Morality

ERIC Educational Resources Information Center

DeScioli, Peter; Kurzban, Robert

2013-01-01

We propose that moral condemnation functions to guide bystanders to choose the same side as other bystanders in disputes. Humans interact in dense social networks, and this poses a problem for bystanders when conflicts arise: which side, if any, to support. Choosing sides is a difficult strategic problem because the outcome of a conflict…

Transfer of Learning Transformed

ERIC Educational Resources Information Center

Larsen-Freeman, Diane

2013-01-01

Instruction is motivated by the assumption that students can transfer their learning, or apply what they have learned in school to another setting. A common problem arises when the expected transfer does not take place, what has been referred to as the inert knowledge problem. More than an academic inconvenience, the failure to transfer is a major…

The Plasticity of Adolescent Cognitions: Data from a Novel Cognitive Bias Modification Training Task

ERIC Educational Resources Information Center

Lau, Jennifer Y. F.; Molyneaux, Emma; Telman, Machteld D.; Belli, Stefano

2011-01-01

Many adult anxiety problems emerge in adolescence. Investigating how adolescent anxiety arises and abates is critical for understanding and preventing adult psychiatric problems. Drawing threat interpretations from ambiguous material is linked to adolescent anxiety but little research has clarified the causal nature of this relationship. Work in…

Coorientational Accuracy during Regional Development of Energy Resources: Problems in Agency-Public Communication.

ERIC Educational Resources Information Center

Bowes, John E.; Stamm, Keith R.

This paper presents a progress report from a research program aimed at elucidating communication problems which arise among citizens and government agencies during the development of regional environmental policy. The eventual objective of the program is to develop a paradigm for evaluative research in communication that will provide for the…

Anger/Frustration, Task Persistence, and Conduct Problems in Childhood: A Behavioral Genetic Analysis

ERIC Educational Resources Information Center

Deater-Deckard, Kirby; Petrill, Stephen A.; Thompson, Lee A.

2007-01-01

Background: Individual differences in conduct problems arise in part from proneness to anger/frustration and poor self-regulation of behavior. However, the genetic and environmental etiology of these connections is not known. Method: Using a twin design, we examined genetic and environmental covariation underlying the well-documented correlations…

A chance constraint estimation approach to optimizing resource management under uncertainty

Treesearch

Michael Bevers

2007-01-01

Chance-constrained optimization is an important method for managing risk arising from random variations in natural resource systems, but the probabilistic formulations often pose mathematical programming problems that cannot be solved with exact methods. A heuristic estimation method for these problems is presented that combines a formulation for order statistic...

Zones of Intervention: Teaching and Learning at All Places and at All Times

ERIC Educational Resources Information Center

Taylor, Jonathan E.; McKissac, Jonathan C.

2014-01-01

This article identifies four distinct zones in which workplace problems can be addressed through education and training. These zones enable educators to address workplace learning more widely and broadly. Very often, problems arising in the workplace are dealt with through training in the classroom, but other options exist. The theoretical…

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Community-University Research Partnerships: Devising a Model for Ethical Engagement

ERIC Educational Resources Information Center

Silka, Linda; Renault-Caragianes, Paulette

2006-01-01

Profound changes taking place in communities and in universities are bringing researchers and community members new opportunities for joint research endeavors and new problems that must be resolved. In such partnerships, questions about shared decision making--about the ethics of collaboration--arise at every stage: Who decides which problems are…

Sparse Measurement Systems: Applications, Analysis, Algorithms and Design

ERIC Educational Resources Information Center

Narayanaswamy, Balakrishnan

2011-01-01

This thesis deals with "large-scale" detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred from noisy observations and where the…

The Changing Demographics of the Hispanic Family.

ERIC Educational Resources Information Center

McKay, Emily Gantz

Hispanics will become the largest United States minority population sometime early in the next century. A problem that arises with attempts to provide Hispanic people with better opportunities is the lack of adequate data on Hispanic socioeconomic status. Those data which do exist focus on problems of the individual, yet one of the greatest…

Projected Issues in the Practice of Educational Administration: The English Context.

ERIC Educational Resources Information Center

Browning, Peter

Current and incipient problems in educational administration in England can be grouped into two areas: those resulting from reorganization and those arising from social and political factors. Many problems faced by educational administrators result from school reorganization that is a result of an increase in the number of comprehensive schools.…

Focal-Plane Alignment Sensing

DTIC Science & Technology

1993-02-01

amplification induced by the inverse filter. The problem of noise amplification that arises in conventional image deblurring problems has often been... noise sensitivity, and strategies for selecting a regularization parameter have been developed. The probability of convergence to within a prescribed...Strategies in Image Deblurring .................. 12 2.2.2 CLS Parameter Selection ........................... 14 2.2.3 Wiener Parameter Selection

Damage Control: Closing Problematic Sequences in Hearing-Impaired Interaction

ERIC Educational Resources Information Center

Skelt, Louise

2007-01-01

When a problem of understanding arises for a hearing-impaired recipient in the course of a conversation, and is detected, repairing that problem is only one of several possible courses of action for participants. Another possibility is the collaborative closing of the part of the conversation which has proved problematic for understanding, to…

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

The geometry of discombinations and its applications to semi-inverse problems in anelasticity

PubMed Central

Yavari, Arash; Goriely, Alain

2014-01-01

The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid. PMID:25197257

On multiple crack identification by ultrasonic scanning

NASA Astrophysics Data System (ADS)

Brigante, M.; Sumbatyan, M. A.

2018-04-01

The present work develops an approach which reduces operator equations arising in the engineering problems to the problem of minimizing the discrepancy functional. For this minimization, an algorithm of random global search is proposed, which is allied to some genetic algorithms. The efficiency of the method is demonstrated by the solving problem of simultaneous identification of several linear cracks forming an array in an elastic medium by using the circular Ultrasonic scanning.

A bicriteria heuristic for an elective surgery scheduling problem.

PubMed

Marques, Inês; Captivo, M Eugénia; Vaz Pato, Margarida

2015-09-01

Resource rationalization and reduction of waiting lists for surgery are two main guidelines for hospital units outlined in the Portuguese National Health Plan. This work is dedicated to an elective surgery scheduling problem arising in a Lisbon public hospital. In order to increase the surgical suite's efficiency and to reduce the waiting lists for surgery, two objectives are considered: maximize surgical suite occupation and maximize the number of surgeries scheduled. This elective surgery scheduling problem consists of assigning an intervention date, an operating room and a starting time for elective surgeries selected from the hospital waiting list. Accordingly, a bicriteria surgery scheduling problem arising in the hospital under study is presented. To search for efficient solutions of the bicriteria optimization problem, the minimization of a weighted Chebyshev distance to a reference point is used. A constructive and improvement heuristic procedure specially designed to address the objectives of the problem is developed and results of computational experiments obtained with empirical data from the hospital are presented. This study shows that by using the bicriteria approach presented here it is possible to build surgical plans with very good performance levels. This method can be used within an interactive approach with the decision maker. It can also be easily adapted to other hospitals with similar scheduling conditions.

Contraceptive services for adolescents in Latin America: facts, problems and perspectives.

PubMed

Pons, J E

1999-12-01

This review presents facts about sexual and contraceptive behavior of Latin American adolescents, analyzes barriers to contraception, and summarizes present perspectives. Between 13 and 30% of Latin American adolescent women live in union before their 20th birthday and between 46 and 63% have had sexual relations. The prevalence of contraceptive use among adolescents at risk of pregnancy remains very low. The pill is the best known contraceptive method. When sexual activity becomes a permanent practice, contraceptive use increases but remains low. Barriers to contraception can be identified as: (1) arising from adolescents themselves (moral objections, alleged medical reasons, lack of confidence in adults and in the health system, promiscuity; (2) arising from the sexual partner (partner's opposition, masculine irresponsibility); (3) arising from adults (moral objections, fear of sex education, adult control and power of decision-making); (4) arising from the health system (inappropriateness of services, regulatory barriers, gender inequality); (5) arising from health professionals (medical barriers to contraceptive use, discomfort with sexual matters); (6) arising from the educational system (educational failure, teachers' reluctance); and (7) arising from other social agents (religious opposition, media ambivalent messages, fund restraints). There have been improvements in recent years, including the achievements of groups working for and with adolescents, and the support from distinguished personalities.

Customer-centered problem solving.

PubMed

Samelson, Q B

1999-11-01

If there is no single best way to attract new customers and retain current customers, there is surely an easy way to lose them: fail to solve the problems that arise in nearly every buyer-supplier relationship, or solve them in an unsatisfactory manner. Yet, all too frequently, companies do just that. Either we deny that a problem exists, we exert all our efforts to pin the blame elsewhere, or we "Band-Aid" the problem instead of fixing it, almost guaranteeing that we will face it again and again.

Robust Consumption-Investment Problem on Infinite Horizon

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

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

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

Bethe-Salpeter Eigenvalue Solver Package (BSEPACK) v0.1

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

SHAO, MEIYEU; YANG, CHAO

2017-04-25

The BSEPACK contains a set of subroutines for solving the Bethe-Salpeter Eigenvalue (BSE) problem. This type of problem arises in this study of optical excitation of nanoscale materials. The BSE problem is a structured non-Hermitian eigenvalue problem. The BSEPACK software can be used to compute all or subset of eigenpairs of a BSE Hamiltonian. It can also be used to compute the optical absorption spectrum without computing BSE eigenvalues and eigenvectors explicitly. The package makes use of the ScaLAPACK, LAPACK and BLAS.

The Soccer-Ball Problem

NASA Astrophysics Data System (ADS)

Hossenfelder, Sabine

2014-07-01

The idea that Lorentz-symmetry in momentum space could be modified but still remain observer-independent has received quite some attention in the recent years. This modified Lorentz-symmetry, which has been argued to arise in Loop Quantum Gravity, is being used as a phenomenological model to test possibly observable effects of quantum gravity. The most pressing problem in these models is the treatment of multi-particle states, known as the 'soccer-ball problem'. This article briefly reviews the problem and the status of existing solution attempts.

Cardiac emergencies and problems of the critical care patient.

PubMed

Marr, Celia M

2004-04-01

Cardiac disease and dysfunction can occur as a primary disorder(ie, with pathology situated in one or more of the cardiac structures) or can be classified as a secondary problem when it occurs in patients with another primary problem that has affected the heart either directly or indirectly. Primary cardiac problems are encountered in horses presented to emergency clinics; however,this occurs much less frequently in equine critical patients than cardiac problems arising secondary to other conditions. Nevertheless,if primary or secondary cardiac problems are not identified and addressed, they certainly contribute to the morbidity and mortality of critical care patients.

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.

Working Mothers

MedlinePlus

... valued and supported by family, friends, and coworkers. Conflicts Problems can arise if a woman does not ... is earning more money than the other. Such conflicts can strain the marriage and may make the ...

Development of a coupled expert system for the spacecraft attitude control problem

NASA Technical Reports Server (NTRS)

Kawamura, K.; Beale, G.; Schaffer, J.; Hsieh, B.-J.; Padalkar, S.; Rodriguezmoscoso, J.; Vinz, F.; Fernandez, K.

1987-01-01

A majority of the current expert systems focus on the symbolic-oriented logic and inference mechanisms of artificial intelligence (AI). Common rule-based systems employ empirical associations and are not well suited to deal with problems often arising in engineering. Described is a prototype expert system which combines both symbolic and numeric computing. The expert system's configuration is presented and its application to a spacecraft attitude control problem is discussed.

Evaluation of emerging factors blocking filtration of high-adjunct-ratio wort.

PubMed

Ma, Ting; Zhu, Linjiang; Zheng, Feiyun; Li, Yongxian; Li, Qi

2014-08-20

Corn starch has become a common adjunct for beer brewing in Chinese breweries. However, with increasing ratio of corn starch, problems like poor wort filtration performance arise, which will decrease production capacity of breweries. To solve this problem, factors affecting wort filtration were evaluated, such as the size of corn starch particle, special yellow floats formed during liquefaction of corn starch, and residual substance after liquefaction. The effects of different enzyme preparations including β-amylase and β-glucanase on filtration rate were also evaluated. The results indicate that the emerging yellow floats do not severely block filtration, while the fine and uniform-shape corn starch particle and its incompletely hydrolyzed residue after liquefaction are responsible for filtration blocking. Application of β-amylase preparation increased the filtration rate of liquefied corn starch. This study is useful for our insight into the filtration blocking problem arising in the process of high-adjunct-ratio beer brewing and also provides a feasible solution using enzyme preparations.

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

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

Hudson, S. R.; Hole, M. J.; Dewar, R. L.

2007-05-15

A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields {nabla}xB={lambda}B, where {lambda} is constant within each domain. Two distinctmore » eigenvalue problems for {lambda} arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.« less

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

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

D'Ambra, P.; Vassilevski, P. S.

2014-05-30

Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. Inmore » this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.« less

Theory of signs and statistical approach to big data in assessing the relevance of clinical biomarkers of inflammation and oxidative stress.

PubMed

Ghezzi, Pietro; Davies, Kevin; Delaney, Aidan; Floridi, Luciano

2018-03-06

Biomarkers are widely used not only as prognostic or diagnostic indicators, or as surrogate markers of disease in clinical trials, but also to formulate theories of pathogenesis. We identify two problems in the use of biomarkers in mechanistic studies. The first problem arises in the case of multifactorial diseases, where different combinations of multiple causes result in patient heterogeneity. The second problem arises when a pathogenic mediator is difficult to measure. This is the case of the oxidative stress (OS) theory of disease, where the causal components are reactive oxygen species (ROS) that have very short half-lives. In this case, it is usual to measure the traces left by the reaction of ROS with biological molecules, rather than the ROS themselves. Borrowing from the philosophical theories of signs, we look at the different facets of biomarkers and discuss their different value and meaning in multifactorial diseases and system medicine to inform their use in patient stratification in personalized medicine.

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

Bai, Zhaojun; Yang, Chao

What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcasemore » some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.« less

A genetic algorithm used for solving one optimization problem

NASA Astrophysics Data System (ADS)

Shipacheva, E. N.; Petunin, A. A.; Berezin, I. M.

2017-12-01

A problem of minimizing the length of the blank run for a cutting tool during cutting of sheet materials into shaped blanks is discussed. This problem arises during the preparation of control programs for computerized numerical control (CNC) machines. A discrete model of the problem is analogous in setting to the generalized travelling salesman problem with limitations in the form of precursor conditions determined by the technological features of cutting. A certain variant of a genetic algorithm for solving this problem is described. The effect of the parameters of the developed algorithm on the solution result for the problem with limitations is investigated.

First Principles Investigation of Fluorine Based Strontium Series of Perovskites

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2016-11-01

Density functional theory is used to explore structural, elastic, and mechanical properties of SrLiF3, SrNaF3, SrKF3 and SrRbF3 fluoroperovskite compounds by means of an ab-initio Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method. Several lattice parameters are employed to obtain accurate equilibrium volume (Vo). The resultant quantities include ground state energy, elastic constants, shear modulus, bulk modulus, young's modulus, cauchy's pressure, poisson's ratio, shear constant, ratio of elastic anisotropy factor, kleinman's parameter, melting temperature, and lame's coefficient. The calculated structural parameters via DFT as well as analytical methods are found to be consistent with experimental findings. Chemical bonding is used to investigate corresponding chemical trends which authenticate combination of covalent-ionic behavior. Furthermore electron density plots as well as elastic and mechanical properties are reported for the first time which reveals that fluorine based strontium series of perovskites are mechanically stable and posses weak resistance towards shear deformation as compared to resistance towards unidirectional compression while brittleness and ionic behavior is dominated in them which decreases from SrLiF3 to SrRbF3. Calculated cauchy's pressure, poisson's ratio and B/G ratio also proves ionic nature in these compounds. The present methodology represents an effective and influential approach to calculate the whole set of elastic and mechanical parameters which would support to understand various physical phenomena and empower device engineers for implementing these materials in numerous applications.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

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

Miyata, Y.; Suzuki, T.; Takechi, M.

2015-07-15

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichletmore » and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.« less

A Cognitive Map of Human Performance Technology: A Study of Domain Expertise.

ERIC Educational Resources Information Center

Villachica, Steven W.; Lohr, Linda L.; Summers, Laura; Lowell, Nate; Roberts, Stephanie; Javeri, Manisha; Hunt, Erin; Mahoney, Chris; Conn, Cyndie

Most representations of academic disciplines have been created when experts depict or report what they know; however, there are potential problems that can arise when practitioners rely on expert self-report. One way to avoid potential problems associated with expert self-report is to employ cognitive task analysis methods. The Pathfinder Scaling…

Development and Evaluation of an Interactive Mobile Learning Environment with Shared Display Groupware

ERIC Educational Resources Information Center

Yang, Jie Chi; Lin, Yi Lung

2010-01-01

When using mobile devices in support of learning activities, students gain mobility, but problems arise when group members share information. The small size of the mobile device screen becomes problematic when it is being used by two or more students to share and exchange information. This problem affects interactions among group members. To…

Administrative Problem-Solving for Writing Programs and Writing Centers: Scenarios in Effective Program Management.

ERIC Educational Resources Information Center

Myers-Breslin, Linda

Addressing the issues and problems faced by writing program administrators (WPAs) and writing center directors (WCDs), and how they can most effectively resolve the political, pedagogical, and financial questions that arise, this book presents essays from experienced WPAs and WCDs at a wide variety of institutions that offer scenarios and case…

Succession Planning in England: New Leaders and New Forms of Leadership

ERIC Educational Resources Information Center

Bush, Tony

2011-01-01

There are concerns about the supply of head teachers in many countries. In England, this problem arises from demographic changes and the perceived difficulty of the job. The National College responded to this problem by initiating a Succession Planning programme. This article reports the main findings from the external evaluation of the programme…

Effects of Inequality and Poverty vs. Teachers and Schooling on America's Youth

ERIC Educational Resources Information Center

Berliner, David C.

2013-01-01

Background/Context: This paper arises out of frustration with the results of school reforms carried out over the past few decades. These efforts have failed. They need to be abandoned. In their place must come recognition that income inequality causes many social problems, including problems associated with education. Sadly, compared to all other…

Practical Solutions to Practically Every Problem: The Early Childhood Teacher's Manual. Revised Edition.

ERIC Educational Resources Information Center

Saifer, Steffen

Based on sound developmentally appropriate theory, this revised guide is designed to help early childhood teachers deal with common problems that arise in all aspects of their work. Following an introduction and a list of the 20 most important principles for successful preschool teaching, the guide is divided into nine parts. Part 1 addresses…

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

NASA Astrophysics Data System (ADS)

Messelmi, Farid

2017-12-01

We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

Co-Rumination Cultivates Anxiety: A Genetically Informed Study of Friend Influence during Early Adolescence

ERIC Educational Resources Information Center

Dirghangi, Shrija; Kahn, Gilly; Laursen, Brett; Brendgen, Mara; Vitaro, Frank; Dionne, Ginette; Boivin, Michel

2015-01-01

This study tested 2 related hypotheses. The first holds that high co-rumination anticipates heightened internalizing problems. The second holds that positive relationships with friends exacerbate the risk for internalizing problems arising from co-rumination. A sample of MZ twins followed from birth (194 girls and 170 boys) completed (a)…

Symmetry of the Adiabatic Condition in the Piston Problem

ERIC Educational Resources Information Center

Anacleto, Joaquim; Ferreira, J. M.

2011-01-01

This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be…

The Perceived Benefits and Problems Associated with Teaching Activities Undertaken by Doctoral Students

ERIC Educational Resources Information Center

Jordan, Katy; Howe, Christine

2018-01-01

Postgraduate students involved in delivering undergraduate teaching while working toward a research degree are known as graduate teaching assistants (GTAs). This study focused upon the problems and benefits arising from this dual role as researchers and teachers, as perceived by GTAs at the University of Cambridge. To this end, GTAs at Cambridge…

Practical Solutions to Practically Every Problem: The Early Childhood Teacher's Manual.

ERIC Educational Resources Information Center

Saifer, Steffen

This book is designed to help early childhood teachers deal with common problems that arise in all aspects of their work. Part one addresses daily dilemmas such as schedule planning, meal and nap times, art, and outdoor play. Part two covers classroom concerns such as the physical environment, curriculum, individual student needs, field trips,…

Measuring forest evapotranspiration--theory and problems

Treesearch

Anthony C. Federer; Anthony C. Federer

1970-01-01

A satisfactory general method of measuring forest evapotranspiration has yet to be developed. Many procedures have been tried, but only the soil-water budget method and the micrometeorological methods offer any degree of success. This paper is a discussion of these procedures and the problems that arise in applying them. It is designed as a reference for scientists and...

Reflections on the surface energy imbalance problem

Treesearch

Ray Leuning; Eva van Gorsela; William J. Massman; Peter R. Isaac

2012-01-01

The 'energy imbalance problem' in micrometeorology arises because at most flux measurement sites the sum of eddy fluxes of sensible and latent heat (H + λE) is less than the available energy (A). Either eddy fluxes are underestimated or A is overestimated. Reasons for the imbalance are: (1) a failure to satisfy the fundamental assumption of one-...

Who Is Listening? An Examination of Gender Effects and Employment Choice in Sustainability Education in an Undergraduate Business School

ERIC Educational Resources Information Center

Weaven, Scott; Griffin, Deborah; McPhail, Ruth; Smith, Calvin

2013-01-01

Whilst universities acknowledge the importance of sustainability education, numerous problems exist in relation to the nature, delivery and outcomes of sustainability instruction. Many of these problems arise due to a lack of understanding about students' perception towards, and knowledge about business sustainability. This article examines…

Estimation of coefficients and boundary parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Murphy, K. A.

1984-01-01

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.