A spatial discretization of the MHD equations based on the finite volume - spectral method
Energy Technology Data Exchange (ETDEWEB)
Miyoshi, Takahiro [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA{sub {phi}}, is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
CSIR Research Space (South Africa)
Bogaers, Alfred EJ
2012-07-01
Full Text Available In this paper we outline the development of a 1D finite volume model to solve for blood flow through the arterial system. The model is based on a staggered spatial discretization which leads to a stable solution scheme. This scheme can accurately...
Compatible Spatial Discretizations for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Discretized Volumes in Numerical Methods
Antal, Miklós
2007-01-01
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.
Volume Effects in Discrete beta functions
Liu, Yuzhi; Zou, Haiyuan
2011-01-01
We calculate discrete beta functions corresponding to the two-lattice matching for the 2D O(N) models and Dyson's hierarchical model. We describe and explain finite-size effects such as the appearance of a nontrivial infrared fixed point that goes to infinity at infinite volume or the merging of an infrared and an ultraviolet fixed point. We present extensions of the RG flows to the complex coupling plane. We discuss the possibility of constructing a continuous beta function from the discrete one by using functional conjugation methods. We briefly discuss the relevance of these findings for the search of nontrivial fixed points in multiflavor lattice gauge theory models.
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact...... attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical...
Electromagnetic scattering by spheroidal volumes of discrete random medium
Mishchenko, Michael I.; Dlugach, Janna M.
2017-10-01
We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing nonsphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.
Energy Technology Data Exchange (ETDEWEB)
Thompson, Kelly Glen [Texas A & M Univ., College Station, TX (United States)
2000-11-01
In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness
Effect of spatial discretization of energy on detonation wave propagation
Mi, XiaoCheng; Higgins, Andrew J
2016-01-01
Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are now embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the lab-fixed reference frame. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as grea...
Discrete spatial solitons formed in periodically poled lithium niobate by electro-optical effect
Institute of Scientific and Technical Information of China (English)
Xi Gu (顾希); Xianfeng Chen (陈险峰); Yuping Chen (陈玉萍); Yuxing Xia (夏宇兴); Yingli Chen (陈英礼)
2003-01-01
We report the numerical observation of discrete spatial solitons in a periodically poled lithium niobate waveguide array by applying an electrical field through electro-optical effect. We show that discrete spatial soliton can be controlled by applied voltage in the periodically poled lithium niobate.
Integrated hydrologic modeling: Effects of spatial scale, discretization and initialization
Seck, A.; Welty, C.; Maxwell, R. M.
2011-12-01
Groundwater discharge contributes significantly to the annual flows of Chesapeake Bay tributaries and is presumed to contribute to the observed lag time between the implementation of management actions and the environmental response in the Chesapeake Bay. To investigate groundwater fluxes and flow paths and interaction with surface flow, we have developed a fully distributed integrated hydrologic model of the Chesapeake Bay Watershed using ParFlow. Here we present a comparison of model spatial resolution and initialization methods. We have studied the effect of horizontal discretization on overland flow processes at a range of scales. Three nested model domains have been considered: the Monocacy watershed (5600 sq. km), the Potomac watershed (92000 sq. km) and the Chesapeake Bay watershed (400,000 sq. km). Models with homogeneous subsurface and topographically-derived slopes were evaluated at 500-m, 1000-m, 2000-m, and 4000-m grid resolutions. Land surface slopes were derived from resampled DEMs and corrected using stream networks. Simulation results show that the overland flow processes are reasonably well represented with a resolution up to 2000 m. We observe that the effects of horizontal resolution dissipate with larger scale models. Using a homogeneous model that includes subsurface and surface terrain characteristics, we have evaluated various initialization methods for the integrated Monocacy watershed model. This model used several options for water table depths and two rainfall forcing methods including (1) a synthetic rainfall-recession cycle corresponding to the region's average annual rainfall rate, and (2) an initial shut-off of rainfall forcing followed by a rainfall-recession cycling. Results show the dominance of groundwater generated runoff during a first phase of the simulation followed by a convergence towards more balanced runoff generation mechanisms. We observe that the influence of groundwater runoff increases in dissected relief areas
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major effort now underway to…
Directory of Open Access Journals (Sweden)
Dalissier E.
2013-12-01
Full Text Available The objective of the ComPASS project is to develop a parallel multiphase Darcy flow simulator adapted to general unstructured polyhedral meshes (in a general sense with possibly non planar faces and to the parallelization of advanced finite volume discretizations with various choices of the degrees of freedom such as cell centres, vertices, or face centres. The main targeted applications are the simulation of CO2 geological storage, nuclear waste repository and reservoir simulations. The CEMRACS 2012 summer school devoted to high performance computing has been an ideal framework to start this collaborative project. This paper describes what has been achieved during the four weeks of the CEMRACS project which has been focusing on the implementation of basic features of the code such as the distributed unstructured polyhedral mesh, the synchronization of the degrees of freedom, and the connection to scientific libraries including the partitioner METIS, the visualization tool PARAVIEW, and the parallel linear solver library PETSc. The parallel efficiency of this first version of the ComPASS code has been validated on a toy parabolic problem using the Vertex Approximate Gradient finite volume spatial discretization with both cell and vertex degrees of freedom, combined with an Euler implicit time integration.
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Azmy, Yousry Y., E-mail: snschune@ncsu.edu, E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States); Fournier, Damien; Le Tellier, Romain, E-mail: damien.fournier@cea.fr, E-mail: romain.le-tellier@cea.fr [CEA, DEN, DER/SPRC/LEPh, Cadarache, Saint Paul-lez-Durance (France)
2011-07-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen's benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semi analytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation. (author)
Energy Technology Data Exchange (ETDEWEB)
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Energy Technology Data Exchange (ETDEWEB)
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo
2015-10-01
The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.
Discrete mathematics for spatial data classification and understanding
Mussio, Luigi; Nocera, Rossella; Poli, Daniela
1998-12-01
Data processing, in the field of information technology, requires new tools, involving discrete mathematics, like data compression, signal enhancement, data classification and understanding, hypertexts and multimedia (considering educational aspects too), because the mass of data implies automatic data management and doesn't permit any a priori knowledge. The methodologies and procedures used in this class of problems concern different kinds of segmentation techniques and relational strategies, like clustering, parsing, vectorization, formalization, fitting and matching. On the other hand, the complexity of this approach imposes to perform optimal sampling and outlier detection just at the beginning, in order to define the set of data to be processed: rough data supply very poor information. For these reasons, no hypotheses about the distribution behavior of the data can be generally done and a judgment should be acquired by distribution-free inference only.
Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
2015-06-01
Discretizations 5a. CONTRACT NUMBER In-House 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mundis , N., Edoh, A. and Sankaran, V. 5d...Schemes for High-order Spatial and Temporal Discretizations Nathan L. Mundis ∗ Ayaboe K. Edoh† Venkateswaran Sankaran‡ * ERC, Inc., †University of...the wave number being the parameter) are overlaid on the contour map of the amplification factor in the complex plane for the chosen temporal scheme
Bunao, J.
2017-02-01
This study considers the operator \\hat{T} corresponding to the classical spacetime four-volume \\tilde{T} (on-shell) of a finite patch of spacetime in the context of unimodular loop quantum cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological ‘constant’, the operator \\hat{T} is constructed by solving its canonical commutation relation with {\\hat Λ } —the operator corresponding to the classical cosmological constant on-shell {\\tilde Λ } . This conjugacy, along with the action of \\hat{T} on definite volume states reducing to \\tilde{T} , allows us to interpret that \\hat{T} is indeed a quantum spacetime four-volume operator. The discrete spectrum of \\hat{T} is calculated by considering the set of all τ’s where the eigenvalue equation has a solution {{ Φ }τ} in the domain of \\hat{T} . It turns out that, upon assigning the maximal domain D≤ft(\\hat{T}\\right) to \\hat{T} , we have {{ Φ }τ}\\in D≤ft(\\hat{T}\\right) for all τ \\in {C} so that the spectrum of \\hat{T} is purely discrete and is the entire complex plane. A family of operators {{\\hat{T}}≤ft({{b0},{φ0}\\right)}} was also considered as possible self-adjoint versions of \\hat{T} . They represent the restrictions of \\hat{T} on their respective domains D≤ft({{\\hat{T}}≤ft({{b0},{φ0}\\right)}}\\right) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers {τm} for m=0,+/- 1,+/- 2,... .
Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Andreianov, Boris; Karlsen, Kenneth H; Pierre, Charles
2010-01-01
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.
Does cooperation mean kinship between spatially discrete ant nests?
Procter, Duncan S; Cottrell, Joan E; Watts, Kevin; A'Hara, Stuart W; Hofreiter, Michael; Robinson, Elva J H
2016-12-01
Eusociality is one of the most complex forms of social organization, characterized by cooperative and reproductive units termed colonies. Altruistic behavior of workers within colonies is explained by inclusive fitness, with indirect fitness benefits accrued by helping kin. Members of a social insect colony are expected to be more closely related to one another than they are to other conspecifics. In many social insects, the colony can extend to multiple socially connected but spatially separate nests (polydomy). Social connections, such as trails between nests, promote cooperation and resource exchange, and we predict that workers from socially connected nests will have higher internest relatedness than those from socially unconnected, and noncooperating, nests. We measure social connections, resource exchange, and internest genetic relatedness in the polydomous wood ant Formica lugubris to test whether (1) socially connected but spatially separate nests cooperate, and (2) high internest relatedness is the underlying driver of this cooperation. Our results show that socially connected nests exhibit movement of workers and resources, which suggests they do cooperate, whereas unconnected nests do not. However, we find no difference in internest genetic relatedness between socially connected and unconnected nest pairs, both show high kinship. Our results suggest that neighboring pairs of connected nests show a social and cooperative distinction, but no genetic distinction. We hypothesize that the loss of a social connection may initiate ecological divergence within colonies. Genetic divergence between neighboring nests may build up only later, as a consequence rather than a cause of colony separation.
Structure Preserving Spatial Discretization of a 1-D Piezoelectric Timoshenko Beam
Voss, T.; Scherpen, J. M. A.
2011-01-01
In this paper we show how to spatially discretize a distributed model of a piezoelectric beam representing the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. This model can then be used to design a controller for the shape of the inflatable structure. Inflatable structures
Kruppa, Lisa; König, Christoph M.; Becker, Martin; Seidel, Torsten
2016-04-01
Most hard rock aquifers, which are important for geothermal use, contain fractures of different type and scale. These fault systems are of major significance for heat flow in the groundwater. The hydrogeological characterization of fault systems must therefore be part of any site investigation in hard rock aquifers and hydraulically important fault systems need to be appropriately represented in associated numerical models. This contribution discusses different spatial discretization methods of fault systems in three-dimensional groundwater models and their impact on the simulated groundwater flow field as well as density and viscosity dependent heat transport. The analysis includes a comparison of the convergence behavior and numerical stability of the different discretization methods. To ensure defendable results, the utilized numerical model SPRING was first verified against data from the Hydrocoin Level 1 Case 2 project. After verification, the software was used to evaluate the impact of different discretization strategies on steady-state and transient groundwater flow and transport model results. The results show a significant influence of the spatial discretization strategy on predicted flow rates and subsequent mass fluxes as well as energy balances.
Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Burton, D.E.
1994-10-17
We consider the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH). Hydrodynamics algorithms are often formulated in a relatively ad hoc manner in which independent discretizations are proposed for mass, momentum, energy, and so forth. We show that, once discretizations for mass and momentum are stated, the remaining discretizations are very nearly uniquely determined, so there is very little latitude for variation. As has been known for some time, the kinetic energy discretization must follow directly from the momentum equation; and the internal energy must follow directly from the energy currents affecting the kinetic energy. A fundamental requirement (termed isentropicity) for numerical hydrodynamics algorithms is the ability to remain on an isentrope in the absence of heating or viscous forces and in the limit of small timesteps. We show that the requirements of energy conservation and isentropicity lead to the replacement of the usual volume calculation with a conservation integral. They further forbid the use of higher order functional representations for either velocity or stress within zones or control volumes, forcing the use of a constant stress element and a constant velocity control volume. This, in turn, causes the point and zone coordinates to formally disappear from the Cartesian formulation. The form of the work equations and the requirement for dissipation by viscous forces strongly limits the possible algebraic forms for artificial viscosity. The momentum equation and a center-of-mass definition lead directly to an angular momentum conservation law that is satisfied by the system. With a few straightforward substitutions, the Cartesian formulation can be converted to a multidimensional curvilinear one. The formulation in 2D symmetric geometry preserves rotational symmetry.
Spatial Economics Model Predicting Transport Volume
Directory of Open Access Journals (Sweden)
Lu Bo
2016-10-01
Full Text Available It is extremely important to predict the logistics requirements in a scientific and rational way. However, in recent years, the improvement effect on the prediction method is not very significant and the traditional statistical prediction method has the defects of low precision and poor interpretation of the prediction model, which cannot only guarantee the generalization ability of the prediction model theoretically, but also cannot explain the models effectively. Therefore, in combination with the theories of the spatial economics, industrial economics, and neo-classical economics, taking city of Zhuanghe as the research object, the study identifies the leading industry that can produce a large number of cargoes, and further predicts the static logistics generation of the Zhuanghe and hinterlands. By integrating various factors that can affect the regional logistics requirements, this study established a logistics requirements potential model from the aspect of spatial economic principles, and expanded the way of logistics requirements prediction from the single statistical principles to an new area of special and regional economics.
Bunao, Joseph
2016-01-01
This study considers the operator $\\hat{T}$ corresponding to the classical spacetime four-volume $T$ of a finite patch of spacetime in the context of Unimodular Loop Quantum Cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since $T$ is canonically conjugate to the cosmological "constant" $\\Lambda$, the operator $\\hat{T}$ is constructed by solving its canonical commutation relation with $\\hat{\\Lambda}$ - the operator corresponding to $\\Lambda$. %This is done by expanding $\\hat{T}$ in terms of Bender-Dunne-like basis operators $\\hat{T}_{m,n}$ and solving for the expansion coefficients. This conjugacy, along with the action of $\\hat{T}$ on definite volume states reducing to $T$, allows us to interpret that $\\hat{T}$ is indeed a quantum spacetime four-volume operator. The eigenstates $\\Phi_{\\tau}$ are calculated and, considering $\\tau\\in\\mathbb{R}$, we find that the $\\Phi_{\\tau}$'s are normalizable suggesting that the real line $\\mathbb{R}$ is in the discret...
Effect of excluded volume on 2D discrete stochastic chemical kinetics
Lampoudi, Sotiria; Gillespie, Dan T.; Petzold, Linda R.
2009-06-01
The stochastic simulation algorithm (SSA) is widely used in the discrete stochastic simulation of chemical kinetics. The propensity functions which play a central role in this algorithm have been derived under the point-molecule assumption, i.e., that the total volume of the molecules is negligible compared to the volume of the container. It has been shown analytically that for a one-dimensional system and the A + A reaction, when the point-molecule assumption is relaxed, the propensity function need only be adjusted by replacing the total volume of the system with the free volume of the system. In this paper we investigate via numerical simulations the impact of relaxing the point-molecule assumption in two dimensions. We find that the distribution of times to the first collision is close to exponential in most cases, so that the formalism of the propensity function is still applicable. In addition, we find that the area excluded by the molecules in two dimensions is usually higher than their close-packed area, requiring a larger correction to the propensity function than just the replacement of the total volume by the free volume.
Institute of Scientific and Technical Information of China (English)
Wenjing Du; Peili Wang; Lipeng Song; Lin Cheng
2015-01-01
A conduction heat transfer process is enhanced by filling prescribed quantity and optimized-shaped high thermal conductivity materials to the substrate. Numerical simulations and analyses are performed on a volume to point conduction problem based on the principle of minimum entropy generation. In the optimization, the arrange-ment of high thermal conductivity materials is variable, the quantity of high thermal-conductivity material is constrained, and the objective is to obtain the maximum heat conduction rate as the entropy is the minimum. A novel algorithm of thermal conductivity discretization is proposed based on large quantity of calculations. Compared with other algorithms in literature, the average temperature in the substrate by the new algorithm is lower, while the highest temperature in the substrate is in a reasonable range. Thus the new algorithm is fea-sible. The optimization of volume to point heat conduction is carried out in a rectangular model with radiation boundary condition and constant surface temperature boundary condition. The results demonstrate that the al-gorithm of thermal conductivity discretization is applicable for volume to point heat conduction problems.
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
2011-01-01
design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems the main difficulty we face is the need to analyze the convergence of fluxes defined on the faces of cells......We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal...
Spatial Visualization Tasks to Support Students' Spatial Structuring in Learning Volume Measurement
Revina, Shintia; Zulkardi; Darmawijoyo; van Galen, Frans
2011-01-01
Many prior researches found that most of students in grade five tended to have difficulty in fully grasping the concept of volume measurement because they have to build their competence in spatial structuring. The unit of volume "packing" measurement must be integrated and coordinated in three-dimension. On the other hand, it is revealed…
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
Spatial Visualization Tasks To Support Students’ Spatial Structuring In Learning Volume Measurement
Directory of Open Access Journals (Sweden)
Shintia Revina
2011-07-01
Full Text Available Many prior researches found that most of students in grade five tended to have difficulty in fully grasping the concept of volume measurement because they have to build their competence in spatial structuring. The unit of volume “packing” measurement must be integrated and coordinated in three-dimension. On the other hand, it is revealed the errors that students made on the volume measurement tasks with threedimensional cube arrays are related to some aspects of spatial visualization, such as the skill to "read off" two-dimensional representation of solid objects. For those reasons, this research is aimed to develop classroom activities with the use of spatial visualization tasks to support students’ spatial structuring in learning volume measurement. Consequently, design research was chosen as an appropriate means to achieve this research goal. In this research, a sequence of instructional activities is designed and developed based on the hypothesis of students’ learning processes. This research was conducted in grade 5 of SD Pupuk Sriwijaya Palembang, Indonesia.Keywords: volume measurement, spatial structuring, spatial visualization, design research. DOI: http://dx.doi.org/10.22342/jme.2.2.745.127-146
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Institute of Scientific and Technical Information of China (English)
LI Qingping,DU Junping; XU Liang
2015-01-01
Multiple visual sensor fusion provides an eff ective way to improve the robustness and accuracy of video surveillance system. Traditional video fusion meth-ods fuse the source videos using static image fusion meth-ods frame-by-frame without considering the information in temporal dimension. The temporal information can’t be fully utilized in fusion procedure. Aiming at this problem, a visible and infrared video fusion method based on Uniform discrete curvelet transform (UDCT) and spatial-temporal information is proposed. The source videos are decomposed by using UDCT, and a set of local spatial-temporal energy based fusion rules are designed for decomposition coeffi-cients. In these rules, we consider the current frame’s co-efficients and the coefficients on temporal dimension which are the coefficients of adjacent frames. Experimental re-sults demonstrated that the proposed method works well and outperforms comparison methods in terms of temporal stability and consistency as well as spatial-temporal infor-mation extraction.
Control theory based airfoil design for potential flow and a finite volume discretization
Reuther, J.; Jameson, A.
1994-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.
Rey, Sergio J.; Kang, Wei; Wolf, Levi
2016-10-01
Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series.
Spatial Visualization Tasks To Support Students’ Spatial Structuring In Learning Volume Measurement
Directory of Open Access Journals (Sweden)
Shintia Revina
2011-07-01
Full Text Available Many prior researches found that most of students in grade five tendedto have difficulty in fully grasping the concept of volume measurementbecause they have to build their competence in spatial structuring. The unit of volume “packing” measurement must be integrated andcoordinated in three-dimension. On the other hand, it is revealed theerrors that students made on the volume measurement tasks with threedimensional cube arrays are related to some aspects of spatialvisualization, such as the skill to "read off" two-dimensionalrepresentation of solid objects. For those reasons, this research is aimed to develop classroom activities with the use of spatial visualization tasks to support students’ spatial structuring in learning volume measurement. Consequently, design research was chosen as an appropriate means to achieve this research goal. In this research, a sequence of instructional activities is designed and developed based on the hypothesis of students’ learning processes. This research was conducted in grade 5 of SD Pupuk Sriwijaya Palembang, Indonesia
Directory of Open Access Journals (Sweden)
Jill Cirasella
2013-08-01
Full Text Available INTRODUCTION Articles in open access (OA journals can be published on a rolling basis, as they become ready, or in complete, discrete issues. This study examines the prevalence of and reasons for rolling volumes vs. discrete issues among scholarly OA library and information science (LIS journals based in the United States. METHODS A survey was distributed to journal editors, asking them about their publication model and their reasons for and satisfaction with that model. RESULTS Of the 21 responding journals, 12 publish in discrete issues, eight publish in rolling volumes, and one publishes in rolling volumes with an occasional special issue. Almost all editors, regardless of model, cited ease of workflow as a justification for their chosen publication model, suggesting that there is no single best workflow for all journals. However, while all rolling-volume editors reported being satisfied with their model, satisfaction was less universal among discrete-issue editors. DISCUSSION The unexpectedly high number of rolling-volume journals suggests that LIS journal editors are making forward-looking choices about publication models even though the topic has not been much addressed in the library literature. Further research is warranted; possibilities include expanding the study’s geographic scope, broadening the study to other disciplines, and investigating publication model trends across the entire scholarly OA universe. CONCLUSION Both because satisfaction is high among editors of rolling-volume journals and because readers and authors appreciate quick publication times, the rolling-volume model will likely become even more prevalent in coming years.
Energy Technology Data Exchange (ETDEWEB)
Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees
1996-12-31
The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.
Spatially-discretized high-temperature approximations and theirO(N) implementation on a grid
Energy Technology Data Exchange (ETDEWEB)
Predescu, Cristian
2006-10-01
We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N) with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter-Suzuki approximation against a recently introduced fourth-order high-temperature approximation, while circumventing the issue of statistical noise, which usually prevents such comparisons from being carried out. We document the appearance of a systematic bias in the Monte Carlo estimators that involve temperature differentiation of the density matrix, bias that is due to the dependence of the eigenvalues on the inverse temperature. This bias is negotiated more successfully by the short-time approximations having higher convergence order, leading to non-trivial computational savings.
DEFF Research Database (Denmark)
Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan;
2015-01-01
This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the force...... in a cell is spread on neighboring cells by applying equivalent pressure jumps at the cell faces. The method shows excellent results when applied for simulating the flow through an actuator disk, which is relevant for wind turbine wake simulations. (c) 2015 Elsevier Ltd. All rights reserved....
Directory of Open Access Journals (Sweden)
J. Dehotin
2008-05-01
Full Text Available Distributed hydrological models are valuable tools to derive distributed estimation of water balance components or to study the impact of land-use or climate change on water resources and water quality. In these models, the choice of an appropriate spatial discretization is a crucial issue. It is obviously linked to the available data, their spatial resolution and the dominant hydrological processes. For a given catchment and a given data set, the "optimal" spatial discretization should be adapted to the modelling objectives, as the latter determine the dominant hydrological processes considered in the modelling. For small catchments, landscape heterogeneity can be represented explicitly, whereas for large catchments such fine representation is not feasible and simplification is needed. The question is thus: is it possible to design a flexible methodology to represent landscape heterogeneity efficiently, according to the problem to be solved? This methodology should allow a controlled and objective trade-off between available data, the scale of the dominant water cycle components and the modelling objectives.
In this paper, we propose a general methodology for such catchment discretization. It is based on the use of nested discretizations. The first level of discretization is composed of the sub-catchments, organised by the river network topology. The sub-catchment variability can be described using a second level of discretizations, which is called hydro-landscape units. This level of discretization is only performed if it is consistent with the modelling objectives, the active hydrological processes and data availability. The hydro-landscapes take into account different geophysical factors such as topography, land-use, pedology, but also suitable hydrological discontinuities such as ditches, hedges, dams, etc. For numerical reasons these hydro-landscapes can be further subdivided into smaller elements that will constitute the
Yousefi, Mahyar; Carranza, Emmanuel John M.
2017-04-01
Two common problems affect integration of exploration criteria for mineral prospectivity mapping (MPM) in geographic information system (GIS): (a) stochastic error associated with sufficiency in number of known mineral occurrences (KMOs) used to estimate evidential weights and (b) systemic error associated with subjectivity of expert judgment applied to process, analyze, and assign weights to evidential data. In this paper we used logistic sigmoid (or S-shaped) function to transform continuous-value evidential data into logistic space without using KMOs as in data-driven MPM and without discretization of evidential data into classes by using arbitrary intervals based on expert judgment as in knowledge-driven MPM. We generated a prospectivity model using discretized evidential data as well. Then, we compared the prospectivity models generated using continuous- and discretized-value evidential data and demonstrated that the former is better model for selecting target areas for further exploration.
Garland, Alexis; Beran, Michael J; McIntyre, Joseph; Low, Jason
2014-08-01
Quantity discrimination for items spread across spatial arrays was investigated in chimpanzees (Pan troglodytes) and North Island New Zealand robins (Petroica longipes), with the aim of examining the role of spatial separation on the ability of these 2 species to sum and compare nonvisible quantities which are both temporally and spatially separated, and to assess the likely mechanism supporting such summation performance. Birds and chimpanzees compared 2 sets of discrete quantities of items that differed in number. Six quantity comparisons were presented to both species: 1v2, 1v3, 1v5, 2v3, 2v4, and 2v5. Each was distributed 1 at a time across 2 7-location arrays. Every individual item was viewed 1 at a time and hidden, with no more than a single item in each location of an array, in contrast to a format where all items were placed together into 2 single locations. Subjects responded by selecting 1 of the 2 arrays and received the entire quantity of food items hidden within that array. Both species performed better than chance levels. The ratio of items between sets was a significant predictor of performance in the chimpanzees, but it was not significant for robins. Instead, the absolute value of the smaller quantity of items presented was the significant factor in robin responses. These results suggest a species difference for this task when considering various dimensions such as ratio or total number of items in quantity comparisons distributed across discrete 7-location arrays.
Institute of Scientific and Technical Information of China (English)
ZHANG Xiang-wei; TAKEUCHI Kuniyoshi; CHEN Jing
2007-01-01
In this article, the finite element solution of quasi-three-dimensional (quasi-3-D) groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model (FEM) is the results choosing the small time step or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.
Kondakci, H Esat; Saleh, Bahaa E A
2016-01-01
When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. Firstly, the fingerprint of localization is embedded in the fluctuations of the discrete speckle and is revealed in the narrowing of the spatial coherence function. Secondly, the transverse coherence length (or speckle grain size) is frozen during propagation. Thirdly, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. We take these unique featu...
Volume of discrete brain structures in complex dissociative disorders: preliminary findings.
Ehling, T; Nijenhuis, E R S; Krikke, A P
2008-01-01
Based on findings in traumatized animals and patients with posttraumatic stress disorder, and on traumatogenic models of complex dissociative disorders, it was hypothesized that (1) patients with complex dissociative disorders have smaller volumes of hippocampus, parahippocampal gyrus, and amygdala than normal controls, (2) these volumes are associated with severity of psychoform and somatoform dissociative symptoms, and (3) patients who recovered from dissociative identity disorder (DID) have more hippocampal volume that patients with florid DID. The preliminary findings of the study are supportive of these hypotheses. Psychotherapy for dissociative disorders may affect hippocampal volume, but longitudinal studies are required to document this potential causal relationship.
Mi, XiaoCheng; Goroshin, Samuel; Bergthorson, Jeffrey M
2015-01-01
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed numerically using a one-dimensional heat equation with a source term for the reaction progress variable, which is specified to have zero diffusivity, and the model reveals a spectrum of flame-propagation regimes. For the case of a switch-type reaction rate and homogeneous media (continuous regime), the flame propagates steadily at a velocity in agreement with analytical solutions. As the sources are spatially concentrated into {\\delta}-function-like sources, propagation approaches the discrete regime with a fixed period between ignition of the sources, for which an analytic solution is also available for validation. When the source term is governed by an Arrhenius rate and the activation energy is increased beyond the stability boundary, the flame begins to exhibit a long-wave...
Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields
El Gawhary, Omar
2017-01-01
The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics.
Directory of Open Access Journals (Sweden)
Junxiao Zheng
2016-01-01
Full Text Available Maintaining the structural integrity of the reactor pressure vessel (RPV is a critical concern related to the safe operation of nuclear power plants. To estimate the structural integrity over the designed lifetime and to support analyses for a potential plant life extension, an accurate calculation of the fast neutron fluence (E>1.0 MeV or E>0.1 MeV at the RPV is significant. The discrete ordinates method is one of the main methods to solve such problems. During the calculation process, many factors will affect the results. In this paper, the deviations introduced by different differencing schemes and mesh sizes on the AP1000 RPV fast neutron fluence have been studied, which are based on new discrete ordinates code ARES. The analysis shows that the differencing scheme (diamond difference with or without linear zero fix-up, theta weighted, directional theta weighted, and exponential directional weighted introduces a deviation within 4%. The coarse mesh (4 × 4 cm meshes in XY plane leads to approximately 23.7% calculation deviation compared to those of refined mesh (1 × 1 cm meshes in XY plane. Comprehensive study on the deviation introduced by differencing scheme and mesh size has great significance for reasoned evaluation of RPV fast neutron fluence calculation results.
Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
Volume of discrete brain structures in complex dissociative disorders : preliminary findings
Ehling, T.; Nijenhuis, E. R. S.; Krikke, A. P.; DeKloet, ER; Vermetten, E
2007-01-01
Based on findings in traumatized animals and patients with posttraumatic stress disorder, and on traumatogenic models of complex dissociative disorders, it was hypothesized that (1) patients with complex dissociative disorders have smaller volumes of hippocampus, parahippocampal gyrus, and amygdala
Volume of discrete brain structures in complex dissociative disorders : preliminary findings
Ehling, T.; Nijenhuis, E. R. S.; Krikke, A. P.; DeKloet, ER; Vermetten, E
2007-01-01
Based on findings in traumatized animals and patients with posttraumatic stress disorder, and on traumatogenic models of complex dissociative disorders, it was hypothesized that (1) patients with complex dissociative disorders have smaller volumes of hippocampus, parahippocampal gyrus, and amygdala
Defect-induced spatial coherence in the discrete nonlinear Schrödinger equation.
Pando, C L; Doedel, E J
2004-03-01
We have considered the discrete nonlinear Schrödinger equation (DNLSE) with periodic boundary conditions in the context of coupled Kerr waveguides. The presence of a defect in the central oscillator equation can induce quasiperiodic or large chaotic amplitude oscillations. As for the quasiperiodic dynamics, an enhancement of the amplitude correlations in certain oscillator pairs can take place. However, when the array dynamics becomes chaotic, these correlations are destroyed, and, for suitable defects, synchronization, in the information sense, of certain signals arises in this Hamiltonian system. A numerical continuation analysis clarifies the onset of this dynamical regime. In this case, phase synchronization follows with a peculiar distribution of the Liapunov exponents. These effects occur for initial conditions in a small neighborhood of a family of stationary solutions. We have also found a regime characterized by persistent localized chaotic amplitudes. We have generalized these results to take into account birefringent effects in waveguides.
Depth measurement using monocular stereo vision system: aspect of spatial discretization
Xu, Zheng; Li, Chengjin; Zhao, Xunjie; Chen, Jiabo
2010-11-01
The monocular stereo vision system, consisting of single camera with controllable focal length, can be used in 3D reconstruction. Applying the system for 3D reconstruction, must consider effects caused by digital camera. There are two possible methods to make the monocular stereo vision system. First one the distance between the target object and the camera image plane is constant and lens moves. The second method assumes that the lens position is constant and the image plane moves in respect to the target. In this paper mathematical modeling of two approaches is presented. We focus on iso-disparity surfaces to define the discretization effect on the reconstructed space. These models are implemented and simulated on Matlab. The analysis is used to define application constrains and limitations of these methods. The results can be also used to enhance the accuracy of depth measurement.
Development of a Discrete Spatial-Temporal SEIR Simulator for Modeling Infectious Diseases
Energy Technology Data Exchange (ETDEWEB)
McKenna, S.A.
2000-11-01
Multiple techniques have been developed to model the temporal evolution of infectious diseases. Some of these techniques have also been adapted to model the spatial evolution of the disease. This report examines the application of one such technique, the SEIR model, to the spatial and temporal evolution of disease. Applications of the SEIR model are reviewed briefly and an adaptation to the traditional SEIR model is presented. This adaptation allows for modeling the spatial evolution of the disease stages at the individual level. The transmission of the disease between individuals is modeled explicitly through the use of exposure likelihood functions rather than the global transmission rate applied to populations in the traditional implementation of the SEIR model. These adaptations allow for the consideration of spatially variable (heterogeneous) susceptibility and immunity within the population. The adaptations also allow for modeling both contagious and non-contagious diseases. The results of a number of numerical experiments to explore the effect of model parameters on the spread of an example disease are presented.
Institute of Scientific and Technical Information of China (English)
ZHAO Ming; CAO Yihua
2012-01-01
A numerical method based on solutions of Euler/Navier-Stokes (N-S) equations is developed for calculating the flow field over a rotor in hover.Jameson central scheme,van Leer flux-vector splitting scheme,advection upwind splitting method (AUSM) scheme,upwind AUSM/van Leer scheme,AUSM+ scheme and AUSMDV scheme are implemented for spatial discretization,and van Albada limiter is also applied.For temporal discretization,both explicit Runge-Kutta method and implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method are attempted.Simultaneously,overset grid technique is adopted.In detail,hole-map method is utilized to identify intergrid boundary points (IGBPs).Furthermore,aimed at identification issue of donor elements,inverse-map method is implemented.Eventually,blade surface pressure distributions derived from numerical simulation are validated compared with experimental data,showing that all the schemes mentioned above have the capability to predict the rotor flow field accurately.At the same time,vorticity contours are illustrated for analysis,and other characteristics are also analyzed.
Kevrekidis, P G; Saxena, A; Frantzeskakis, D J; Bishop, A R
2014-01-01
We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios ...
Discreteness of the volume of space from Bohr-Sommerfeld quantization
Bianchi, Eugenio
2011-01-01
A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.
Cherenkov detectors for spatial imaging applications using discrete-energy photons
Energy Technology Data Exchange (ETDEWEB)
Rose, Paul B.; Erickson, Anna S., E-mail: erickson@gatech.edu [Georgia Institute of Technology, Nuclear and Radiological Engineering, G.W. Woodruff School of Mechanical Engineering, 770 State St., Atlanta, Georgia 30332 (United States)
2016-08-14
Cherenkov detectors can offer a significant advantage in spatial imaging applications when excellent timing response, low noise and cross talk, large area coverage, and the ability to operate in magnetic fields are required. We show that an array of Cherenkov detectors with crude energy resolution coupled with monochromatic photons resulting from a low-energy nuclear reaction can be used to produce a sharp image of material while providing large and inexpensive detector coverage. The analysis of the detector response to relative transmission of photons with various energies allows for reconstruction of material's effective atomic number further aiding in high-Z material identification.
Cherenkov detectors for spatial imaging applications using discrete-energy photons
Rose, Paul B.; Erickson, Anna S.
2016-08-01
Cherenkov detectors can offer a significant advantage in spatial imaging applications when excellent timing response, low noise and cross talk, large area coverage, and the ability to operate in magnetic fields are required. We show that an array of Cherenkov detectors with crude energy resolution coupled with monochromatic photons resulting from a low-energy nuclear reaction can be used to produce a sharp image of material while providing large and inexpensive detector coverage. The analysis of the detector response to relative transmission of photons with various energies allows for reconstruction of material's effective atomic number further aiding in high-Z material identification.
Fernández, María Del Pilar; Cecere, María Carla; Lanati, Leonardo Alejandro; Lauricella, Marta Alicia; Schijman, Alejandro Gabriel; Gürtler, Ricardo Esteban; Cardinal, Marta Victoria
2014-12-01
We assessed the diversity and distribution of Trypanosoma cruzi discrete typing units (DTU) in Triatoma infestans populations and its association with local vector-borne transmission levels at various geographic scales. At a local scale, we found high predominance (92.4%) of TcVI over TcV in 68 microscope-positive T. infestans collected in rural communities in Santiago del Estero province in northern Argentina. TcV was more often found in communities with higher house infestation prevalence compatible with active vector-borne transmission. Humans and dogs were the main bloodmeal sources of the TcV- and TcVI-infected bugs. At a broader scale, the greatest variation in DTU diversity was found within the Argentine Chaco (227 microscope-positive bugs), mainly related to differences in equitability between TcVI and TcV among study areas. At a country-wide level, a meta-analysis of published data revealed clear geographic variations in the distribution of DTUs across countries. A correspondence analysis showed that DTU distributions in domestic T. infestans were more similar within Argentina (dominated by TcVI) and within Bolivia (where TcI and TcV had similar relative frequencies), whereas large heterogeneity was found within Chile. DTU diversity was lower in the western Argentine Chaco region and Paraguay (D=0.14-0.22) than in the eastern Argentine Chaco, Bolivia and Chile (D=0.20-0.68). Simultaneous DTU identifications of T. cruzi-infected hosts and triatomines across areas differing in epidemiological status are needed to shed new light on the structure and dynamics of parasite transmission cycles.
DEFF Research Database (Denmark)
Saffman, Mark; Zoletnik, S.; Basse, Nils Plesner
2001-01-01
We describe and demonstrate a two-volume collective scattering system for localized measurements of plasma turbulence. The finite crossfield correlation length of plasma turbulence combined with spatial variations in the magnetic field direction are used to obtain spatially localized turbulence...
Directory of Open Access Journals (Sweden)
Wang Zhenhua
2015-02-01
Full Text Available To improve the computational efficiency and hold calculation accuracy at the same time, we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method (DOM and the spatial domain decomposition parallelization (DDP are combined by message passing interface (MPI language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-, two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.
Kolomenskiy, Dmitry; Schneider, Kai
2014-01-01
We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretisation and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.
Spontaneous breaking of discrete symmetries in QCD on a small volume
Lucini, Biagio; Pica, Claudio
2007-01-01
In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C), spatial reflection (P) and time reversal (T) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show that a physical signature for the symmetry breaking is a persistent baryonic current wrapping in the compact directions. The existence of such a current is derived analytically at first order in perturbation theory and confirmed in the non-perturbative regime by lattice simulations.
High-throughput in-volume processing in glass with isotropic spatial resolutions in three dimensions
Tan, Yuanxin; Chu, Wei; Liao, Yang; Qiao, Lingling; Cheng, Ya
2016-01-01
We report on fabrication of three dimensional (3D) microstructures in glass with isotropic spatial resolutions. To achieve high throughput fabrication, we expand the focal spot size with a low-numerical-aperture lens, which naturally results in a degraded axial resolution. We solve the problem with simultaneous spatial temporal focusing which leads to an isotropic laser-affected volume with a spatial resolution of ~100 micron.
A Spatial Visual Words of Discrete Image Scene for Indoor Localization
Directory of Open Access Journals (Sweden)
Abbas M. Ali
2014-04-01
Full Text Available One of the fundamental problems in accurate indoor place recognition is the presence of similar scene images in different places in the environmental space of the mobile robot, such as the presence of computer or office table in many rooms. This problem causes bewilderment and confusion among different places. To overcome this, the local features of these image scenes should be represented in more discriminate and more robust way. However to perform this, the spatial relation of the local features should be considered. This study introduces a novel approach for place recognition based on correlation degree for the entropy of covariance feature vectors. In fact, these feature vectors are being extracted from the minimum distance of SIFT grid features of the image scene and optimized K entries from the codebook which is constructed by K means. The Entropy of Covariance features (ECV issued to represent the scene image in order to remove the confusion of similar images that are related to different places. The conclusion observed from the acquired results showed that this approach has a stable manner due to its reliability in the place recognition for the robot localization and outperforms the other approaches. Finally, the proposed ECV approach gives an intelligent way for the robot localization through the correlation of entropy covariance feature vectors for the scene images.
Deen, Niels G.; Sint Annaland, van Martin; Kuipers, J.A.M.
2007-01-01
In this paper a hybrid model is presented for the numerical simulation of gas-liquid-solid flows using a combined Volume Of Fluid (VOF) and Discrete Particle (DP) approach applied for respectively dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP mo
Deen, Niels G.; Sint Annaland, van Martin; Kuipers, J.A.M.
2006-01-01
In this paper a hybrid model is presented for the numerical simulation of gas-liquid-solid flows using a combined Volume Of Fluid (VOF) and Discrete Particle (DP) approach applied for respectively dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP mo
Zhang, Wenjuan; Al Kobaisi, Mohammed
2017-10-01
A novel Two-Step cell-centered Finite Volume Method (TSFVM) is developed in this work to discretize the heterogeneous and anisotropic pressure equation on triangular and quadrilateral grids in 2D and hexahedral and tetrahedral grids in 3D. Physical properties such as permeability and porosity are piece-wise constant on each grid cell. In the first step, the Galerkin Finite Element Method (FEM) is utilized to compute pressure solutions at all cell vertices. In the second step, pressure values at cell vertices are used to derive continuous two-point flux stencils for cell faces. Mass conservation equations are then written for each cell to obtain a system of linear equations that can be solved for pressure at cell centers. Extensive numerical experiments are carried out to test the performance of our TSFVM. In particular, we compare TSFVM with the classical Multipoint Flux Approximation (MPFA-O) method as well as a more recently developed MPFA method with full pressure support called enhanced MPFA (eMPFA). The results show that the TSFVM compares well with eMPFA for challenging test cases for which MPFA-O breaks down. Specifically, and as a significant step forward, our TSFVM is quite robust for challenging problems involving heterogeneous and highly anisotropic permeability tensors when both MPFA-O and eMPFA suffer from unphysical oscillations. Finally, the numerical convergence study demonstrates that TSFVM has comparable convergence behavior to MPFA-O method for both homogeneous and discontinuous permeability fields.
How to get spatial resolution inside probe volumes of commercial 3D LDA systems
Energy Technology Data Exchange (ETDEWEB)
Strunck, V.; Sodomann, T.; Mueller, H.; Dopheide, D. [Section of Fluid Flow Measuring Techniques, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116, Braunschweig (Germany)
2004-01-01
In laser Doppler anemometry (LDA) it is often the aim to determine the velocity profile for a given fluid flow. The spatial resolution of such velocity profiles is limited in principal by the size of the probe volume. The method of using time of flight data from two probe volumes allows improvements of the spatial resolution by at least one order of magnitude and measurements of small-scale velocity profiles inside the measuring volume along the optical axis of commercial available 3D anemometers without moving the probe. No change of the optical set-up is necessary. An increased spatial resolution helps to acquire more precise data in areas where the flow velocity changes rapidly as shown in the vicinity of the stagnation point of a cuboid. In the overlapping region of three measuring volumes a spatially resolved 3D velocity vector profile is obtained in the direction of the optical axis in near plane flow conditions. In plane laminar flows the probe volume is extended by a few millimetres. The limitation of the method to a plane flow is that it would require a two-component LDA in a very special off-axis arrangement, but this arrangement is available in most commercial 3D systems. (orig.)
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Directory of Open Access Journals (Sweden)
Olympia eKremmyda
2016-03-01
Full Text Available Bilateral vestibulopathy (BVP is defined as the impairment or loss of function of either the labyrinths or the eighth nerves. Patients with total BVP due to bilateral vestibular nerve section exhibit difficulties in spatial memory and navigation and show a loss of hippocampal volume. In clinical practice, most patients do not have a complete loss of function but rather an asymmetrical residual functioning of the vestibular system. The purpose of the current study was to investigate navigational ability and hippocampal atrophy in BVP patients with residual vestibular function. Fifteen patients with BVP and a group of age- and gender- matched healthy controls were examined. Self-reported questionnaires on spatial anxiety and wayfinding were used to assess the applied strategy of wayfinding and quality of life. Spatial memory and navigation were tested directly using a virtual Morris Water Maze Task. The hippocampal volume of these two groups was evaluated by voxel-based morphometry. In the patients, the questionnaire showed a higher spatial anxiety and the Morris Water Maze Task a delayed spatial learning performance. MRI revealed a significant decrease in the gray matter mid-hippocampal volume (Left: p = 0.006, Z = 4.58, Right: p < 0.001, Z = 3.63 and posterior parahippocampal volume (Right: p = 0.005, Z = 4.65, Left: p < 0.001, Z = 3.87 compared to those of healthy controls. In addition, a decrease in hippocampal formation volume correlated with a more dominant route-finding strategy. Our current findings demonstrate that even partial bilateral vestibular loss leads to anatomical and functional
Arun, K. R.; Kraft, M.; Lukáčová-Medvid'ová, M.; Prasad, Phoolan
2009-02-01
We present a generalization of the finite volume evolution Galerkin scheme [M. Lukáčová-Medvid'ová, J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533- 562; M. Lukáčová-Medvid'ová, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.
One spatial dimensional finite volume three-body interaction for a short-range potential
Guo, Peng
2016-01-01
In this work, we use McGuire's model to describe scattering of three spinless identical particles in one spatial dimension, we first present analytic solutions of Faddeev's equation for scattering of three spinless particles in free space. The three particles interaction in finite volume is derived subsequently, and the quantization conditions by matching wave functions in free space and finite volume are presented in terms of two-body scattering phase shifts. The quantization conditions obtained in this work for short range interaction are L\\"uscher's formula like and consistent with Yang's results in \\cite{Yang:1967bm}.
Ewerlöf, Maria; Larsson, Marcus; Salerud, E. Göran
2017-02-01
Hyperspectral imaging (HSI) can estimate the spatial distribution of skin blood oxygenation, using visible to near-infrared light. HSI oximeters often use a liquid-crystal tunable filter, an acousto-optic tunable filter or mechanically adjustable filter wheels, which has too long response/switching times to monitor tissue hemodynamics. This work aims to evaluate a multispectral snapshot imaging system to estimate skin blood volume and oxygen saturation with high temporal and spatial resolution. We use a snapshot imager, the xiSpec camera (MQ022HG-IM-SM4X4-VIS, XIMEA), having 16 wavelength-specific Fabry-Perot filters overlaid on the custom CMOS-chip. The spectral distribution of the bands is however substantially overlapping, which needs to be taken into account for an accurate analysis. An inverse Monte Carlo analysis is performed using a two-layered skin tissue model, defined by epidermal thickness, haemoglobin concentration and oxygen saturation, melanin concentration and spectrally dependent reduced-scattering coefficient, all parameters relevant for human skin. The analysis takes into account the spectral detector response of the xiSpec camera. At each spatial location in the field-of-view, we compare the simulated output to the detected diffusively backscattered spectra to find the best fit. The imager is evaluated for spatial and temporal variations during arterial and venous occlusion protocols applied to the forearm. Estimated blood volume changes and oxygenation maps at 512x272 pixels show values that are comparable to reference measurements performed in contact with the skin tissue. We conclude that the snapshot xiSpec camera, paired with an inverse Monte Carlo algorithm, permits us to use this sensor for spatial and temporal measurement of varying physiological parameters, such as skin tissue blood volume and oxygenation.
Konstantinou, Nikos; Constantinidou, Fofi; Kanai, Ryota
2017-02-01
Working memory is responsible for keeping information in mind when it is no longer in view, linking perception with higher cognitive functions. Despite such crucial role, short-term maintenance of visual information is severely limited. Research suggests that capacity limits in visual short-term memory (VSTM) are correlated with sustained activity in distinct brain areas. Here, we investigated whether variability in the structure of the brain is reflected in individual differences of behavioral capacity estimates for spatial and object VSTM. Behavioral capacity estimates were calculated separately for spatial and object information using a novel adaptive staircase procedure and were found to be unrelated, supporting domain-specific VSTM capacity limits. Voxel-based morphometry (VBM) analyses revealed dissociable neuroanatomical correlates of spatial versus object VSTM. Interindividual variability in spatial VSTM was reflected in the gray matter density of the inferior parietal lobule. In contrast, object VSTM was reflected in the gray matter density of the left insula. These dissociable findings highlight the importance of considering domain-specific estimates of VSTM capacity and point to the crucial brain regions that limit VSTM capacity for different types of visual information. Hum Brain Mapp 38:767-778, 2017. © 2016 Wiley Periodicals, Inc.
Raimonet, M.; Oudin, L.; Rabouille, C.; Garnier, J.; Silvestre, M.; Vautard, R.; Thieu, V.
2016-12-01
Water quality management of fresh and marine aquatic systems requires modelling tools along the land-ocean continuum in order to evaluate the effect of climate change on nutrient transfer and on potential ecosystem dysfonctioning (e.g. eutrophication, anoxia). In addition to direct effects of climate change on water temperature, it is essential to consider indirect effects of precipitation and temperature changes on hydrology since nutrient transfers are particularly sensitive to the partition of streamflow between surface flow and baseflow. Yet, the determination of surface flow and baseflow, their spatial repartition on drainage basins, and their relative potential evolution under climate change remains challenging. In this study, we developed a generic approach to determine 10-day surface flow and baseflow using a regionalized hydrological model applied at a high spatial resolution (unitary catchments of area circa 10km²). Streamflow data at gauged basins were used to calibrate hydrological model parameters that were then applied on neighbor ungauged basins to estimate streamflow at the scale of the French territory. The proposed methodology allowed representing spatialized surface flow and baseflow that are consistent with climatic and geomorphological settings. The methodology was then used to determine the effect of climate change on the spatial repartition of surface flow and baseflow on the Seine drainage bassin. Results showed large discrepancies of both the amount and the spatial repartition of changes of surface flow and baseflow according to the several GCM and RCM used to derive projected climatic forcing. Consequently, it is expected that the impact of climate change on nutrient transfer might also be quite heterogeneous for the Seine River. This methodology could be applied in any drainage basin where at least several gauged hydrometric stations are available. The estimated surface flow and baseflow can then be used in hydro-ecological models in
Directory of Open Access Journals (Sweden)
Szu-Wei Lee
2014-03-01
Full Text Available Knowledge of the discrete cosine transform coefficient distribution (DCT-DIST is important for the encoder design. For example, rate control relies on this knowledge to estimate a possible bit rate and then decide proper coding parameters before the actual encoding task is performed. Therefore the rate control performance is fairly dependent on how accurately the DCT-DIST is modelled. The spatial enhancement layer (SL DCT-DIST for H.264 scalable video coding (SVC is studied in this Letter. SL DCT-DIST knowledge is furthermore used to derive a novel rate model. Our results can help design a proper rate control module for the H.264/SVC encoder.
SpringSaLaD: A Spatial, Particle-Based Biochemical Simulation Platform with Excluded Volume.
Michalski, Paul J; Loew, Leslie M
2016-02-02
We introduce Springs, Sites, and Langevin Dynamics (SpringSaLaD), a comprehensive software platform for spatial, stochastic, particle-based modeling of biochemical systems. SpringSaLaD models biomolecules in a coarse-grained manner as a group of linked spherical sites with excluded volume. This mesoscopic approach bridges the gap between highly detailed molecular dynamics simulations and the various methods used to study network kinetics and diffusion at the cellular level. SpringSaLaD is a standalone tool that supports model building, simulation, visualization, and data analysis, all through a user-friendly graphical user interface that should make it more accessible than tools built into more comprehensive molecular dynamics infrastructures. Importantly, for bimolecular reactions we derive an exact expression relating the macroscopic on-rate to the various microscopic parameters with the inclusion of excluded volume; this makes SpringSaLaD more accurate than other tools, which rely on approximate relationships between these parameters.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Thomsen, Maria; Rasmussen, Christian Hove; Refsgaard, Hanne H F; Pedersen, Karen-Margrethe; Kirk, Rikke K; Poulsen, Mette; Feidenhans'l, Robert
2015-11-15
The spatial distribution of a soluble insulin formulation was visualized and quantified in 3-dimensions using X-ray computed tomography. The drug distribution was visualized for ex vivo injections in pig subcutaneous tissue. Pig subcutaneous tissue has very distinct layers, which could be separated in the tomographic reconstructions and the amount of drug in each tissue class was quantified. With a scan time of about 45min per sample, and a robust segmentation it was possible to analyze differences in the spatial drug distribution between several similar injections. It was studied how the drug distribution was effected by needle length, injection speed and injected volume. For an injected volume of 0.1ml and injection depth of 8mm about 50% of the injections were partly intramuscular. Using a 5mm needle resulted in purely subcutaneous injections with minor differences in the spatial drug distribution between injections. Increasing the injected volume from 0.1ml to 1ml did not increase the intramuscular volume fraction, but gave a significantly higher volume fraction placed in the fascia separating the deep and superficial subcutaneous fat layers. Varying the injection speed from 25l/s up to 300l/s gave no changes in the drug concentration distribution. The method presented gives novel insight into subcutaneous injections of soluble insulin drugs and can be used to optimize the injection technique for subcutaneous drug administration in preclinical studies of rodents. Copyright © 2015 Elsevier B.V. All rights reserved.
水文响应单元空间离散化及SWAT模型改进%Spatial discretization of hydrological response units and improved SWAT model
Institute of Scientific and Technical Information of China (English)
宁吉才; 刘高焕; 刘庆生; 谢传节
2012-01-01
水文响应单元(Hydrological Response Units,HRU)是SWAT模型模拟的基本单元,传统方法划分的水文响应单元在空间分布上不连续且难以确定其明确的空间位置,不能反映HRU间的相互作用和进行精确空间分析.利用GIS工具对土地利用和土壤类型数据进行概化处理,提出了HRU空间离散化的方法,实现了水文响应单元在空间上的准确定位.在此基础上,针对SWAT模型中同一子流域所有HRU采取相同延迟的弱点进行改进,并选择太湖地区西苕溪流域对改进的SWAT模型进行水文模拟验证.改进后,校正期港口站Nash效率系数ENS(Nash-Sutcliffe Efficiency)从0.64提高到0.67,验证期ENS系数从0.70提高到0.76.研究表明:修正后的SWAT模型更能反映流域的水文特征,可以达到非常好的效果,考虑到HRU距离因素的径流延迟更为准确地刻画径流过程.实现HRU空间离散化将为模型改进和更小尺度的空间分析提供数据基础.%The SWAT (Soil and Water Assessment Tools) is a physically based semi-distributed hydrological model. The basic computational unit in the SWAT is the hydrological response unit (HRU) that is usually determined by land uses, soil types, and slope and aspect of an area. Each HRU is assumed to have a homogeneous hydrological response. HRUs obtained with the traditional approaches for delineation of hydrologic response units are often spatially discontinuous and it is difficult to locate them in a catchment. The interaction among HRUs cannot be precisely described and analyzed. In this study, the land use and soil type data from a typical watershed in the Taihu Lake region are processed using the geographic information system ( GIS ) tools. A new approach for spatial discretization of hydro-logic response units is proposed and applied to the processed data. As the result, the location of each HRU in the watershed can be accurately identified. Accordingly, different values of the surface
Chen, Jianwu; Liu, Ping; Chen, Wenjuan; Bai, Penggang; Li, Jiangshan; Ni, Xiaolei; Chen, Kaiqiang; Li, Qixin
2016-12-01
To investigate the early changes of volume and spatial location in target and normal tissues caused by intensity-modulated radiotherapy (IMRT) for cervical cancer. Forty patients with cervical cancer were included in this study and treated by IMRT. Computed tomography (CT) was performed before radiotherapy and when the patient had received 27 Gy in 15 fractions. After image registration, the volume of interest (VOI) for the targets and organs at risk was delineated by clinicians on the CT images. Changes of volume, spatial location and Dice similarity were calculated for all VOIs. There were significant changes in gross tumor volume (GTV) in the primary tumor (GTV-T) with t = 8.304 (p<0.01) and visible pelvic lymph nodes (GTV-N) with t = 4.996 (p<0.01) caused by IMRT. The mean volume differences for GTV-T and GTV-N were 38.64% ± 19.50% (range 3.16%-86.49%) and 42.49% ± 25.68% (range 2.79%-87.42%), respectively. Among the organs at risk, the bladder had the greatest volume change with 55.13% ± 33.40% (range 3.25%-116.01%). The Dice similarity for GTV-T and GTV-N was 0.50 ± 0.18 (range 0.10-0.85) and 0.31 ± 0.20 (range 0.00-0.71), respectively. The rectum had the least Dice similarity among the normal tissues, with a mean value of 0.57 ± 0.14 (range 0.18-0.76). There were significant changes in volume and spatial location of the target and normal tissues after 27 Gy IMRT. In order to maintain the radiation dose to the targets and minimize the radiation to normal tissues, it is necessary to modify the radiotherapy planning.
Energy Technology Data Exchange (ETDEWEB)
McHugh, P.R.
1995-10-01
Fully coupled, Newton-Krylov algorithms are investigated for solving strongly coupled, nonlinear systems of partial differential equations arising in the field of computational fluid dynamics. Primitive variable forms of the steady incompressible and compressible Navier-Stokes and energy equations that describe the flow of a laminar Newtonian fluid in two-dimensions are specifically considered. Numerical solutions are obtained by first integrating over discrete finite volumes that compose the computational mesh. The resulting system of nonlinear algebraic equations are linearized using Newton`s method. Preconditioned Krylov subspace based iterative algorithms then solve these linear systems on each Newton iteration. Selected Krylov algorithms include the Arnoldi-based Generalized Minimal RESidual (GMRES) algorithm, and the Lanczos-based Conjugate Gradients Squared (CGS), Bi-CGSTAB, and Transpose-Free Quasi-Minimal Residual (TFQMR) algorithms. Both Incomplete Lower-Upper (ILU) factorization and domain-based additive and multiplicative Schwarz preconditioning strategies are studied. Numerical techniques such as mesh sequencing, adaptive damping, pseudo-transient relaxation, and parameter continuation are used to improve the solution efficiency, while algorithm implementation is simplified using a numerical Jacobian evaluation. The capabilities of standard Newton-Krylov algorithms are demonstrated via solutions to both incompressible and compressible flow problems. Incompressible flow problems include natural convection in an enclosed cavity, and mixed/forced convection past a backward facing step.
Zhu, Ming-Liang; Zhang, Qing-Hang; Lupton, Colin; Tong, Jie
2016-04-01
The measurement uncertainty of strains has been assessed in a bone analogue (sawbone), bovine trabecular bone and bone-cement interface specimens under zero load using the Digital Volume Correlation (DVC) method. The effects of sub-volume size, sample constraint and preload on the measured strain uncertainty have been examined. There is generally a trade-off between the measurement uncertainty and the spatial resolution. Suitable sub-volume sizes have been be selected based on a compromise between the measurement uncertainty and the spatial resolution of the cases considered. A ratio of sub-volume size to a microstructure characteristic (Tb.Sp) was introduced to reflect a suitable spatial resolution, and the measurement uncertainty associated was assessed. Specifically, ratios between 1.6 and 4 appear to give rise to standard deviations in the measured strains between 166 and 620 με in all the cases considered, which would seem to suffice for strain analysis in pre as well as post yield loading regimes. A microscale finite element (μFE) model was built from the CT images of the sawbone, and the results from the μFE model and a continuum FE model were compared with those from the DVC. The strain results were found to differ significantly between the two methods at tissue level, consistent in trend with the results found in human bones, indicating mainly a limitation of the current DVC method in mapping strains at this level.
Luo, Yuan; Gelsinger-Austin, Paul J; Watson, Jonathan M; Barbastathis, George; Barton, Jennifer K; Kostuk, Raymond K
2008-09-15
A three-dimensional imaging system incorporating multiplexed holographic gratings to visualize fluorescence tissue structures is presented. Holographic gratings formed in volume recording materials such as a phenanthrenquinone poly(methyl methacrylate) photopolymer have narrowband angular and spectral transmittance filtering properties that enable obtaining spatial-spectral information within an object. We demonstrate this imaging system's ability to obtain multiple depth-resolved fluorescence images simultaneously.
Ramirez-Lovering, Diego
2017-01-01
This PhD explores architectural contributions in the design and delivery of volume housing, which provides the most affordable housing option in the Australian market. The study develops different design strategies for incorporating spatial flexibility in four housing projects: The Dividable House, The Adaptable House, The Adaptable Apartment and The Flexible Townhouse, stemming from the Sustainable Affordable Home initiative (SAHI) and Designing Affordable Sustainable Housing (DASH). Thes...
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Wayfinding in the Blind: Larger Hippocampal Volume and Supranormal Spatial Navigation
Fortin, Madeleine; Voss, Patrice; Lord, Catherine; Lassonde, Maryse; Pruessner, Jens; Saint-Amour, Dave; Rainville, Constant; Lepore, Franco
2008-01-01
In the absence of visual input, the question arises as to how complex spatial abilities develop and how the brain adapts to the absence of this modality. We explored navigational skills in both early and late blind individuals and structural differences in the hippocampus, a brain region well known to be involved in spatial processing.…
Foster, Erin R.; Black, Kevin J.; Antenor-Dorsey, Jo Ann V.; Perlmutter, Joel S.; Hershey, Tamara
2008-01-01
Studies suggest motor deficit asymmetry may help predict the pattern of cognitive impairment in individuals with Parkinson disease (PD). We tested this hypothesis using a highly validated and sensitive spatial memory task, spatial delayed response (SDR), and clinical and neuroimaging measures of PD asymmetry. We predicted SDR performance would be…
Moskvin, Pavel; Kryzhanivskyy, Vyacheslav; Lytvyn, Petro; Rashkovetskyi, Liubomyr
2016-09-01
Multifractal (MF) analysis is used to describe volumes of spatial forms that are formed on the surface of thin layers of ZnxCd1-xTe solid solution grown on the Si (111) substrate. MF analysis is performed on the basis of AFM images of the solid solution surface. The parameters of the MF spectrums for the distribution of volumes of the spatial forms, which formed the surface relief, were found. On the basis of a formal approach and data on the multifractal parameters for the volume and the area of the surface spatial forms the mathematic expression which takes into account the contribution of the fractal surface structure in its surface energy were proposed. The behavior of the surface energy of the system depending on the fractal parameters that describe the volume and the area of the spatial forms on the fractal surface were discussed.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Directory of Open Access Journals (Sweden)
Augusto Hernández Vidal
2011-12-01
Full Text Available In order to strengthen the concept of municipal autonomy, this essay proposes an extensive interpretation of administrative discretion. Discretion is the exercise of free judgment given by law to authorities for performing official acts. This legislative technique seems to be suitable whenever the legislative is intended to legislate over the essential core of municipal autonomy. This way, an eventual abuse of that autonomy could be avoided, for the disproportional restriction of the local faculty to oversee the local issues. This alternative is presented as a tool to provide with dynamism the performing of administrative activities as well, aiming to assimilate public administration new practices.
Automated modelling of spatially-distributed glacier ice thickness and volume
James, William H. M.; Carrivick, Jonathan L.
2016-07-01
Ice thickness distribution and volume are both key parameters for glaciological and hydrological applications. This study presents VOLTA (Volume and Topography Automation), which is a Python script tool for ArcGISTM that requires just a digital elevation model (DEM) and glacier outline(s) to model distributed ice thickness, volume and bed topography. Ice thickness is initially estimated at points along an automatically generated centreline network based on the perfect-plasticity rheology assumption, taking into account a valley side drag component of the force balance equation. Distributed ice thickness is subsequently interpolated using a glaciologically correct algorithm. For five glaciers with independent field-measured bed topography, VOLTA modelled volumes were between 26.5% (underestimate) and 16.6% (overestimate) of that derived from field observations. Greatest differences were where an asymmetric valley cross section shape was present or where significant valley infill had occurred. Compared with other methods of modelling ice thickness and volume, key advantages of VOLTA are: a fully automated approach and a user friendly graphical user interface (GUI), GIS consistent geometry, fully automated centreline generation, inclusion of a side drag component in the force balance equation, estimation of glacier basal shear stress for each individual glacier, fully distributed ice thickness output and the ability to process multiple glaciers rapidly. VOLTA is capable of regional scale ice volume assessment, which is a key parameter for exploring glacier response to climate change. VOLTA also permits subtraction of modelled ice thickness from the input surface elevation to produce an ice-free DEM, which is a key input for reconstruction of former glaciers. VOLTA could assist with prediction of future glacier geometry changes and hence in projection of future meltwater fluxes.
Discrete breathers in crystals
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
Directory of Open Access Journals (Sweden)
Sascha Nink
2015-09-01
Full Text Available The availability of accurate and timely information on timber volume is important for supporting operational forest management. One option is to combine statistical concepts (e.g., small area estimates with specifically designed terrestrial sampling strategies to provide estimations also on the level of administrative units such as forest districts. This may suffice for economic assessments, but still fails to provide spatially explicit information on the distribution of timber volume within these management units. This type of information, however, is needed for decision-makers to design and implement appropriate management operations. The German federal state of Rhineland-Palatinate is currently implementing an object-oriented database that will also allow the direct integration of Earth observation data products. This work analyzes the suitability of forthcoming multi- and hyperspectral satellite imaging systems for producing local distribution maps for timber volume of Norway spruce, one of the most economically important tree species. In combination with site-specific inventory data, fully processed hyperspectral data sets (HyMap were used to simulate datasets of the forthcoming EnMAP and Sentinel-2 systems to establish adequate models for estimating timber volume maps. The analysis included PLS regression and the k-NN method. Root Mean Square Errors between 21.6% and 26.5% were obtained, where k-NN performed slightly better than PLSR. It was concluded that the datasets of both simulated sensor systems fulfill accuracy requirements to support local forest management operations and could be used in synergy. Sentinel-2 can provide meaningful volume distribution maps in higher geometric resolution, while EnMAP, due to its hyperspectral coverage, can contribute complementary information, e.g., on biophysical conditions.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Wild, Heather M; Heckemann, Rolf A; Studholme, Colin; Hammers, Alexander
2017-01-01
Accurately describing the anatomy of individual brains enables interlaboratory communication of functional and developmental studies and is crucial for possible surgical interventions. The human parietal lobe participates in multimodal sensory integration including language processing and also contains the primary somatosensory area. We describe detailed protocols to subdivide the parietal lobe, analyze morphological and volumetric characteristics, and create probabilistic atlases in MNI152 stereotaxic space. The parietal lobe was manually delineated on 3D T1 MR images of 30 healthy subjects and divided into four regions: supramarginal gyrus (SMG), angular gyrus (AG), superior parietal lobe (supPL) and postcentral gyrus (postCG). There was the expected correlation of male gender with larger brain and intracranial volume. We examined a wide range of anatomical features of the gyri and the sulci separating them. At least a rudimentary primary intermediate sulcus of Jensen (PISJ) separating SMG and AG was identified in nearly all (59/60) hemispheres. Presence of additional gyri in SMG and AG was related to sulcal features and volumetric characteristics. The parietal lobe was slightly (2%) larger on the left, driven by leftward asymmetries of the postCG and SMG. Intersubject variability was highest for SMG and AG, and lowest for postCG. Overall the morphological characteristics tended to be symmetrical, and volumes also tended to covary between hemispheres. This may reflect developmental as well as maturation factors. To assess the accuracy with which the labels can be used to segment newly acquired (unlabelled) T1-weighted brain images, we applied multi-atlas label propagation software (MAPER) in a leave-one-out experiment and compared the resulting automatic labels with the manually prepared ones. The results showed strong agreement (mean Jaccard index 0.69, corresponding to a mean Dice index of 0.82, average mean volume error of 0.6%). Stereotaxic probabilistic
Watanabe, Tomoaki; Nagata, Koji
2016-11-01
The mixing volume model (MVM), which is a mixing model for molecular diffusion in Lagrangian simulations of turbulent mixing problems, is proposed based on the interactions among spatially distributed particles in a finite volume. The mixing timescale in the MVM is derived by comparison between the model and the subgrid scale scalar variance equation. A-priori test of the MVM is conducted based on the direct numerical simulations of planar jets. The MVM is shown to predict well the mean effects of the molecular diffusion under various conditions. However, a predicted value of the molecular diffusion term is positively correlated to the exact value in the DNS only when the number of the mixing particles is larger than two. Furthermore, the MVM is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (ILES/LPS). The ILES/LPS with the present mixing model predicts well the decay of the scalar variance in planar jets. This work was supported by JSPS KAKENHI Nos. 25289030 and 16K18013. The numerical simulations presented in this manuscript were carried out on the high performance computing system (NEC SX-ACE) in the Japan Agency for Marine-Earth Science and Technology.
A Pipeline for Neuron Reconstruction Based on Spatial Sliding Volume Filter Seeding
Directory of Open Access Journals (Sweden)
Dong Sui
2014-01-01
Full Text Available Neuron’s shape and dendritic architecture are important for biosignal transduction in neuron networks. And the anatomy architecture reconstruction of neuron cell is one of the foremost challenges and important issues in neuroscience. Accurate reconstruction results can facilitate the subsequent neuron system simulation. With the development of confocal microscopy technology, researchers can scan neurons at submicron resolution for experiments. These make the reconstruction of complex dendritic trees become more feasible; however, it is still a tedious, time consuming, and labor intensity task. For decades, computer aided methods have been playing an important role in this task, but none of the prevalent algorithms can reconstruct full anatomy structure automatically. All of these make it essential for developing new method for reconstruction. This paper proposes a pipeline with a novel seeding method for reconstructing neuron structures from 3D microscopy images stacks. The pipeline is initialized with a set of seeds detected by sliding volume filter (SVF, and then the open curve snake is applied to the detected seeds for reconstructing the full structure of neuron cells. The experimental results demonstrate that the proposed pipeline exhibits excellent performance in terms of accuracy compared with traditional method, which is clearly a benefit for 3D neuron detection and reconstruction.
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mu-rong Jiang; Bo-ling Guo
2001-01-01
In this paper, Ginzburg-Landau equation coupled with BBM equationwith periodic initial boundary value conditions are discreted by the finite difference method in spatial direction. Existence of the attractors for the spatially discreted Ginzburg-Landau-BBM equations is proved. For each mesh size, there exist attractors for the discretized system. Moreover, finite Hausdorff and fractal dimensions of the discrete attractors are obtained and the bounds are independent of the mesh sizes.
Projected discrete ordinates methods for numerical transport problems
Energy Technology Data Exchange (ETDEWEB)
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Handbook of Spatial Statistics
Gelfand, Alan E
2010-01-01
Offers an introduction detailing the evolution of the field of spatial statistics. This title focuses on the three main branches of spatial statistics: continuous spatial variation (point referenced data); discrete spatial variation, including lattice and areal unit data; and, spatial point patterns.
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
1991-05-22
Eisenberg 1987). Among other formulations, the existing models are based on the theories of elasticity, hypoelasticity , plasticity and viscoplasticity...AD-A238 158 AFOSR4R. 91 069.1 A STUDY OF THE BEHAVIOR AND MICROMECHANICAL MODELLING OF GRANULAR SOIL DTIC VOLUME mI ELECTIE A NUMERICAL INVESTIGATION...Final 1/6/ 9-5/15/91 4. nU AN SUS"Ll5. FUNDING NUMBERS A Study of the Behavior and Micromechanical Modelling of Grant AFOSR-89-0350 Granular Soil PR
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Bodi, Geoffroy; Bérubé-Lauzière, Yves
2009-06-01
We recently developed a time-domain technique for localizing in 3D discrete fluorescent inclusions embedded in a scattering medium. It exploits early photon arrival times (EPATs), that is the time of flight of early arriving photons at a detector determined via numerical constant fraction discrimination. Our localization technique requires the knowledge of the speed of propagation of diffuse light pulses in the turbid medium to convert measured propagation times to distances. We have developed an experimental method for measuring the speed of propagation of such pulses. We have shown that time differences between a reference detector position and other positions around the medium allow finding the position of the inclusion. Our technique allows localizing inclusions to millimeter precision in a thick 5 cm diameter turbid medium. Herein, we analyze the stability of EPAT differences introduced above and propagation speeds with respect to changes in the medium's optical properties for optical properties typical of biological tissues. As we target small animal imaging, we concentrate on optical properties of mouse organs and tissues. Our objective is to determine bounds to be expected on the precision that can be achieved when media properties can vary and determine the limits of validity of our localization technique. Our results show that EPAT differences and propagation speeds obtained by our approach can vary; these values depend on the medium. We study 5 kinds of mouse organs and tissues. Propagations speeds are between 2.97 × 107ms-1 and 5.52 × 107ms-1. Thus, it becomes important to evaluate the discrepancy between true geometrical distance differences and distances as obtained by our approach using a constant propagation speed and the measurement of EPAT differences. It is such discrepancies that ultimately determine the localization accuracy of our algorithm because if distance differences based on EPATs are far from true distances, our algorithm although it
Directory of Open Access Journals (Sweden)
C. I. Lehmann
2012-07-01
Full Text Available Convective gravity wave (GW sources are spatially localized and emit at the same time waves with a wide spectrum of phase speeds. Any wave analysis therefore compromises between spectral and spatial resolution. Future satellite borne limb imagers will for a first time provide real 3-D volumes of observations. These volumes will be however limited which will impose further constraints on the analysis technique. In this study a three dimensional few-wave approach fitting sinusoidal waves to limited 3-D volumes is introduced. The method is applied to simulated GWs above typhoon Ewiniar and GW momentum flux is estimated from temperature fluctuations. Phase speed spectra as well as average profiles of positive, negative and net momentum fluxes are compared to momentum flux estimated by Fourier transform as well as spatial averaging of wind fluctuations. The results agree within 10–20%. The few-wave method can also reveal the spatial orientation of the GWs with respect to the source. The relevance of the results for different types of measurements as well as its applicability to model data is discussed.
CSIR Research Space (South Africa)
Roux, D
2007-08-01
Full Text Available This report forms the river component of the National Spatial Biodiversity Assessment, which focuses on spatial conservation assessments for South Africa’s terrestrial, river, marine, estuarine and wetland ecosystems. The results presented form...
Cagnoli, Bruno; Piersanti, Antonio
2017-02-01
We have carried out new three-dimensional numerical simulations by using a discrete element method (DEM) to study the mobility of dry granular flows of angular rock fragments. These simulations are relevant for geophysical flows such as rock avalanches and pyroclastic flows. The model is validated by previous laboratory experiments. We confirm that (1) the finer the grain size, the larger the mobility of the center of mass of granular flows; (2) the smaller the flow volume, the larger the mobility of the center of mass of granular flows and (3) the wider the channel, the larger the mobility of the center of mass of granular flows. The grain size effect is due to the fact that finer grain size flows dissipate intrinsically less energy. This volume effect is the opposite of that experienced by the flow fronts. The original contribution of this paper consists of providing a comparison of the mobility of granular flows in six channels with a different cross section each. This results in a new scaling parameter χ that has the product of grain size and the cubic root of flow volume as the numerator and the product of channel width and flow length as the denominator. The linear correlation between the reciprocal of mobility and parameter χ is statistically highly significant. Parameter χ confirms that the mobility of the center of mass of granular flows is an increasing function of the ratio of the number of fragments per unit of flow mass to the total number of fragments in the flow. These are two characteristic numbers of particles whose effect on mobility is scale invariant.
Three-phase flow simulations in discrete fracture networks
Geiger, S.; Niessner, J.; Matthai, S. K.; Helmig, R.
2006-12-01
Fractures are often the key conduits for fluid flow in otherwise low permeability rocks. Their presence in hydrocarbon reservoirs leads to complex production histories, unpredictable coupling of wells, rapidly changing flow rates, possibly early water breakthrough, and low final recovery. Recently, it has been demonstrated that a combination of finite volume and finite element discretization is well suited to model incompressible, immiscible two-phase flow in 3D discrete fracture networks (DFN) representing complexly fractured rocks. Such an approach has been commercialized in Golder Associates' FracMan Reservoir Edition software. For realistic reservoir simulations, however, it would be desirable if a third compressible gas phase can be included which is often present at reservoir conditions. Here we present the extension of an existing node-centred finite volume - finite element (FEFV) discretization for the efficient and accurate simulations of three-component - three-phase flow in geologically realistic representations of fractured porous media. Two possible types of fracture networks can be used: In 2D, they are detailed geometrical representations of fractured rock masses mapped in field studies. In 3D, they are geologically constrained, stochastically generated discrete fracture networks. Flow and transport can be simulated for fractures only or for fractures and matrix combined. The governing equations are solved decoupled using an implicit-pressure, explicit-saturation (IMPES) approach. Flux and concentration terms can be treated with higher-order accuracy in the finite volume scheme to preserve shock fronts. The method is locally mass conservative and works on unstructured, spatially refined grids. Flash calculations are carried out by a new description of the Black-Oil model. Capillary and gravity effects are included in this formulation. The robustness and accuracy of this formulation is shown in several applications. First, grid convergence is
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Energy Technology Data Exchange (ETDEWEB)
Stenta, Herman Roberto; Riccardi, Gerardo A; Basile, Pedro A [Universidad Nacional de Rosario (Mexico)
2008-07-15
Distributed hydrological models are suitable for the determination of time and space variability of hydrological responses within a given watershed. In a watershed, the model can be implemented with different levels of space resolution, mainly as a function of data availability, objectives of the numerical study, and requirements of the system to be modeled. In this paper, the effects on landscape representation due to different cell sizes are analyzed and scaling of parameters in a lower spatial resolution level is proposed in order to obtain similarity in hydrological responses between different degrees of discretization. The comparison was made in terms of maximum discharge, maximum flow velocity, and maximum water depth by simulating a number of observed and hypothetical hydrological events. The concept of total equilibrium state of the watershed was used. Under these circumstances, the roughness coefficients associated to overland and stream flow and the storage function of each discretization element were adjusted separately for the lower spatial resolution level. The results show that the similarity in hydrological responses, in terms of maximum water depth, obtained by adjusting the storage function of the cells, is better than that corresponding to the adjustment of roughness coefficients. [Spanish] Los modelos matematicos de parametros distribuidos resultan particularmente apropiados para determinar la variabilidad espacial y temporal de las respuestas hidrologicas dentro de un determinado sistema hidrico. En una cuenca es posible realizar la constitucion de un modelo con diferentes niveles de detalle en funcion principalmente de la disponibilidad de informacion de entrada necesaria, de los objetivos de estudio y de los requerimientos de modelado del sistema. En el presente trabajo se analizan los efectos producidos en la representacion del relieve debido a los diferentes tamanos de celda en que se ha discretizado una cuenca de llanura y se propone el
The remarkable discreteness of being
Indian Academy of Sciences (India)
Bahram Houchmandzadeh
2014-04-01
Life is a discrete, stochastic phenomenon: for a biological organism, the time of the two most important events of its life (reproduction and death) is random and these events change the number of individuals of the species by single units. These facts can have surprising, counterintuitive consequences. I review here three examples where these facts play, or could play, important roles: the spatial distribution of species, the structuring of biodiversity and the (Darwinian) evolution of altruistic behaviour.
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
The remarkable discreteness of being
Houchmandzadeh, Bahram
2013-01-01
Life is a discrete, stochastic phenomena : for a biological organism, the time of the two most important events of its life (reproduction and death) is random and these events change the number of individuals of the species by single units. These facts can have surprising, counter-intuitive consequences. I review here three examples where these facts play, or could play, important roles : the spatial distribution of species, the biodiversity and the (Darwinian) evolution of altruistic behavior.
Radiative transfer on discrete spaces
Preisendorfer, Rudolph W; Stark, M; Ulam, S
1965-01-01
Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles.Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative tran
Spurious haloes and discreteness-driven relaxation in cosmological simulations
Power, C.; Robotham, A. S. G.; Obreschkow, D.; Hobbs, A.; Lewis, G. F.
2016-10-01
There is strong evidence that cosmological N-body simulations dominated by warm dark matter (WDM) contain spurious or unphysical haloes, most readily apparent as regularly spaced low-mass haloes strung along filaments. We show that spurious haloes are a feature of traditional N-body simulations of cosmological structure formation models, including WDM and cold dark matter models, in which gravitational collapse proceeds in an initially anisotropic fashion, and arises naturally as a consequence of discreteness-driven relaxation. We demonstrate this using controlled N-body simulations of plane-symmetric collapse and show that spurious haloes are seeded at shell crossing by localized velocity perturbations induced by the discrete nature of the density field, and that their characteristic separation should be approximately the mean inter-particle separation of the N-body simulation, which is fixed by the mass resolution within the volume. Using cosmological N-body simulations in which particles are split into two collisionless components of fixed mass ratio, we find that the spatial distribution of the two components show signatures of discreteness-driven relaxation on both large and small scales. Adopting a spline kernel gravitational softening that is of order the comoving mean inter-particle separation helps to suppress the effect of discreteness-driven relaxation, but cannot eliminate it completely. These results provide further motivation for recent developments of new algorithms, which include, for example, revisions of the traditional N-body approach by means of spatially adaptive anistropric gravitational softenings or explicit solution of the evolution of dark matter in phase space.
Groupoids, Discrete Mechanics, and Discrete Variation
Institute of Scientific and Technical Information of China (English)
GUO Jia-Feng; JIA Xiao-Yu; WU Ke; ZHAO Wei-Zhong
2008-01-01
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.
Zhou, Jianqin
2011-01-01
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
Analysis of triangular C-grid finite volume scheme for shallow water flows
Shirkhani, Hamidreza; Mohammadian, Abdolmajid; Seidou, Ousmane; Qiblawey, Hazim
2015-08-01
In this paper, a dispersion relation analysis is employed to investigate the finite volume triangular C-grid formulation for two-dimensional shallow-water equations. In addition, two proposed combinations of time-stepping methods with the C-grid spatial discretization are investigated. In the first part of this study, the C-grid spatial discretization scheme is assessed, and in the second part, fully discrete schemes are analyzed. Analysis of the semi-discretized scheme (i.e. only spatial discretization) shows that there is no damping associated with the spatial C-grid scheme, and its phase speed behavior is also acceptable for long and intermediate waves. The analytical dispersion analysis after considering the effect of time discretization shows that the Leap-Frog time stepping technique can improve the phase speed behavior of the numerical method; however it could not damp the shorter decelerated waves. The Adams-Bashforth technique leads to slower propagation of short and intermediate waves and it damps those waves with a slower propagating speed. The numerical solutions of various test problems also conform and are in good agreement with the analytical dispersion analysis. They also indicate that the Adams-Bashforth scheme exhibits faster convergence and more accurate results, respectively, when the spatial and temporal step size decreases. However, the Leap-Frog scheme is more stable with higher CFL numbers.
Energy Technology Data Exchange (ETDEWEB)
Goes, E.G., E-mail: eggoes@terra.com.b [Regional Blood Center of Ribeirao Preto, Ribeirao Preto, SP (Brazil); Nicolucci, P.; Nali, I.C. [Physics and Mathematics Department, University of Sao Paulo, Ribeirao Preto, SP (Brazil); Pela, C.A.; Bruco, J.L. [Physics and Mathematics Department, University of Sao Paulo, Ribeirao Preto, SP (Brazil); Center of Instrumentation, Dosimetry and Radioprotection, University of Sao Paulo, Ribeirao Preto, SP (Brazil); Borges, J.C. [Center of Instrumentation, Dosimetry and Radioprotection, University of Sao Paulo, Ribeirao Preto, SP (Brazil); Covas, D.T. [Regional Blood Center of Ribeirao Preto, Ribeirao Preto, SP (Brazil); Center for Cell-Based Therapy, Ribeirao Preto Medical School, University of Sao Paulo, Ribeirao Preto, SP (Brazil)
2010-06-15
Blood irradiation can be performed using a dedicated blood irradiator or a teletherapy unit. A thermal device providing appropriate storage conditions during blood components irradiation with a teletherapy unit has been recently proposed. However, the most appropriated volume of the thermal device was not indicated. The goal of this study was to indicate the most appropriated blood volume for irradiation using a teletherapy unit in order to minimize both the dose heterogeneity in the volume and the blood irradiation time using these equipments. Theoretical and experimental methods were used to study the dose distribution in the blood volume irradiated using a linear accelerator and a cobalt-60 therapy machine. The calculation of absorbed doses in the middle plane of cylindrical acrylic volumes was accomplished by a treatment planning system. Experimentally, we also used cylindrical acrylic phantoms and thermoluminescent dosimeters to confirm the calculated doses. The data obtained were represented by isodose curves. We observed that an irradiation volume should have a height of 28 cm and a diameter of 28 cm and a height of 35 cm and a diameter of 35 cm, when the irradiation is to be performed by a linear accelerator and a cobalt-60 teletherapy unit, respectively. Calculated values of relative doses varied from 93% to 100% in the smaller volume, and from 66% to 100% in the largest one. A difference of 5.0%, approximately, was observed between calculated and experimental data. The size of these volumes permits the irradiation of blood bags in only one bath without compromising the homogeneity of the absorbed dose over the irradiated volume. Thus, these irradiation volumes can be recommend to minimize the irradiation time when a teletherapy unit is used to irradiate blood.
Góes, E. G.; Nicolucci, P.; Nali, I. C.; Pelá, C. A.; Bruço, J. L.; Borges, J. C.; Covas, D. T.
2010-06-01
Blood irradiation can be performed using a dedicated blood irradiator or a teletherapy unit. A thermal device providing appropriate storage conditions during blood components irradiation with a teletherapy unit has been recently proposed. However, the most appropriated volume of the thermal device was not indicated. The goal of this study was to indicate the most appropriated blood volume for irradiation using a teletherapy unit in order to minimize both the dose heterogeneity in the volume and the blood irradiation time using these equipments. Theoretical and experimental methods were used to study the dose distribution in the blood volume irradiated using a linear accelerator and a cobalt-60 therapy machine. The calculation of absorbed doses in the middle plane of cylindrical acrylic volumes was accomplished by a treatment planning system. Experimentally, we also used cylindrical acrylic phantoms and thermoluminescent dosimeters to confirm the calculated doses. The data obtained were represented by isodose curves. We observed that an irradiation volume should have a height of 28 cm and a diameter of 28 cm and a height of 35 cm and a diameter of 35 cm, when the irradiation is to be performed by a linear accelerator and a cobalt-60 teletherapy unit, respectively. Calculated values of relative doses varied from 93% to 100% in the smaller volume, and from 66% to 100% in the largest one. A difference of 5.0%, approximately, was observed between calculated and experimental data. The size of these volumes permits the irradiation of blood bags in only one bath without compromising the homogeneity of the absorbed dose over the irradiated volume. Thus, these irradiation volumes can be recommend to minimize the irradiation time when a teletherapy unit is used to irradiate blood.
Radix Representation of Triangular Discrete Grid System
Ben, J.; Li, Y. L.; Wang, R.
2016-11-01
Discrete Global Grid Systems (DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. It provides an organizational structure that permits fast integration between multiple sources of large and variable geospatial data. Although many endeavors have been done to describe certain discrete grid systems, there still lack of a uniform mathematical framework for them. This paper simplifies the planar class I aperture 4 triangular discrete grid system into a hierarchical lattice model which is proved to be a radix system in the complex number plane. Mathematical properties of the radix system reveal the discrete grid system is equivalent to the set of complex numbers with special form. The conclusion provides a potential way to build a uniform mathematical framework of DGGS and can be used to design efficient encoding and spatial operation scheme for DGGS.
Discrete Wigner function dynamics
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B; Munoz, C [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jalisco (Mexico)
2005-12-01
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
Finite-volume discretizations and immersed boundaries
Hassen, Y.J.; Koren, B.
2009-01-01
In this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed `Cartesian' grid. The essence of the present method is that speci
Zheng, Guoyan
2008-01-01
This paper addresses the problem of estimating the 3D rigid pose of a CT volume of an object from its 2D X-ray projections. We use maximization of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measure only takes intensity values into account without considering spatial information and its robustness is questionable. In this paper, instead of directly maximizing mutual information, we propose to use a variational approximation derived from the Kullback-Leibler bound. Spatial information is then incorporated into this variational approximation using a Markov random field model. The newly derived similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experimental results are presented on X-ray and CT datasets of a plastic phantom and a cadaveric spine segment.
Directory of Open Access Journals (Sweden)
Magnólia Fernandes Florêncio de Araújo
2008-02-01
Full Text Available The temporal and spatial fluctuations of Bacterioplankton in a fluvial-lagunar system of a tropical region (Pitimbu River and Jiqui Lake, RN were studied during the dry and the rainy periods. The bacterial abundance varied from 2.67 to 5.1 Cells10(7mL-1 and did not show a typical temporal variation, presenting only small oscillations between the rainy and the dry periods. The bacterial biomass varied from 123 µgC L-1 to 269 µgC L-1 in the sampling sites and the average cellular volume varied from 0.12 to 0.54µm³, showing a predominance of the rods. The temperature showed a positive correlation with the cellular volume of the rods (R=0.55; p=0.02 and vibrio (R=0.53; p=0.03. Significant spatial differences of biomass (Mann Whitney: p=0.01 and cellular volume of the morphotypes (Mann Whitney: p=0.003 were found between the sampling sites. The strong positive correlations of the water temperature and oxygen with bacterioplankton showed a probable high bacterial activity in this system.A variação temporal e espacial do bacterioplâncton em um sistema fluvial-lagunar de região tropical foi estudada em períodos seco e chuvoso. As médias da abundância bacteriana variaram de 2,67 a 5,1 x 10(7 e não exibiram uma variação temporal marcante, tendo apresentado apenas pequenas oscilações entre os períodos chuvoso e seco. A biomassa bacteriana variou de 123 µg C L-1 a 269 µg C L-1 entre os locais de coleta e o volume celular médio de 0,12µm³ a 0,54µm³, ocorrendo predominância de bacilos. A temperatura mostrou correlação positiva com o volume celular de bacilos (R=0,55; p=0,02 e de vibriões (R=0,53; p=0,03. Foram encontradas diferenças espaciais significativas de biomassa (Mann Whitney: p=0,01 e volume celular dos morfotipos (Mann Whitney: p= 0,003, entre os locais de coleta. As fortes correlações positivas da temperatura da água e do oxigênio, com o bacterioplâncton, são sugestivas de uma provavelmente elevada atividade
Directory of Open Access Journals (Sweden)
Niva Kiran Verma
2016-05-01
Full Text Available Studies estimating canopy volume are mostly based on laborious and time-consuming field measurements; hence, there is a need for easier and convenient means of estimation. Accordingly, this study investigated the use of remotely sensed data (WorldView-2 and LiDAR for estimating tree height, canopy height and crown diameter, which were then used to infer the canopy volume of remnant eucalypt trees at the Newholme/Kirby ‘SMART’ farm in north-east New South Wales. A regression model was developed with field measurements, which was then applied to remote-sensing-based measurements. LiDAR estimates of tree dimensions were generally lower than the field measurements (e.g., 6.5% for tree height although some of the parameters (such as tree height may also be overestimated by the clinometer/rangefinder protocols used. The WorldView-2 results showed both crown projected area and crown diameter to be strongly correlated to canopy volume, and that crown diameter yielded better results (Root Mean Square Error RMSE 31% than crown projected area (RMSE 42%. Although the better performance of LiDAR in the vertical dimension cannot be dismissed, as suggested by results obtained from this study and also similar studies conducted with LiDAR data for tree parameter measurements, the high price and complexity associated with the acquisition and processing of LiDAR datasets mean that the technology is beyond the reach of many applications. Therefore, given the need for easier and convenient means of tree parameters estimation, this study filled a gap and successfully used 2D multispectral WorldView-2 data for 3D canopy volume estimation with satisfactory results compared to LiDAR-based estimation. The result obtained from this study highlights the usefulness of high resolution data for canopy volume estimations at different locations as a possible alternative to existing methods.
Invariants of Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Modelling Mobility: A Discrete Revolution
Clementi, Andrea; Silvestri, Riccardo
2010-01-01
We introduce a new approach to model and analyze \\emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \\emph{Markov Trace} Model. This model can be seen as the discrete version of the \\emph{Random Trip} Model including all variants of the \\emph{Random Way-Point} Model \\cite{L06}. We derive fundamental properties and \\emph{explicit} analytical formulas for the \\emph{stationary distributions} yielded by the Markov Trace Model. Such results can be exploited to compute formulas and properties for concrete cases of the Markov Trace Model by just applying counting arguments. We apply the above general results to the discrete version of the \\emph{Manhattan Random Way-Point} over a square of bounded size. We get formulas for the total stationary distribution and for two important \\emph{conditional} ones: the agent spatial and destination distributions. Our method makes the analysis of complex mobile systems a feasible task. As a further evidence of this important...
The Random Discrete Action for 2-Dimensional Spacetime
Benincasa, Dionigi M T; Schmitzer, Bernhard
2010-01-01
A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.
The random discrete action for two-dimensional spacetime
Benincasa, Dionigi M. T.; Dowker, Fay; Schmitzer, Bernhard
2011-05-01
A one-parameter family of random variables, called the Discrete Action, is defined for a two-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this discrete action is calculated for various regions of 2D Minkowski spacetime, {M}^2. When a causally convex region of {M}^2 is divided into subregions using null lines the mean of the discrete action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to 0 as the discreteness scale is taken to 0. This result is used to predict that the mean of the discrete action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The 'topological' character of the discrete action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
A priori discretization error metrics for distributed hydrologic modeling applications
Liu, Hongli; Tolson, Bryan A.; Craig, James R.; Shafii, Mahyar
2016-12-01
Watershed spatial discretization is an important step in developing a distributed hydrologic model. A key difficulty in the spatial discretization process is maintaining a balance between the aggregation-induced information loss and the increase in computational burden caused by the inclusion of additional computational units. Objective identification of an appropriate discretization scheme still remains a challenge, in part because of the lack of quantitative measures for assessing discretization quality, particularly prior to simulation. This study proposes a priori discretization error metrics to quantify the information loss of any candidate discretization scheme without having to run and calibrate a hydrologic model. These error metrics are applicable to multi-variable and multi-site discretization evaluation and provide directly interpretable information to the hydrologic modeler about discretization quality. The first metric, a subbasin error metric, quantifies the routing information loss from discretization, and the second, a hydrological response unit (HRU) error metric, improves upon existing a priori metrics by quantifying the information loss due to changes in land cover or soil type property aggregation. The metrics are straightforward to understand and easy to recode. Informed by the error metrics, a two-step discretization decision-making approach is proposed with the advantage of reducing extreme errors and meeting the user-specified discretization error targets. The metrics and decision-making approach are applied to the discretization of the Grand River watershed in Ontario, Canada. Results show that information loss increases as discretization gets coarser. Moreover, results help to explain the modeling difficulties associated with smaller upstream subbasins since the worst discretization errors and highest error variability appear in smaller upstream areas instead of larger downstream drainage areas. Hydrologic modeling experiments under
Lee, Taeyoung; McClamroch, N Harris
2007-01-01
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics. In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability, controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of the corresponding control problems. Despite the critical role of geometry and mechanics in the analysis of nonlinear control systems, non...
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Burgin, Mark
2010-01-01
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. At the same time, continuous models that are in the background of discrete representations use mathematical technology developed for continuous media. The most important example of such a technology is calculus, which is so useful in physics and other sciences. The main goal of this paper is to synthesize continuous features and powerful technology of the classical calculus with the discrete approach of numerical mathematics and computational physics. To do this, we further develop the theory of fuzzy continuous functions and apply this theory to functions defined on discrete sets. The main interest is the classical Intermediate Value theorem. Although the result of this theorem is completely based on continuity, utilization of a relaxed version of contin...
Energy Technology Data Exchange (ETDEWEB)
Mejia, J.; Galvis-Alonso, O.Y. [Faculdade de Medicina de Sao Jose do Rio Preto (FAMERP), SP (Brazil). Faculdade de Medicina. Dept. de Biologia Molecular], e-mail: mejia_famerp@yahoo.com.br; Braga, J. [Faculdade de Medicina de Sao Jose do Rio Preto (FAMERP), SP (Brazil). Div. de Astrofisica; Correa, R. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Ciencia Espacial e Atmosferica; Leite, J.P. [Faculdade de Medicina de Sao Jose do Rio Preto (FAMERP), SP (Brazil). Dept. de Neurologia, Psiquiatria e Psicologia Medica; Simoes, M.V. [Faculdade de Medicina de Sao Jose do Rio Preto (FAMERP), SP (Brazil). Dept. de Clinica Medica
2009-08-15
Single-photon emission computed tomography (SPECT) is a non-invasive imaging technique, which provides information reporting the functional states of tissues. SPECT imaging has been used as a diagnostic tool in several human disorders and can be used in animal models of diseases for physiopathological, genomic and drug discovery studies. However, most of the experimental models used in research involve rodents, which are at least one order of magnitude smaller in linear dimensions than man. Consequently, images of targets obtained with conventional gamma-cameras and collimators have poor spatial resolution and statistical quality. We review the methodological approaches developed in recent years in order to obtain images of small targets with good spatial resolution and sensitivity. Multi pinhole, coded mask- and slit-based collimators are presented as alternative approaches to improve image quality. In combination with appropriate decoding algorithms, these collimators permit a significant reduction of the time needed to register the projections used to make 3-D representations of the volumetric distribution of target's radiotracers. Simultaneously, they can be used to minimize artifacts and blurring arising when single pinhole collimators are used. Representation images are presented, which illustrate the use of these collimators. We also comment on the use of coded masks to attain tomographic resolution with a single projection, as discussed by some investigators since their introduction to obtain near-field images. We conclude this review by showing that the use of appropriate hardware and software tools adapted to conventional gamma-cameras can be of great help in obtaining relevant functional information in experiments using small animals. (author)
Torus Bifurcation Under Discretization
Institute of Scientific and Technical Information of China (English)
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
Cortical Neural Computation by Discrete Results Hypothesis
Castejon, Carlos; Nuñez, Angel
2016-01-01
One of the most challenging problems we face in neuroscience is to understand how the cortex performs computations. There is increasing evidence that the power of the cortical processing is produced by populations of neurons forming dynamic neuronal ensembles. Theoretical proposals and multineuronal experimental studies have revealed that ensembles of neurons can form emergent functional units. However, how these ensembles are implicated in cortical computations is still a mystery. Although cell ensembles have been associated with brain rhythms, the functional interaction remains largely unclear. It is still unknown how spatially distributed neuronal activity can be temporally integrated to contribute to cortical computations. A theoretical explanation integrating spatial and temporal aspects of cortical processing is still lacking. In this Hypothesis and Theory article, we propose a new functional theoretical framework to explain the computational roles of these ensembles in cortical processing. We suggest that complex neural computations underlying cortical processing could be temporally discrete and that sensory information would need to be quantized to be computed by the cerebral cortex. Accordingly, we propose that cortical processing is produced by the computation of discrete spatio-temporal functional units that we have called “Discrete Results” (Discrete Results Hypothesis). This hypothesis represents a novel functional mechanism by which information processing is computed in the cortex. Furthermore, we propose that precise dynamic sequences of “Discrete Results” is the mechanism used by the cortex to extract, code, memorize and transmit neural information. The novel “Discrete Results” concept has the ability to match the spatial and temporal aspects of cortical processing. We discuss the possible neural underpinnings of these functional computational units and describe the empirical evidence supporting our hypothesis. We propose that fast
DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS
Institute of Scientific and Technical Information of China (English)
Qicheng Sun
2003-01-01
Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.
Directory of Open Access Journals (Sweden)
Yue Jiang
2016-03-01
Full Text Available In order to study the spatial breakup characteristics of the initial section of low-pressure jets, an experiment was performed to investigate the flow fields and concentration fields of jet flows with different nozzle geometric parameters and also the different working pressures using a particle image velocimetry system. The flow field of different axial planes, axial time-average velocity, and the length of the initial sections of jet flows were also analyzed. A numerical simulation was carried out using finite volume method and volume of fluid–level set method to describe the breaking process of the initial section, capturing unstable development of gas–fluid interface, measuring the length of the initial sections of jet flows. Both experiment and simulation results show that the broken degree of jet is more intense for nozzles with smaller aspect ratio; the outlet velocity of jet increases with the working pressure; and the value of u / u m decreases with the increase in pressures in the same cross section of jet flow. The experimental values are slightly higher than the simulation values with an error of <8% for the cross-sectional velocity distribution. The initial length of jet increases with pressures, where the experimental values are lower than the simulation values with an error of <5%. The experimental data from particle image velocimetry agreed well with the simulation results. Therefore, the accuracy and reliability of the particle image velocimetry experiment and the computational fluid dynamics result simulation were both validated.
San José Martínez, Fernando; Caniego, Javier; García-Gutiérrez, Carlos
2016-04-01
Lacunarity can be seen as a scale dependent measure of heterogeneity or texture ―in terms of image analysis― that was first introduced to quantify different patterns of dispersion and clustering that display geometrical objects with the same fractal dimension. Notwithstanding, lacunarity functions have been revealed as means to measure the deviation of object's geometrical structure from translational invariance beyond self-similarity and fractal geometry. In this work, we will explore how lacunarity quantifies different patterns of dispersion and clustering of different geometrical structures of soil macropore volumes imaged by X-ray computed tomography. Samples extracted from columns were collected at the experimental farm "Finca La Grajera" in La Rioja (Spain), property of La Rioja Regional Government (northern Spain). The vineyard selected was established in 1996. During the 1996 to 2004 period, the soil management was conventional tillage. Before the vineyard was established in 1996, a pasture-legume-cereal rotation was used. In 2004 an experiment was established with different types of soil cover management in between. On December 2010 columns were extracted vertically by percussion drilling between rows of the vineyard.
Discrete-event control of stochastic networks multimodularity and regularity
Altman, Eitan; Hordijk, Arie
2003-01-01
Opening new directions in research in both discrete event dynamic systems as well as in stochastic control, this volume focuses on a wide class of control and of optimization problems over sequences of integer numbers. This is a counterpart of convex optimization in the setting of discrete optimization. The theory developed is applied to the control of stochastic discrete-event dynamic systems. Some applications are admission, routing, service allocation and vacation control in queueing networks. Pure and applied mathematicians will enjoy reading the book since it brings together many disciplines in mathematics: combinatorics, stochastic processes, stochastic control and optimization, discrete event dynamic systems, algebra.
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
Energy Technology Data Exchange (ETDEWEB)
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Pearls of Discrete Mathematics
Erickson, Martin
2009-01-01
Presents methods for solving counting problems and other types of problems that involve discrete structures. This work illustrates the relationship of these structures to algebra, geometry, number theory and combinatorics. It addresses topics such as information and game theories
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
A priori discretization quality metrics for distributed hydrologic modeling applications
Liu, Hongli; Tolson, Bryan; Craig, James; Shafii, Mahyar; Basu, Nandita
2016-04-01
In distributed hydrologic modelling, a watershed is treated as a set of small homogeneous units that address the spatial heterogeneity of the watershed being simulated. The ability of models to reproduce observed spatial patterns firstly depends on the spatial discretization, which is the process of defining homogeneous units in the form of grid cells, subwatersheds, or hydrologic response units etc. It is common for hydrologic modelling studies to simply adopt a nominal or default discretization strategy without formally assessing alternative discretization levels. This approach lacks formal justifications and is thus problematic. More formalized discretization strategies are either a priori or a posteriori with respect to building and running a hydrologic simulation model. A posteriori approaches tend to be ad-hoc and compare model calibration and/or validation performance under various watershed discretizations. The construction and calibration of multiple versions of a distributed model can become a seriously limiting computational burden. Current a priori approaches are more formalized and compare overall heterogeneity statistics of dominant variables between candidate discretization schemes and input data or reference zones. While a priori approaches are efficient and do not require running a hydrologic model, they do not fully investigate the internal spatial pattern changes of variables of interest. Furthermore, the existing a priori approaches focus on landscape and soil data and do not assess impacts of discretization on stream channel definition even though its significance has been noted by numerous studies. The primary goals of this study are to (1) introduce new a priori discretization quality metrics considering the spatial pattern changes of model input data; (2) introduce a two-step discretization decision-making approach to compress extreme errors and meet user-specified discretization expectations through non-uniform discretization threshold
An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations
Directory of Open Access Journals (Sweden)
João Luiz F. Azevedo
2009-06-01
Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.
Control-volume representation of molecular dynamics.
Smith, E R; Heyes, D M; Dini, D; Zaki, T A
2012-05-01
A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] over a finite cubic volume of molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, which yields an equivalent to Reynolds' transport theorem for the discrete system. This approach casts the dynamics of the molecular system into a form that can be readily compared to the continuum equations. The MD equations of motion are reinterpreted in terms of a Lagrangian-to-control-volume (LCV) conversion function ϑ(i) for each molecule i. The LCV function and its spatial derivatives are used to express fluxes and relevant forces across the control surfaces. The relationship between the local pressures computed using the volume average [Lutsko, J. Appl. Phys. 64, 1152 (1988)] techniques and the method of planes [Todd et al., Phys. Rev. E 52, 1627 (1995)] emerges naturally from the treatment. Numerical experiments using the MD CV method are reported for equilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages of the formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideally suited to obtain macroscopic properties from a discrete system.
Zheng, Guoyan
2010-10-01
This paper addresses the problem of estimating the 3D rigid poses of a CT volume of an object from its 2D X-ray projection(s). We use maximization of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measures only take intensity values into account without considering spatial information and their robustness is questionable. In this paper, instead of directly maximizing mutual information, we propose to use a variational approximation derived from the Kullback-Leibler bound. Spatial information is then incorporated into this variational approximation using a Markov random field model. The newly derived similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experiments were conducted on datasets from two applications: (a) intra-operative patient pose estimation from a limited number (e.g. 2) of calibrated fluoroscopic images, and (b) post-operative cup orientation estimation from a single standard X-ray radiograph with/without gonadal shielding. The experiment on intra-operative patient pose estimation showed a mean target registration accuracy of 0.8mm and a capture range of 11.5mm, while the experiment on estimating the post-operative cup orientation from a single X-ray radiograph showed a mean accuracy below 2 degrees for both anteversion and inclination. More importantly, results from both experiments demonstrated that the newly derived similarity measures were robust to occlusions in the X-ray image(s).
Directory of Open Access Journals (Sweden)
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Discrete Classical Electromagnetic Fields
De Souza, M M
1997-01-01
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
Integral and discrete inequalities and their applications
Qin, Yuming
2016-01-01
This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Chen, Huangxin
2017-09-01
In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
A COMPARISON OF INTERCELL METRICS ON DISCRETE GLOBAL GRID SYSTEMS
A discrete global grid system (DGGS) is a spatial data model that aids in global research by serving as a framework for environmental modeling, monitoring and sampling across the earth at multiple spatial scales. Topological and geometric criteria have been proposed to evaluate a...
Tarasova, L.; Knoche, M.; Dietrich, J.; Merz, R.
2016-06-01
Glacierized high-mountainous catchments are often the water towers for downstream region, and modeling these remote areas are often the only available tool for the assessment of water resources availability. Nevertheless, data scarcity affects different aspects of hydrological modeling in such mountainous glacierized basins. On the example of poorly gauged glacierized catchment in Central Asia, we examined the effects of input discretization, model complexity, and calibration strategy on model performance. The study was conducted with the GSM-Socont model driven with climatic input from the corrected High Asia Reanalysis data set of two different discretizations. We analyze the effects of the use of long-term glacier volume loss, snow cover images, and interior runoff as an additional calibration data. In glacierized catchments with winter accumulation type, where the transformation of precipitation into runoff is mainly controlled by snow and glacier melt processes, the spatial discretization of precipitation tends to have less impact on simulated runoff than a correct prediction of the integral precipitation volume. Increasing model complexity by using spatially distributed input or semidistributed parameters values does not increase model performance in the Gunt catchment, as the more complex model tends to be more sensitive to errors in the input data set. In our case, better model performance and quantification of the flow components can be achieved by additional calibration data, rather than by using a more distributed model parameters. However, a semidistributed model better predicts the spatial patterns of snow accumulation and provides more plausible runoff predictions at the interior sites.
Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Dorlas, T. C.; Thomas, E. G. F.
2008-01-01
We construct a genuine Radon measure with values in B(l(2)(Z(d))) on the set of paths in Z(d) representing Feynman's integral for the discrete Laplacian on l(2)(Z(d)), and we prove the Feynman integral formula for the solutions of the Schrodinger equation with Hamiltonian H=-1/2 Delta+ V, where Delt
Bergstra, J.A.; Baeten, J.C.M.
1996-01-01
The axiom system ACP of [BeK84a] was extended with real time features in [BaB91]. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NiS94]. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. T
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
The discrete regime of flame propagation
Tang, Francois-David; Goroshin, Samuel; Higgins, Andrew
The propagation of laminar dust flames in iron dust clouds was studied in a low-gravity envi-ronment on-board a parabolic flight aircraft. The elimination of buoyancy-induced convection and particle settling permitted measurements of fundamental combustion parameters such as the burning velocity and the flame quenching distance over a wide range of particle sizes and in different gaseous mixtures. The discrete regime of flame propagation was observed by substitut-ing nitrogen present in air with xenon, an inert gas with a significantly lower heat conductivity. Flame propagation in the discrete regime is controlled by the heat transfer between neighbor-ing particles, rather than by the particle burning rate used by traditional continuum models of heterogeneous flames. The propagation mechanism of discrete flames depends on the spa-tial distribution of particles, and thus such flames are strongly influenced by local fluctuations in the fuel concentration. Constant pressure laminar dust flames were observed inside 70 cm long, 5 cm diameter Pyrex tubes. Equally-spaced plate assemblies forming rectangular chan-nels were placed inside each tube to determine the quenching distance defined as the minimum channel width through which a flame can successfully propagate. High-speed video cameras were used to measure the flame speed and a fiber optic spectrometer was used to measure the flame temperature. Experimental results were compared with predictions obtained from a numerical model of a three-dimensional flame developed to capture both the discrete nature and the random distribution of particles in the flame. Though good qualitative agreement was obtained between model predictions and experimental observations, residual g-jitters and the short reduced-gravity periods prevented further investigations of propagation limits in the dis-crete regime. The full exploration of the discrete flame phenomenon would require high-quality, long duration reduced gravity environment
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Brunner, Ilka; Plencner, Daniel
2014-01-01
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories. In the case of Landau-Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of `projective matrix factorisations', show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges. Roughly half of our results are not restricted to Landau-Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be be obtained by orbifo...
Discrete Variational Optimal Control
Jimenez, Fernando; de Diego, David Martin
2012-01-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.
Discrete Variational Optimal Control
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Linearity stabilizes discrete breathers
Indian Academy of Sciences (India)
T R Krishna Mohan; Surajit Sen
2011-11-01
The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi–Pasta–Ulam (FPU) and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced by the harmonic term stabilize the discrete breather by suppressing the breather’s tendency to delocalize and disperse. We conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these systems.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Heterogeneous Speed Profiles in Discrete Models for Pedestrian Simulation
Bandini, Stefania; Crociani, Luca; Vizzari, Giuseppe
2014-01-01
Discrete pedestrian simulation models are viable alternatives to particle based approaches based on a continuous spatial representation. The effects of discretisation, however, also imply some difficulties in modelling certain phenomena that can be observed in reality. This paper focuses on the possibility to manage heterogeneity in the walking speed of the simulated population of pedestrians by modifying an existing multi-agent model extending the floor field approach. Whereas some discrete ...
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely, a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, an...
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Karimi-Fard, M.; Durlofsky, L. J.
2016-10-01
A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.
Multiphase flow through porous media: an adaptive control volume finite element formulation
Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.
2012-12-01
Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.
Institute of Scientific and Technical Information of China (English)
李晟彬; 唐小明; 李志清; 殷君茹; 李惺颖
2016-01-01
According to the characteristics of spatial data and their relationships,we proposed a load balanced spatial vector data layout target,and combined with the specific environment,using the algorithm of spatial data layout based on graph coloring theory and data security mechanism of multiple replica.Spatial data deployed in parallel environment,and improved the execution efficiency and data security of task on the data nodes.Experimental results show that the layout method can achieve balanced layout of data, take into account the efficiency and security of the parallel computing,and adapt to more query applications.%根据空间数据的特点及其关系，提出一个负载均衡的空间矢量数据布局目标，并结合特定环境，采用基于图着色理论的空间数据布局算法及多副本的数据安全机制，提高了空间数据部署在并行环境下，数据节点上任务的执行效率和数据安全性。实验结果表明，该布局方法能实现数据的均衡布局，兼顾了并行计算的效率和安全性，适应并行计算下更多的查询应用。
Brauer, Fred; Feng, Zhilan; Castillo-Chavez, Carlos
2010-01-01
The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about decades ago. This gave a simple answer to the long-standing question of why epidemics woould appear suddenly and then disappear just as suddenly without having infected an entire population. Therefore it seemed natural to expect that theoreticians would immediately proceed to expand this mathematical framework both because the need to handle recurrent single infectious disease outbreaks has always been a priority for public health officials and because theoreticians often try to push the limits of exiting theories. However, the expansion of the theory via the inclusion of refined epidemiological classifications or through the incorporation of categories that are essential for the evaluation of intervention strategies, in the context of ongoing epidemic outbreaks, did not materialize. It was the global threat posed by SARS in that caused theoreticians to expand the Kermack-McKendrick single-outbreak framework. Most recently, efforts to connect theoretical work to data have exploded as attempts to deal with the threat of emergent and re-emergent diseases including the most recent H1N1 influenza pandemic, have marched to the forefront of our global priorities. Since data are collected and/or reported over discrete units of time, developing single outbreak models that fit collected data naturally is relevant. In this note, we introduce a discrete-epidemic framework and highlight, through our analyses, the similarities between single-outbreak comparable classical continuous-time epidemic models and the discrete-time models introduced in this note. The emphasis is on comparisons driven by expressions for the final epidemic size.
Observation of a Discrete Time Crystal
Zhang, J; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I -D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C
2016-01-01
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbat...
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
Energy Technology Data Exchange (ETDEWEB)
Leung, Terence S [Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT (United Kingdom); Tachtsidis, Ilias [Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT (United Kingdom); Smith, Martin [Department of Neuroanaesthesia and Neurocritical Care, The National Hospital for Neurology and Neurosurgery, London (United Kingdom); Delpy, David T [Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT (United Kingdom); Elwell, Clare E [Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT (United Kingdom)
2006-02-07
A hybrid differential and spatially resolved spectroscopy (SRS) technique has been developed to measure absolute absorption coefficient ({mu}{sub a}), reduced scattering coefficient ({mu}'{sub s}) and cerebral blood volume (CBV) in the adult human head. A spectrometer with both differential and SRS capabilities has been used to carry out measurements in 12 subjects. Two versions of the calculation have been considered using the hybrid technique, with one considering water as a chromophore as well as oxy- and deoxy-haemoglobin, and one ignoring water. The CBV has also been measured using a previously described technique based on changing the arterial saturation (SaO{sub 2}) measured separately by a pulse oximeter, resulting in mean {+-} SD CBV{sup a} (intra-individual coefficient of variation) = 2.22 {+-} 1.06 ml/100 g (29.9%). (The superscript on CBV indicates the different calculation basis.) Using the hybrid technique with water ignored, CBV{sup 0} = 3.18 {+-} 0.73 ml/100 g (10.0%), {mu}{sup 0}{sub a}(813 nm) = 0.010 {+-} 0.003 mm{sup -1} and {mu}'{sup 0}{sub s}(813 nm) = 1.19 {+-} 0.55 mm{sup -1} (data quoted at 813 nm). With water considered, CBV{sup w} = 3.05 {+-} 0.77 ml/100 g (10.5%), {mu}{sup w}{sub a}(813 nm) = 0.010 {+-} 0.003 mm{sup -1} and {mu}'{sup w}{sub s}(813 nm) = 1.28 {+-} 0.56 mm{sup -1}. The mean biases between CBV{sup 0}/CBV{sup w}, CBV{sup 0}/CBV{sup a} and CBV{sup w}/CBV{sup a} are 0.14 {+-} 0.09, 0.79 {+-} 1.22 and 0.65 {+-} 1.24 ml/100 g. The mean biases between {mu}{sup 0}{sub a}(813 nm)/{mu}{sup w}{sub a}(813 nm) and {mu}'{sup 0}{sub s}(813 nm)/{mu}'{sup w}{sub s}(813 nm) are (5.9 {+-} 10.0) x 10{sup -4} mm{sup -1} and -0.084 {+-} 0.266 mm{sup -1}, respectively. The method we describe extends the functionality of the current SRS instrumentation.
Reflection-free finite volume Maxwell's solver for adaptive grids
Elkina, Nina
2015-01-01
We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law. High spatial accuracy is achieved with help of non-oscillatory extrema preserving piece-wise or piece-wise-quadratic reconstructions. The semi-discrete equations are solved by implicit-explicit Runge-Kutta method. The new adaptive grid Maxwell's solver is examined based on several 1d examples, including the an propagation of a Gaussian pulse through vacuum and partially ionised gas. Two-dimensional extension is tested with a Gaussian pulse incident on dielectric disc. Additionally, we focus on testing computational accuracy and efficiency.
Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
Institute of Scientific and Technical Information of China (English)
LUO Xu-Dong; GUO Han-Ying; LI Yu-Qi; WU Ke
2004-01-01
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Discrete R Symmetries and Anomalies
Michael Dine(Santa Cruz Institute for Particle Physics and Department of Physics, Santa Cruz CA 95064, U.S.A.); Angelo Monteux(Santa Cruz Institute for Particle Physics, University of California Santa Cruz, 1156 High Street, Santa Cruz, U.S.A.)
2012-01-01
We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples...
Discrete solitons in coupled active lasing cavities
Prilepsky, Jaroslaw E; Johansson, Magnus; Derevyanko, Stanislav A
2012-01-01
We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active media, where the gain exceeds damping in the linear limit. A zoo of stable localized structures is found and classified: these are bright and grey cavity solitons with different symmetry. It is shown that several new types of solitons with a nontrivial intensity distribution pattern can emerge in the coupled cavities due to the stability of a periodic extended state. The latter can be stable even when a bistability of homogenous states is absent.
Angular Distributions of Discrete Mesoscale Mapping Functions
Directory of Open Access Journals (Sweden)
Kroszczyński Krzysztof
2015-08-01
Full Text Available The paper presents the results of analyses of numerical experiments concerning GPS signal propagation delays in the atmosphere and the discrete mapping functions defined on their basis. The delays were determined using data from the mesoscale non-hydrostatic weather model operated in the Centre of Applied Geomatics, Military University of Technology. A special attention was paid to investigating angular characteristics of GPS slant delays for low angles of elevation. The investigation proved that the temporal and spatial variability of the slant delays depends to a large extent on current weather conditions
Discrete Variational Approach for Modeling Laser-Plasma Interactions
Reyes, J. Paxon; Shadwick, B. A.
2014-10-01
The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie M.; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.
Discrete Thermodynamics of Lasers
Zilbergleyt, B
2007-01-01
The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic expression for such equilibrium is a logistic map, graphical solutions to which are pitchfork bifurcation diagrams. As pumping force increases, the relative populations on the ground and lasing branches tend to zero and unity correspondingly. An interesting feature of this model is the line spectrum of the up and down transitions between the branches beyond bifurcation point. Even in a simple case of 2-level laser with only 2 possible transition types (up and down), the spectra look like sets of the line packets, starting well before the population inversion. This effect is an independent confirmation of the Einstein's prohibition on practical realization of 2-level laser. Multilevel lasers may be approached by employing the idea of thermodynamic activity for the emitting atom...
Noyes, H. Pierre; Starson, Scott
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields with the relativistic Wheeler-Feynman action at a distance, allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound.
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P. (Stanford Linear Accelerator Center, Menlo Park, CA (USA)); Starson, S. (STARSON Corp. (USA))
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
Discrete Pearson distributions
Energy Technology Data Exchange (ETDEWEB)
Bowman, K.O. [Oak Ridge National Lab., TN (United States); Shenton, L.R. [Georgia Univ., Athens, GA (United States); Kastenbaum, M.A. [Kastenbaum (M.A.), Basye, VA (United States)
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Immigration and Prosecutorial Discretion.
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration.
McKenzie, Alan
2016-01-01
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic to the group of block universes containing all of the outcomes of all of the events, and so, in that sense, the group of block universes is a more fundamental representation. Different branches of the MWI tree, representing different universes in MWI, ultimately share the same quantum state in a common ancestor branch. This branching topology is incompatible with that of the Minkowski block universe; the resolution is to replace the branches with discrete, parallel block universes, each of which extends from the trunk to the outermost twigs. The number of universes in a branch is proportional to its thickness which, in turn, depends upon the absolute square of the probability amplitude for the state in that branch. Every quantum event may be represented by a kernel of unive...
Thermodynamics of discrete quantum processes
Anders, Janet; Giovannetti, Vittorio
2013-03-01
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Institute of Scientific and Technical Information of China (English)
黄建华; 路钢
2000-01-01
In this paper, we discuss the asymptotic behaviour of spatial disretization of Fitz-Hugh-Nagumo equations and bistable reaction diffusion equations with Neumamn boundary conditions, and the invariant regions, absorbing sets and global attractors are obtained and the estimation of Hausdorff dimension is given.%本文利用扰动方法，研究了Fitz-Hugh-Nagumo方程和双稳反应扩散方程在Neuman边值条件下空间离散后的渐近行为，证明了两个格微分方程组的不变区域、吸引集和整体吸引子的存在性，并给出了离散Fitz-Hugh-Nagumo方程的整体吸引子的Hausdorff维数估计．
The random discrete action for two-dimensional spacetime
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Dionigi M T; Dowker, Fay; Schmitzer, Bernhard, E-mail: db1808@ic.ac.uk [Theoretical Physics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ (United Kingdom)
2011-05-21
A one-parameter family of random variables, called the Discrete Action, is defined for a two-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this discrete action is calculated for various regions of 2D Minkowski spacetime, M{sup 2}. When a causally convex region of M{sup 2} is divided into subregions using null lines the mean of the discrete action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to 0 as the discreteness scale is taken to 0. This result is used to predict that the mean of the discrete action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The 'topological' character of the discrete action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Kvrekidis, Panayotis G
2009-01-01
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connection to applications, a subsequent analysis of the existence and the stability of fundamental nonlinear structures in 1, 2 and even 3 spatial lattice dimensions. It also covers the case of defocusing nonlinearities, the modulational instabilities of plane wave solutions, and the extension to multi-component lattices. In addition, it features a final chapter on special topics written by a wide array of experts in the field, addressing through short reviews, areas of particular recent interest.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
Lattice Boltzmann based discrete simulation for gas-solid fluidization
Wang, Limin; Wang, Xiaowei; Ge, Wei
2013-01-01
Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), SPH (Smoothed Particle Hydrodynamics), PIC (Particle-In-Cell), etc., is becoming a practical tool for exploring lab-scale gas-solid systems owing to the fast development of its parallel computation. However, the gas-solid coupling and the corresponding fluid flow solver remain immature. In this work, we presented a modified lattice Boltzmann approach to consider the effect of both the local solid volume fraction and the local relative velocity between the particles and the fluid, which was different from the traditional volume-averaged Navier-Stokes equations. This approach is combined with a time-driven hard sphere algorithm to simulate the motion of individual particles in which particles interact with each other via hard-sphere collisions but the collision detection and motion of the particle are performed at constant time intervals, and the EMMS (energy minimization...
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, William S.; Einstein, Herbert H.; LaPoint, Paul R.; Eiben, Thorsten; Wadleigh, Eugene; Ivanova, Violeta
1998-12-01
This report summarizes research conducted for the Fractured Reservoir Discrete Feature Network Technologies Project. The five areas studied are development of hierarchical fracture models; fractured reservoir compartmentalization, block size, and tributary volume analysis; development and demonstration of fractured reservoir discrete feature data analysis tools; development of tools for data integration and reservoir simulation through application of discrete feature network technologies for tertiary oil production; quantitative evaluation of the economic value of this analysis approach.
Asynchronous discrete event schemes for PDEs
Stone, D.; Geiger, S.; Lord, G. J.
2017-08-01
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Discrete dynamics versus analytic dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2014-01-01
For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Roberts, Fred; Thrall, Robert
1983-01-01
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises be covered in one class, are included in most chapters. Some units can whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in ...
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions "chaos-order" is discussed.
Modéliser les dynamiques spatiales d’un tissu urbain dans la longue durée (en plan et en volume
Directory of Open Access Journals (Sweden)
Bastien Lefebvre
2012-04-01
Full Text Available Pour travailler sur les dynamiques spatiales du tissu urbain implanté sur l’amphithéâtre antique de Tours, nous avons engagé une réflexion sur l’organisation des données mobilisées. Isolées, celles-ci permettent d’obtenir des renseignements significatifs mais ponctuels sur l’occupation du site. L’analyse spatiale doit donc porter sur une mise en commun de ces informations. La modélisation des données selon la méthode HBDS (Hypergraph Based Data Structure apparaît comme une solution tout à fait efficace. Une déconstruction géographique des données historiques et archéologiques est alors nécessaire. Cette étape fondamentale permet en effet non seulement de rendre compte d’états successifs mais aussi des dynamiques spatiales.In order to understand the spatial dynamics of the urban fabric implanted on the site of the antique amphitheatre of Tours, it is necessary to analyse the data gathered. In isolation, this data allows for certain significant items of information to be collated concerning for example the occupation of the site, but this information is of a partial nature. Spatial analysis can only be based on the confrontation of different levels of data. Modelling data using the HBDS method (Hypergraph Based Data Structure emerges as an efficient method. The geographical deconstruction of the historical and archaeological data is first necessary. This preliminary stage allows not only to account for succeeding states but also to understand spatial dynamics.
Discrete Darboux transformation for discrete polynomials of hypergeometric type
Bangerezako, Gaspard
1998-03-01
The Darboux transformation, well known in second-order differential operator theory, is applied to the difference equations satisfied by the discrete hypergeometric polynomials (Charlier, Meixner-Kravchuk, Hahn).
The origin of discrete particles
Bastin, T
2009-01-01
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction
Cheng, Chingwen
2016-01-01
Green infrastructure serves as a critical no-regret strategy to address climate change mitigation and adaptation in climate action plans. Climate justice refers to the distribution of climate change-induced environmental hazards (e.g., increased frequency and intensity of floods) among socially vulnerable groups. Yet no index has addressed both climate justice and green infrastructure planning jointly in the USA. This paper proposes a spatial climate justice and green infrastructure assessmen...
Foundations of the probabilistic mechanics of discrete media
Axelrad, D R
1984-01-01
This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of s
On the mixed discretization of the time domain magnetic field integral equation
Ulku, Huseyin Arda
2012-09-01
Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.
The Discrete Fourier Transform on hexagonal remote sensing image
Li, Yalu; Ben, Jin; Wang, Rui; Du, Lingyu
2016-11-01
Global discrete grid system will subdivide the earth recursively to form a multi-resolution grid hierarchy with no Overlap and seamless which help build global uniform spatial reference datum and multi-source data processing mode which takes the position as the object and in the aspect of data structure supports the organization, process and analysis of the remote sensing big data. This paper adopts the base transform to realize the mutual transformation of square pixel and hexagonal pixel. This paper designs the corresponding discrete Fourier transform algorithm for any lattice. Finally, the paper show the result of the DFT of the remote sensing image of the hexagonal pixel.
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-05-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)
2016-05-16
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Causal Dynamics of Discrete Surfaces
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2014-03-01
Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
Discrete Event Programming with Simkit
Buss, Arnold
2001-01-01
This paper is a brief introduction to the use of Simkit, a software package for implementing Discrete Event Simulation (DES) models. Simkit is written in Java (for any operating system with Java 2TM ).
Multiscale expansions in discrete world
Indian Academy of Sciences (India)
Ömer Ünsal; Filiz Taşcan; Mehmet Naci Özer
2014-07-01
In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.
Discrete solitons in graphene metamaterials
Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail
2014-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...
Discrete solitons in graphene metamaterials
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
Doyle, Michael Robert
2016-01-01
This dissertation looks at the urban volume, in its natural and artificial materiality, as a source of potential for future urbanization. Underground resourcesâfor buildable space, geomaterials, groundwater and geothermal energyâtend to be addressed only as needs arise. This has historically led to conflicts between uses: basements and tunnels flooded by rising aquifers; drinking water sources endangered by infrastructures that carry pollutants into groundwater systems. The work was carri...
Energy Technology Data Exchange (ETDEWEB)
Goettler, Jens; Preibisch, Christine [TU Muenchen, Department of Neuroradiology, Klinikum rechts der Isar, Munich (Germany); TU Muenchen, TUM Neuroimaging Center (TUM-NIC), Klinikum rechts der Isar, Munich (Germany); Lukas, Mathias; Mustafa, Mona; Schwaiger, Markus; Pyka, Thomas [TU Muenchen, Department of Nuclear Medicine, Klinikum rechts der Isar, Munich (Germany); Kluge, Anne; Kaczmarz, Stephan; Zimmer, Claus [TU Muenchen, Department of Neuroradiology, Klinikum rechts der Isar, Munich (Germany); Gempt, Jens; Ringel, Florian; Meyer, Bernhard [TU Muenchen, Department of Neurosurgery, Klinikum rechts der Isar, Munich (Germany); Foerster, Stefan [TU Muenchen, TUM Neuroimaging Center (TUM-NIC), Klinikum rechts der Isar, Munich (Germany); TU Muenchen, Department of Nuclear Medicine, Klinikum rechts der Isar, Munich (Germany); Klinikum Bayreuth, Department of Nuclear Medicine, Bayreuth (Germany)
2017-03-15
{sup 18}F-fluorethyltyrosine-(FET)-PET and MRI-based relative cerebral blood volume (rCBV) have both been used to characterize gliomas. Recently, inter-individual correlations between peak static FET-uptake and rCBV have been reported. Herein, we assess the local intra-lesional relation between FET-PET parameters and rCBV. Thirty untreated glioma patients (27 high-grade) underwent simultaneous PET/MRI on a 3 T hybrid scanner obtaining structural and dynamic susceptibility contrast sequences. Static FET-uptake and dynamic FET-slope were correlated with rCBV within tumour hotspots across patients and intra-lesionally using a mixed-effects model to account for inter-individual variation. Furthermore, maximal congruency of tumour volumes defined by FET-uptake and rCBV was determined. While the inter-individual relationship between peak static FET-uptake and rCBV could be confirmed, our intra-lesional, voxel-wise analysis revealed significant positive correlations (median r = 0.374, p < 0.0001). Similarly, significant inter- and intra-individual correlations were observed between FET-slope and rCBV. However, rCBV explained only 12% of the static and 5% of the dynamic FET-PET variance and maximal overlap of respective tumour volumes was 37% on average. Our results show that the relation between peak values of MR-based rCBV and static FET-uptake can also be observed intra-individually on a voxel basis and also applies to a dynamic FET parameter, possibly determining hotspots of higher biological malignancy. However, just a small part of the FET-PET signal variance is explained by rCBV and tumour volumes determined by the two modalities showed only moderate overlap. These findings indicate that FET-PET and MR-based rCBV provide both congruent and complimentary information on glioma biology. (orig.)
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds
Directory of Open Access Journals (Sweden)
Vojtěch Uher
2016-01-01
Full Text Available The Differential Evolution (DE is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE applying the principle of the discrete-coded DE in discrete point clouds (PCs. The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.
Uher, Vojtěch; Gajdoš, Petr; Radecký, Michal; Snášel, Václav
2016-01-01
The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.
Directory of Open Access Journals (Sweden)
M. P. Menguc
2011-09-01
Full Text Available We embark on this preliminary study of the suitability of the discrete dipole approximation with surface interaction (DDA-SI method to model electric field scattering from noble metal nano-structures on dielectric substrates. The refractive index of noble metals, particularly due to their high imaginary components, require smaller lattice spacings and are especially sensitive to the shape integrity and the volume of the dipole model. The results of DDA-SI method are validated against those of the well-established finite element method (FEM and the finite difference time domain (FDTD method.
Efficient discretization in finite difference method
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
A discrete element model for simulating saturated granular soil
Institute of Scientific and Technical Information of China (English)
Mahan Lamei; Ali Asghar Mirghasemi
2011-01-01
A numerical model is developed to simulate saturated granular soil,based on the discrete element method.Soil particles are represented by Lagrangian discrete elements,and pore fluid,by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space.Macroscale behavior of the model is verified by simulating undrained biaxial compression tests.Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests,it is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves.These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change,ultimately leading to liquefaction in loose sands.Thus,this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.
Relativity and the question of discretization in astronomy
Edelen, Dominic G B
1970-01-01
Theoretical researches in general relativity and observational data from galactic astronomy combine in this volume in contributions to one of the oldest questions of natural philosophy: Is the structure of the physical world more adequately described by a continuous or a discrete mode of representation? Since the days of the Pythagoreans, this question has surfaced from time to time in various guises in science as well as in philosophy. One of the most bitterly contested and illuminating controversies between the continuous and the discrete viewpoints is to be found in the wave versus corpuscular description of optical phenom enae. This controversy was not resolved to the satisfaction of most of its protaganists until the development of the quantum theory. However, several obscurities that still becloud the question suggest that some deeper formulation may be necessary before more satisfactory answers can be given 1. The firm establishment of the validity of quantized structure and discrete energy distribut...
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Quantum cosmology based on discrete Feynman paths
Energy Technology Data Exchange (ETDEWEB)
Chew, Geoffrey F.
2002-10-10
Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''.
Dimensional flow in discrete quantum geometries
Calcagni, Gianluca; Thürigen, Johannes
2014-01-01
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number $0<\\alpha
Nambu quantum mechanics on discrete 3-tori
Energy Technology Data Exchange (ETDEWEB)
Axenides, M [National Research Center ' Demokritos' , 15310 Aghia Paraskevi, Athens (Greece); Floratos, E G [Nuclear and Particle Physics Section, University of Athens, 15771 Athens (Greece); Nicolis, S [CNRS-Laboratoire de Mathematiques et Physique Theorique (UMR 6083) Federation Denis Poisson (FR 9164) Universite de Tours ' Francois Rabelais' , Parc Grandmont, 37200 Tours (France)], E-mail: axenides@inp.demokritos.gr, E-mail: mflorato@physics.uoa.gr, E-mail: Stam.Nicolis@lmpt.univ-tours.fr
2009-07-10
We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T{sub N}{sup 3} represented by elements of the group SL(3,Z{sub N}). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of T{sub N}{sup 3}. We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of a element of SL(3,Z{sub N}), which is an SL(2,Z{sub N}) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,Z{sub N}) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.
Forner-Cuenca, A.; Manzi-Orezzoli, V.; Kristiansen, P. M.; Gubler, L.; Schmidt, T. J.; Boillat, P.
2017-06-01
The spatial resolution aspects of the local modification of porous materials by electron induced graft-polymerization were studied by a combination of experiments and numerical simulations. Using blocking masks, only selected regions of the material were exposed to radiation and subsequently grafted. The main focus of this study is the application to gas diffusion layers, a carbonaceous 200 μm thick porous substrate widely used in fuel cells, with the goal of improving water management by locally tuning the wettability. The comparison of experiments performed with different electron energies and corresponding simulations shows good agreement, identifying the energy threshold necessary to graft through the material to be approximately 150 keV. The impact of electron energy on spatial resolution was studied, showing that the blurring effects due to electron scattering reach a maximum at around 200 keV and are reduced at higher electron energies. Finally, the numerical simulations were used to define the conditions necessary to selectively graft only parts of bi-layer fuel cell materials.
Serological evidence of discrete spatial clusters of Plasmodium falciparum parasites
DEFF Research Database (Denmark)
Bejon, Philip; Turner, Louise; Lavstsen, Thomas
2011-01-01
Malaria transmission may be considered to be homogenous with well-mixed parasite populations (as in the classic Ross/Macdonald models). Marked fine-scale heterogeneity of transmission has been observed in the field (i.e., over a few kilometres), but there are relatively few data on the degree of ...... of mixing. Since the Plasmodium falciparum Erythrocyte Membrane Protein 1 (PfEMP1) is highly polymorphic, the host's serological responses may be used to infer exposure to parasite sub-populations....
Discrete prostatic (paraprostatic) cysts in the dog.
Weaver, A D
1978-05-20
A description is given of the history, clinical features, surgery, outcome and pathology of 12 dogs with discrete prostatic cysts over 50 ml in volume. The dogs were middle-aged and presented with either urinary or alimentary signs or both. The cyst was usually palpable in the posterior abdomen as a smooth, non-painful mass, readily demonstrable on contrast radiography (pneumocystogram). Attempts were made to drain and resect the cysts, but resection often proved difficult due to its attachment to the region of bladder neck and ureters. In no case could the origin be shown to be from an enlarged uterus masculinus. The cyst content was invariably sterile, but its nature and the pathology of the cyst wall varied considerably between individuals. Since the long-term outcome was only satisfactory in three cases, the prognosis must be guarded.
Cosmology of biased discrete symmetry breaking
Gelmini, Graciela B.; Gleiser, Marcelo; Kolb, Edward W.
1988-01-01
The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.
Analysis of Discrete Mittag - Leffler Functions
Directory of Open Access Journals (Sweden)
N. Shobanadevi
2015-03-01
Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.
Stochastic discrete model of karstic networks
Jaquet, O.; Siegel, P.; Klubertanz, G.; Benabderrhamane, H.
Karst aquifers are characterised by an extreme spatial heterogeneity that strongly influences their hydraulic behaviour and the transport of pollutants. These aquifers are particularly vulnerable to contamination because of their highly permeable networks of conduits. A stochastic model is proposed for the simulation of the geometry of karstic networks at a regional scale. The model integrates the relevant physical processes governing the formation of karstic networks. The discrete simulation of karstic networks is performed with a modified lattice-gas cellular automaton for a representative description of the karstic aquifer geometry. Consequently, more reliable modelling results can be obtained for the management and the protection of karst aquifers. The stochastic model was applied jointly with groundwater modelling techniques to a regional karst aquifer in France for the purpose of resolving surface pollution issues.
A posteriori error estimator and AMR for discrete ordinates nodal transport methods
Energy Technology Data Exchange (ETDEWEB)
Duo, Jose I. [The Pennsylvania State University, 138 Reber Bldg, University Park (United States); Azmy, Yousry Y. [The Pennsylvania State University, 229 Reber Bldg, University Park (United States); Zikatanov, Ludmil T. [The Pennsylvania State University, 218 McAllister Bldg, University Park (United States)
2008-07-01
In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. Error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posterior error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L{sub 2} error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of discrete variables unknowns solved for to achieve a prescribed solution accuracy in global L{sub 2} error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns. (authors)
Spengler, Nils; Höfflin, Jens; Moazenzadeh, Ali; Mager, Dario; MacKinnon, Neil; Badilita, Vlad; Wallrabe, Ulrike; Korvink, Jan G
2016-01-01
We present a completely revised generation of a modular micro-NMR detector, featuring an active sample volume of ∼ 100 nL, and an improvement of 87% in probe efficiency. The detector is capable of rapidly screening different samples using exchangeable, application-specific, MEMS-fabricated, microfluidic sample containers. In contrast to our previous design, the sample holder chips can be simply sealed with adhesive tape, with excellent adhesion due to the smooth surfaces surrounding the fluidic ports, and so withstand pressures of ∼2.5 bar, while simultaneously enabling high spectral resolution up to 0.62 Hz for H2O, due to its optimised geometry. We have additionally reworked the coil design and fabrication processes, replacing liquid photoresists by dry film stock, whose final thickness does not depend on accurate volume dispensing or precise levelling during curing. We further introduced mechanical alignment structures to avoid time-intensive optical alignment of the chip stacks during assembly, while we exchanged the laser-cut, PMMA spacers by diced glass spacers, which are not susceptible to melting during cutting. Doing so led to an overall simplification of the entire fabrication chain, while simultaneously increasing the yield, due to an improved uniformity of thickness of the individual layers, and in addition, due to more accurate vertical positioning of the wirebonded coils, now delimited by a post base plateau. We demonstrate the capability of the design by acquiring a 1H spectrum of ∼ 11 nmol sucrose dissolved in D2O, where we achieved a linewidth of 1.25 Hz for the TSP reference peak. Chemical shift imaging experiments were further recorded from voxel volumes of only ∼ 1.5 nL, which corresponded to amounts of just 1.5 nmol per voxel for a 1 M concentration. To extend the micro-detector to other nuclei of interest, we have implemented a trap circuit, enabling heteronuclear spectroscopy, demonstrated by two 1H/13C 2D HSQC experiments.
Directory of Open Access Journals (Sweden)
Nils Spengler
Full Text Available We present a completely revised generation of a modular micro-NMR detector, featuring an active sample volume of ∼ 100 nL, and an improvement of 87% in probe efficiency. The detector is capable of rapidly screening different samples using exchangeable, application-specific, MEMS-fabricated, microfluidic sample containers. In contrast to our previous design, the sample holder chips can be simply sealed with adhesive tape, with excellent adhesion due to the smooth surfaces surrounding the fluidic ports, and so withstand pressures of ∼2.5 bar, while simultaneously enabling high spectral resolution up to 0.62 Hz for H2O, due to its optimised geometry. We have additionally reworked the coil design and fabrication processes, replacing liquid photoresists by dry film stock, whose final thickness does not depend on accurate volume dispensing or precise levelling during curing. We further introduced mechanical alignment structures to avoid time-intensive optical alignment of the chip stacks during assembly, while we exchanged the laser-cut, PMMA spacers by diced glass spacers, which are not susceptible to melting during cutting. Doing so led to an overall simplification of the entire fabrication chain, while simultaneously increasing the yield, due to an improved uniformity of thickness of the individual layers, and in addition, due to more accurate vertical positioning of the wirebonded coils, now delimited by a post base plateau. We demonstrate the capability of the design by acquiring a 1H spectrum of ∼ 11 nmol sucrose dissolved in D2O, where we achieved a linewidth of 1.25 Hz for the TSP reference peak. Chemical shift imaging experiments were further recorded from voxel volumes of only ∼ 1.5 nL, which corresponded to amounts of just 1.5 nmol per voxel for a 1 M concentration. To extend the micro-detector to other nuclei of interest, we have implemented a trap circuit, enabling heteronuclear spectroscopy, demonstrated by two 1H/13C 2D HSQC
Accurate implementation of leaping in space: The spatial partitioned-leaping algorithm
Iyengar, Krishna A; Clancy, Paulette; 10.1063/1.3310808
2010-01-01
There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in biology and nanoscale materials science, where the common assumptions of deterministic dynamics and well-mixed reaction volumes often break down. In this article, we present a spatial version of the partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic simulation approach built upon the tau-leaping framework of Gillespie. We pay special attention to the details of the implementation, particularly as it pertains to the time step calculation procedure. We point out conceptual errors that have been made in this regard in prior implementations of spatial tau-leaping and illustrate the manifestation of these errors through practical examples. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, su...
Quantum Trilogy: Discrete Toda, Y-System and Chaos
Yamazaki, Masahito
2016-01-01
We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra $G$, generalizing the previous construction of discrete quantum Liouville theory for the case $G=A_1$. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length $L$. In addition we also find a "discretized extra dimension" whose width is given by the rank $r$ of $G$, which decompactifies in the large $r$ limit. For the case of $G=A_N$ or $A_{N-1}^{(1)}$, we find a symmetry exchanging $L$ and $N$ under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is a quantizations of the so-called Y-system, and the theory can be well-described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmuller theory of type $A_N$.
Minisuperspace models of discrete systems
Baytaş, Bekir
2016-01-01
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building-up and stability of long-range correlations. Different types of homogeneous minisuperspace models are introduced for the system, including one based on condensate states, and shown to capture different aspects of the discrete system. They are evaluated with effective methods and by means of continuum limits, showing good agreement with operator calculations whenever the latter are available. As a possibly quite general result, it is concluded that an analysis of the building-up of long-range correlations in discrete systems requires non-perturbative solutions of the dynamical equations. Some questions related to stability can be analyzed perturbatively, but suggest that matter couplings may be relevant for this question in the context o...
Interference in discrete Wigner functions
Cormick, C; Cormick, Cecilia; Paz, Juan Pablo
2006-01-01
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We consider "cat" states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase-space (including the regions where the two interfering states are localized). This is a generic property which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this...
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Discrete Space-Time: History and Recent Developments
Crouse, David
2017-01-01
Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
DISCRETE ROTATIONS AND CELLULAR AUTOMATA
Nouvel, Bertrand
2006-01-01
In a discrete space, such as the set of integer-coordinate points, the modelization of isotropy may lead to noticeable theoretical difficulties. At this time, we do not know any gerometric theory on $\\ZZ^n$ that would be suitable to describe the isotropy the same way it is perceived by Euclidean geometry. With respect to this problematic, our aim is to describe some algorithms that would give to the discrete rotations some properties that would be similar to the properties of the Euclidean ro...
Stable discrete surface light bullets.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-01-22
We analyze spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides and demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons, the so-called discrete surface light bullets. We show that their properties are strongly affected by the presence of the surface. To this end the crossover between surface and quasi-bulk bullets is studied by analyzing the families of solitons propagating at different distances from the edge of the waveguide array.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Uniform Deterministic Discrete Method for Three Dimensional Systems
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
For radiative direct exchange areas in three dimensional system,the Uniform Deterministic Discrete Method(UDDM) was adopted.The spherical surface dividing method for sending area element and the regular icosahedron for sending volume element can meet with the direct exchange area computation of any kind of zone pairs.The numerical examples of direct exchange area in three dimensional system with nonhomogeneous attenuation coefficients indicated that the UDDM can give very high numercal accuracy.
Discrete Scale Axis Representations for 3D Geometry
Miklos, Balint; Giesen, Joachim; Pauly, Mark
2010-01-01
This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a spatially adaptive classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape repre...
Energy Technology Data Exchange (ETDEWEB)
Herrmann, K.P. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik; Mueller, W.H. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mechanical and Chemical Engineering; Neumann, S. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik
2001-07-01
The objective of our contribution is to present the discrete Fouriertransformation (DFT) as a serious alternative for the numerical computation of local stresses and strains in a two dimensional representative volume element (RVE) containing heterogeneities of complex shape and high volume fractions. The methodology is based on the application of the so-called ''equivalent inclusion method'' (Mura 1987). This method is used to devolve the original problem onto the determination of an auxiliary strain field which is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. The resulting partial differential equations (PDE) are firstly approximated by difference schemes leading to a linear system of equations (LSE) to solve. Two different types of difference schemes for an approximation are presented, a 9-pixelstar which is well-known in this context and a new one which uses 21 pixel for the numerical approach in order to increase the quality of the numerical solution. In a second step the DFT has been used which allows to solve the LSE analytically, obtaining a functional relation for the auxiliary strain field. Finally the solution of this equation is determined approximately by virtue of a Neumann iteration procedure. Different heterogeneity problems are considered where the accuracy of both difference stars is checked by existing analytical solutions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Gunzburger, Max
2013-03-12
The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.
Some discrete multiple orthogonal polynomials
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Solving discrete zero point problems
van der Laan, G.; Talman, A.J.J.; Yang, Z.F.
2004-01-01
In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and termi
A nonlocal discretization of fields
Campos, R G; Pimentel, L O; Campos, Rafael G.; Tututi, Eduardo S.
2001-01-01
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion doubling or the breaking of chiral symmetry for the massless case, are absent in this method.
Discrete breathers in Josephson ladders
Trias, E.; Mazo, J.J.; Brinkman, A.; Orlando, T.P.
2001-01-01
We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups [Phys. Rev. Lett. 84 (2000) 741; Phys. Rev. Lett. 84 (2000) 745; Phys.
Directory of Open Access Journals (Sweden)
David Eduardo Dávila
2012-12-01
Full Text Available The spatial distribution of Colombobalanus excelsa forests in the Cueva de los Guácharos Natural National Park and its buffer zone was determined. The forest’s structural parameters were determined by conducting a stratified forest inventory that consisted of four plots of 0.5 ha distributed in two strata. The first stratum was located in the park and the second in its buffer zone. Each strip consisted of plots of 20 x 50 m within which individuals with diameters at breast height = 10 cm DBH were measured for total height, crown diameter and the condition of each tree. Within each strip a 10 x 10 m subplot was used to assess individuals with DBH = 10 cm and heights greater than 3 m. In addition the number of seedlings of height = 0.3 m were counted in subplots of 5 x 5 m. Models were generated to estimate the height and volume as a function of DBH. We report a total of eight natural stands of black oak reaching 2000 ha of which 28.3 ha were found within the park. We report a density of 281.7 trees ha-1 with a basal area of 52.33 m2 ha-1 and a volume of 761.65 m3 ha-1. The form-factor for the species was of 0.76041. Six models were fitted to estimate the height and six for volume adjustments of 0.90 and 0.988, respectively.
Feki, Saber
2013-07-01
An explicit marching-on-in-time (MOT)-based time-domain volume integral equation (TDVIE) solver has recently been developed for characterizing transient electromagnetic wave interactions on arbitrarily shaped dielectric bodies (A. Al-Jarro et al., IEEE Trans. Antennas Propag., vol. 60, no. 11, 2012). The solver discretizes the spatio-temporal convolutions of the source fields with the background medium\\'s Green function using nodal discretization in space and linear interpolation in time. The Green tensor, which involves second order spatial and temporal derivatives, is computed using finite differences on the temporal and spatial grid. A predictor-corrector algorithm is used to maintain the stability of the MOT scheme. The simplicity of the discretization scheme permits the computation of the discretized spatio-temporal convolutions on the fly during time marching; no \\'interaction\\' matrices are pre-computed or stored resulting in a memory efficient scheme. As a result, most often the applicability of this solver to the characterization of wave interactions on electrically large structures is limited by the computation time but not the memory. © 2013 IEEE.
Dimitrov, Nikola; Koteski, Cane
2016-01-01
The professional book ,, Space planning "processed chapters on: space, concept and definition of space, space as a system, spatial economics, economic essence of space, space planning, social determinants of spatial planning, spatial planning as a process, factors development and elements in spatial planning, methodology, components and content of spatial planning stages and types of preparation of spatial planning, spatial planning and industrialization, industrialization, urbanization and s...
Dimitrov, Nikola; Koteski, Cane
2016-01-01
The professional book ,, Space planning "processed chapters on: space, concept and definition of space, space as a system, spatial economics, economic essence of space, space planning, social determinants of spatial planning, spatial planning as a process, factors development and elements in spatial planning, methodology, components and content of spatial planning stages and types of preparation of spatial planning, spatial planning and industrialization, industrialization, urbanization and s...
Continuous-Time Modeling with Spatial Dependence
Oud, J.H.L.; Folmer, H.; Patuelli, R.; Nijkamp, P.
2012-01-01
(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous-time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete
Continuous-Time Modeling with Spatial Dependence
Oud, J.; Folmer, H.; Patuelli, R.; Nijkamp, P.
(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous-time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete
Discrete implementations of scale transform
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
SDPG: Spatial Data Processing Grid
Institute of Scientific and Technical Information of China (English)
XIAO Nong(肖侬); FUV Wei(付伟)
2003-01-01
Spatial applications will gain high complexity as the volume of spatial data increases rapidly. A suitable data processing and computing infrastructure for spatial applications needs to be established. Over the past decade, grid has become a powerful computing environment for data intensive and computing intensive applications. Integrating grid computing with spatial data processing technology, the authors designed a spatial data processing grid (called SDPG) to address the related problems. Requirements of spatial applications are examined and the architecture of SDPG is described in this paper. Key technologies for implementing SDPG are discussed with emphasis.
Discrete Multiscale Analysis: A Biatomic Lattice System
Contra, G A Cassatella; 10.1142/S1402925110000957
2010-01-01
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\\"odinger differential equation.
Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds
Ibanez, L E; Uranga, A M
2012-01-01
Motivated by the necessity of discrete Z_N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)xU(2)xU(1)xU(1) and U(3)xSp(2)xU(1)xU(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z_2 (R-parity) and Z_3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Discrete gauge symmetries in discrete MSSM-like orientifolds
Ibáñez, L. E.; Schellekens, A. N.; Uranga, A. M.
2012-12-01
Motivated by the necessity of discrete ZN symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z2 (R-parity) and Z3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Hartmeyer, Ingo; Keuschnig, Markus; Delleske, Robert; Wichmann, Volker; Hoffmann, Thomas; Schrott, Lothar
2015-04-01
) calculation of uncertainty statistics. From 2009 until 2014 over 100 rockfall release zones have been detected. All rockfall events combined amount to a total volume of approx. 5000 m³. Two thirds of the detected rockfall release zones possess volumes release zones display volumes larger than 100 m³. The spatial distribution of the rockfall release zones displays a distinct pattern: 54% of the detected rockfall release zones are located triggered from areas located release zones located 15-30 m from the glacier surface. Thus, areas that have been exposed over the last 1-2 decades by the thinning of the Schmiedingerkees are particularly likely to be affected by rockfall.
Discretizing a backward stochastic differential equation
Yinnan Zhang; Weian Zheng
2002-01-01
We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.
Discrete and Continuous Linearizable Equations
Lafortune, S; Ramani, A
1998-01-01
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one and reduce the system to a single differential equation. This equation is of the form of those singled-out by Painlevé in his quest for integrable forms. In the discrete case, we extend previous results of ours showing that, again by elimination of variables, the general projective system can be written as a mapping for a single variable. We show that this mapping is a member of the family of multilinear systems (which is not integrable in general). The continuous limit of multilinear mappings is also discussed.
Discrete mathematics using a computer
Hall, Cordelia
2000-01-01
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Discrete fields on the lightcone
De Souza, M M
1997-01-01
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point- particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It results on a description of discrete (pointwise) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant $(1+1)$-dimensional dynamics in a $(3+1)$ spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete fields. Singularities are the by-products of the averaging proccess. This new formalism enlighten the meaning and the problems of field theory, and may allow a softer transition to a quantum th...
Discrete symmetries in the MSSM
Energy Technology Data Exchange (ETDEWEB)
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
National Oceanic and Atmospheric Administration, Department of Commerce — NODC Accession 0112171 includes profile, discrete sample and biological data collected aboard the NATHANIEL B. PALMER during cruises NBP0103, NBP0104, NBP0202 and...
National Oceanic and Atmospheric Administration, Department of Commerce — NODC Accession 0112170 includes profile, discrete sample and biological data collected aboard the LAURENCE M. GOULD during cruises LMG0104 and LMG0203 in the South...
Discrete mathematics: methods and challenges
Alon, Noga
2002-01-01
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight connection between Discrete Mathematics and Theoretical Computer Science, and the rapid development of the latter. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown ...
Manpower Analysis Using Discrete Simulation
2015-12-01
Course STA-21 Seaman to Admiral (21st century) SQL Structured Query Language TOS Time on Station xiv THIS PAGE INTENTIONALLY LEFT BLANK...using Simkit—a widely available library based in the Java programming language for building Discrete Event Simulation (DES) models. By overriding...intervals (i.e., quarterly), while holding attrition negligible. For the purposes of modeling each new accession to the system, the Arrival
Discretized configurations and partial partitions
Abrams, Aaron; Hower, Valerie
2010-01-01
We show that the discretized configuration space of $k$ points in the $n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$. This space is homeomorphic to the order complex of the poset of ordered partial partitions of $\\{1,\\...,n+1\\}$ with exactly $k$ parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.
DEFF Research Database (Denmark)
Rasmusson, Allan; Hahn, Ute; Larsen, Jytte Overgaard
2013-01-01
to identify the specific tissue region under study. In order to use the spatial rotator in practice, however, it is necessary to be able to identify intersection points between cell boundaries and test rays in a series of parallel focal planes, also at the peripheral parts of the cell boundaries. In cases......This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making...... the spatial rotator fast to use. Since a 3D probe is involved, it is expected that the spatial rotator will be more efficient than the the nucleator and the planar rotator, which are based on measurements in a single plane. An extensive simulation study shows that the spatial rotator may be more efficient...
Observability of discretized partial differential equations
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Energy Technology Data Exchange (ETDEWEB)
Joseph, D.
2004-04-01
The prediction of pollutant species such as soots and NO{sub x} emissions and lifetime of the walls in a combustion chamber is strongly dependant on heat transfer by radiation at high temperatures. This work deals with the development of a code based on the Discrete Ordinates Method (DOM) aiming at providing radiative source terms and wall fluxes with a good compromise between cpu time and accuracy. Radiative heat transfers are calculated using the unstructured grids defined by the Computational Fluid Dynamics (CFD) codes. The spectral properties of the combustion gases are taken into account by a statistical narrow bands correlated-k model (SNB-ck). Various types of angular quadrature are tested and three different spatial differencing schemes were integrated and compared. The validation tests show the limit at strong optical thicknesses of the finite volume approximation used the Discrete Ordinates Method. The first calculations performed on LES solutions are presented, it provides instantaneous radiative source terms and wall heat fluxes. Those results represent a first step towards radiation/combustion coupling. (author)
Discretization of Preisach hysteresis model
Institute of Scientific and Technical Information of China (English)
安凯; 蔡国平
2015-01-01
In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data, the concept and correlative method of discretization of Preisach hysteresis model are proposed, the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral, which is defined as the weight of a certain point in that region. For the input composed of an ascending segment and a descending segment, a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments. If the number of input ascending segments increases, the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points. A prominent advantage of discrete Preisach hysteresis model is its memory efficiency. Another advantage of discrete Preisach hysteresis model is that there is no function in the model, and thus, it can be expediently operated using a computer. By generalizing the above updating rectangle method to the continuous Preisach hysteresis model, identification method of distribution density can be given as well.
Discrete port-Hamiltonian systems : mixed interconnections
Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der
2005-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Energy Technology Data Exchange (ETDEWEB)
Breier, J. A.; Rauch, C. G.; McCartney, K.; Toner, B. M.; Fakra, S. C.; White, S. N.; German, C. R.
2010-06-22
To enable detailed investigations of early stage hydrothermal plume formation and abiotic and biotic plume processes we developed a new oceanographic tool. The Suspended Particulate Rosette sampling system has been designed to collect geochemical and microbial samples from the rising portion of deep-sea hydrothermal plumes. It can be deployed on a remotely operated vehicle for sampling rising plumes, on a wire-deployed water rosette for spatially discrete sampling of non-buoyant hydrothermal plumes, or on a fixed mooring in a hydrothermal vent field for time series sampling. It has performed successfully during both its first mooring deployment at the East Pacific Rise and its first remotely-operated vehicle deployments along the Mid-Atlantic Ridge. It is currently capable of rapidly filtering 24 discrete large-water-volume samples (30-100 L per sample) for suspended particles during a single deployment (e.g. >90 L per sample at 4-7 L per minute through 1 {mu}m pore diameter polycarbonate filters). The Suspended Particulate Rosette sampler has been designed with a long-term goal of seafloor observatory deployments, where it can be used to collect samples in response to tectonic or other events. It is compatible with in situ optical sensors, such as laser Raman or visible reflectance spectroscopy systems, enabling in situ particle analysis immediately after sample collection and before the particles alter or degrade.
Three particles in a finite volume
Polejaeva, Kathryn
2012-01-01
Within the non-relativistic potential scattering theory, we derive a generalized version of the L\\"uscher formula, which includes three-particle inelastic channels. Faddeev equations in a finite volume are discussed in detail. It is proved that, even in the presence of the three-particle intermediate states, the discrete spectrum in a finite box is determined by the infinite-volume elements of the scattering S-matrix up to corrections, exponentially suppressed at large volumes.
Spatial Characteristics of Head-Related Transfer Function
Institute of Scientific and Technical Information of China (English)
ZHONG Xiao-Li; XIE Bo-Sun
2005-01-01
@@ The spatial characteristics of head-related transfer functions (HRTFs) are studied by a spatial Fourier analysis.A law of the HRTF spatial sampling in different elevation planes is obtained, and the corresponding spatial interpolating method used to recover the continuous HRTF is proposed. The method is valid, for the average error between the measured and interpolated HRTFs in the horizontal plane is about 0.5%. These results provide guidance for the discrete spatial measurement of HRTFs.
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure—in doing so we try to bring together various fundamental concepts...
Pascal Mossay
2004-01-01
We consider a continuous spatial economy consisting of pure exchange local economies. Agents are allowed to change their location over time as a response to spatial utility differentials. These spatial adjustments toward higher utility neighborhoods lead the spatial economy to converge to a spatially uniform allocation of resources, provided that the matrix of price effects is quasi-negative definite. Furthermore our model provides a real time interpretation of the tâtonnement story. Also, sp...
A Discrete Equivalent of the Logistic Equation
Directory of Open Access Journals (Sweden)
Petropoulou EugeniaN
2010-01-01
Full Text Available A discrete equivalent and not analogue of the well-known logistic differential equation is proposed. This discrete equivalent logistic equation is of the Volterra convolution type, is obtained by use of a functional-analytic method, and is explicitly solved using the -transform method. The connection of the solution of the discrete equivalent logistic equation with the solution of the logistic differential equation is discussed. Also, some differences of the discrete equivalent logistic equation and the well-known discrete analogue of the logistic equation are mentioned. It is hoped that this discrete equivalent of the logistic equation could be a better choice for the modelling of various problems, where different versions of known discrete logistic equations are used until nowadays.
Directory of Open Access Journals (Sweden)
Seth H. Weinberg
2012-01-01
Full Text Available Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume with the corresponding deterministic model (an approximation that assumes large system size. When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers.
Robust Video Watermarking Based on Discrete Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
NIU Xiamu; SUN Shenghe
2001-01-01
A video watermarking techniquebased on discrete fractional Fourier transform(DFRFT) is proposed. Each frame of an original videois first decomposed into two-dimensional (2-D) mul-tiresolution representations by 2-D discrete wavelettransforms (DWT) along the spatial axis. Then thewavelet coefficient frames in each group of pictures(GOP, each GOP has 16 frames) are transformed intoDFRFT coefficient frames by one-dimensional (1-D)DFRFT along the temporal axis. The watermark isembedded into each DFRFT coefficient frame in theGOP, and the angular parameter of the DFRFT canbe changed to adapt itself to the original video. Experimental results show that the proposed techniqueis robust enough against the attacks of frame dropping, averaging and lossy compression.
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Discrete low-discrepancy sequences
Angel, Omer; Martin, James B; Propp, James
2009-01-01
Holroyd and Propp used Hall's marriage theorem to show that, given a probability distribution pi on a finite set S, there exists an infinite sequence s_1,s_2,... in S such that for all integers k >= 1 and all s in S, the number of i in [1,k] with s_i = s differs from k pi(s) by at most 1. We prove a generalization of this result using a simple explicit algorithm. A special case of this algorithm yields an extension of Holroyd and Propp's result to the case of discrete probability distributions on infinite sets.
Discrete and finite General Relativity
De Souza, M M; Souza, Manoelito M. de; Silveira, Robson N.
1999-01-01
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a finite, singularity-free, point-like field that we associate to a ``classical graviton". The standard Einstein's continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chsosen imposed symetry. The Schwarzschild metric is obtained by the imposition of spherical symmetry on the averaged field.
Fundamental approach to discrete mathematics
Acharjya, DP
2009-01-01
About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include: Strong coverage of key topics involving recurrence relation, combinatorics, Boolean algebra, graph theory and fuzzy set theory. Algorithms and examples integrated throughout the book to bring clarity to the fundamental concepts. Each concept and definition is followed by thoughtful examples.
Discrete gravity from statistical mechanics
Romano, Antonio Enea
2011-01-01
We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the quantum wave function of the universe using the sum over the histories approach to quantum gravity. Motivated by this isomorphism we show how the Regge equations, i.e. the discrete equivalent of the vacuum Einstein equations, can be derived using statistical mechanics under the assumption that the energy of a given space time geometry is proportional to the Regge action.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Sarvari, S. M. Hosseini
2017-09-01
The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.
Metal-Grid Spatial Filter. Volume I.
1980-07-01
onactngCrose Stip it DilcrcNa6 rasd 95 -Vt- Figure 4-21 Round Hole Samples for Near-Broadside Simulator 96 FREQUENCY C6HZ) FREQUENCY (GHz) 4.0 4.2 4.4 4.6...4.8 5.0 4.0 4.2 4.4 4.6 4 9 5.0 -2- -2rO 00 0 HOLES :0:00w% HOLES 0 DATA 0-6~ - DATA -1 -14 Fiue42 aa o on oesNa rasd z 97 computed curve is given. No
Entwinement in discretely gauged theories
Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.
2016-12-01
We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
Supervised Discrete Hashing With Relaxation.
Gui, Jie; Liu, Tongliang; Sun, Zhenan; Tao, Dacheng; Tan, Tieniu
2016-12-29
Data-dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high-dimensional data, such as documents, images, and videos. In this paper, we propose a novel learning-based hashing method called ''supervised discrete hashing with relaxation'' (SDHR) based on ''supervised discrete hashing'' (SDH). SDH uses ordinary least squares regression and traditional zero-one matrix encoding of class label information as the regression target (code words), thus fixing the regression target. In SDHR, the regression target is instead optimized. The optimized regression target matrix satisfies a large margin constraint for correct classification of each example. Compared with SDH, which uses the traditional zero-one matrix, SDHR utilizes the learned regression target matrix and, therefore, more accurately measures the classification error of the regression model and is more flexible. As expected, SDHR generally outperforms SDH. Experimental results on two large-scale image data sets (CIFAR-10 and MNIST) and a large-scale and challenging face data set (FRGC) demonstrate the effectiveness and efficiency of SDHR.
Entwinement in discretely gauged theories
Balasubramanian, V; Craps, B; De Jonckheere, T; Galli, F
2016-01-01
We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_N$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS$_3$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the...
Discrete auroras and magnetotail processes.
Lyons, L. R.
Important information about magnetospheric phenomena associated with auroras and substorms can be inferred from low-altitude auroral observations. Satellite observations have shown that discrete auroral arcs lie within a boundary plasma sheet (BPS) region that is outside the central plasma sheet (CPS). The observations imply that arcs are generated along BPS field lines by magnetospheric processes that form large, perpendicular electric field structures. The BPS and the arc generation processes apparently lie along field lines that are in the vicinity of the boundary between open and closed field lines and cross the tail (or magnetopause) current sheet. Ground-based observations show that the first indication of a substorm onset is the brightening of a quiet, discrete arc. This suggests that substorms are initiated along the BPS field lines associated with arc generation, and not within the CPS. Finally, auroral observations have shown that the area of open, polar-cap field lines varies considerably during periods of geomagnetic activity. Expansion of the polar cap has the potential for releasing trapped plasma sheet particles along freshly open field lines. The resulting evacuation of field lines has the potential for being an important loss process for the plasma sheet and for being a source of tailward flows and energetic particle bursts in the tail.
Lawson, Andrew B
2002-01-01
Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal ...
Finite Volumes for Complex Applications VII
Ohlberger, Mario; Rohde, Christian
2014-01-01
The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative propert...
Parallel, explicit, and PWTD-enhanced time domain volume integral equation solver
Liu, Yang
2013-07-01
Time domain volume integral equations (TDVIEs) are useful for analyzing transient scattering from inhomogeneous dielectric objects in applications as varied as photonics, optoelectronics, and bioelectromagnetics. TDVIEs typically are solved by implicit marching-on-in-time (MOT) schemes [N. T. Gres et al., Radio Sci., 36, 379-386, 2001], requiring the solution of a system of equations at each and every time step. To reduce the computational cost associated with such schemes, [A. Al-Jarro et al., IEEE Trans. Antennas Propagat., 60, 5203-5215, 2012] introduced an explicit MOT-TDVIE method that uses a predictor-corrector technique to stably update field values throughout the scatterer. By leveraging memory-efficient nodal spatial discretization and scalable parallelization schemes [A. Al-Jarro et al., in 28th Int. Rev. Progress Appl. Computat. Electromagn., 2012], this solver has been successfully applied to the analysis of scattering phenomena involving 0.5 million spatial unknowns. © 2013 IEEE.
Astuti, Valerio; Rovelli, Carlo
2016-01-01
Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent states --with finite-volume individual nodes-- describing a region with total volume smaller than $V$, has \\emph{finite} dimension, bounded by $V \\log V$. This allows us to introduce the notion of "volume entropy": the von Neumann entropy associated to the measurement of volume.
Localized solutions for a nonlocal discrete NLS equation
Energy Technology Data Exchange (ETDEWEB)
Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)
2015-09-04
We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.
Spatial coherence of random laser emission.
Redding, Brandon; Choma, Michael A; Cao, Hui
2011-09-01
We experimentally studied the spatial coherence of random laser emission from dye solutions containing nanoparticles. The spatial coherence, measured in a double slit experiment, varied significantly with the density of scatterers and the size and shape of the excitation volume. A qualitative explanation is provided, illustrating the dramatic difference from the spatial coherence of a conventional laser. This work demonstrates that random lasers can be controlled to provide intense, spatially incoherent emission for applications in which spatial cross talk or speckle limit performance.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Liu, Yang
2016-03-25
A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.
Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case
Guo, Zhaoli; Xu, Kun
2014-01-01
This paper is a continuation of our earlier work [Z.L. Guo {\\it et al.}, Phys. Rev. E {\\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the fluxes at cell interfaces, so that the nice asymptotic preserving (AP) property is retained, such that the time step is limited only by the CFL number, the distribution function at cell interface recovers to the Chapman-Enskog one in the continuum limit while reduces to that of free-transport for free-molecular flow, and the time and spatial accuracy is of second-order accuracy in smooth region. These features make the DUGK...
Discrete quantum geometries and their effective dimension
Thürigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the ef...
Hodgetts, David; Seers, Thomas
2015-04-01
-deterministic, outcrop constrained discrete fracture network modeling code to derive volumetric fault intensity measures (fault area per unit volume / fault volume per unit volume). Producing per-vertex measures of volumetric intensity; our method captures the spatial variability in 3D fault density across a surveyed outcrop, enabling first order controls to be probed. We demonstrate our approach on pervasively faulted exposures of a Permian aged reservoir analogue from the Vale of Eden Basin, UK.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
A Nuclear Reactor Transient Methodology Based on Discrete Ordinates Method
Directory of Open Access Journals (Sweden)
Shun Zhang
2014-01-01
Full Text Available With the rapid development of nuclear power industry, simulating and analyzing the reactor transient are of great significance for the nuclear safety. The traditional diffusion theory is not suitable for small volume or strong absorption problem. In this paper, we have studied the application of discrete ordinates method in the numerical solution of space-time kinetics equation. The fully implicit time integration was applied and the precursor equations were solved by analytical method. In order to improve efficiency of the transport theory, we also adopted some advanced acceleration methods. Numerical results of the TWIGL benchmark problem presented demonstrate the accuracy and efficiency of this methodology.
Stochastic analysis in discrete and continuous settings with normal martingales
Privault, Nicolas
2009-01-01
This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.
Wegner estimate for discrete alloy-type models
Veselić, Ivan
2010-01-01
We study discrete alloy-type random Schr\\"odinger operators on $\\ell^2(\\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.
A Note on Discrete Einstein Metric
Ge, Huabin
2015-01-01
In this short note, we prove that the space of all admissible piecewise linear metrics parameterized by length square on a triangulated manifolds is a convex cone. We further study Regge's Einstein-Hilbert action and give a much more reasonable definition of discrete Einstein metric than our former version in \\cite{G}. Finally, we introduce a discrete Ricci flow for three dimensional triangulated manifolds, which is closely related to the existence of discrete Einstein metrics.
Discrete complex analysis on isoradial graphs
Chelkak, Dmitry; Smirnov, Stanislav
2008-01-01
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures, Green's functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models.
Simulation of neutrino oscillations using discrete-time quantum walk
Mallick, Arindam; Chandrashekar, C M
2016-01-01
Neutrino oscillation is a well-known phenomenon observed in high energy physics. Here starting from a one-spatial dimensional discrete-time quantum walk we present a method to simulate neutrino oscillation. We present the set of walk parameters with which we can obtain the same oscillation probability profile obtained in both, long range and short range neutrino experiment. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental setup with access to control a single six-level system, a multiparticle three-qubits or a qubit-qutrit system.
Multi-Volume High Resolution RGB-D Mapping with Dynamic Volume Placement
Salvato, Michael; Finman, Ross; Leonard, John
2015-01-01
We present a novel RGB-D mapping system for generating 3D maps over spatially extended regions with higher resolution than current methods using multiple, dynamically placed mapping volumes. Our method takes in RGB-D frames and dynamically assigns multiple mapping volumes to the environment, exchanging mapping volumes between the CPU and GPU. Mapping volumes are added or removed as needed to allow for spatially extended, high resolution mapping. Our system is designed to maximize the resoluti...
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Modeling discrete competitive facility location
Karakitsiou, Athanasia
2015-01-01
This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions. While many optimization approaches simplify location problems by assuming decision making in isolation, this monograph focuses on models which take into account the competitive environment in which such decisions are made. New insights in modeling, algorithmic and theoretical possibilities are opened by this approach and new applications are possible. Competition on equal term plus competition between market leader and followers are considered in this study, consequently bi-level optimization methodology is emphasized and further developed. This book provides insights regarding modeling complexity and algorithmic approaches to discrete competitive location problems. In traditional location modeling, assignment of customer demands to supply sources are made ...
Efficient Discretization of Stochastic Integrals
Fukasawa, Masaaki
2012-01-01
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
Quantum evolution by discrete measurements
Energy Technology Data Exchange (ETDEWEB)
Roa, L [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Guevara, M L Ladron de [Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta (Chile); Delgado, A [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Olivares-RenterIa, G [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico)
2007-10-15
In this article we review two ways of driving a quantum system to a known pure state via a sequence discrete of von Neumann measurements. The first of them assumes that the initial state of the system is unknown, and the evolution is attained only with the help of two non-commuting observables. For this method, the overall success probability is maximized when the eigentstates of the involved observables constitute mutually unbiased bases. The second method assumes the initial state is known and it uses N observables which are consecutively measured to make the state of the system approach the target state. The probability of success of this procedure converges to 1 as the number of observables increases.
Lepton mixing and discrete symmetries
Hernandez, D.; Smirnov, A. Yu.
2012-09-01
The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4, and A5. We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S4 model and reproduces the allowed values of the mixing angles, we predict δ=(90°-120°).
Weak complementarity from discrete symmetries
Merlo, Luca
2009-01-01
The neutrino oscillation data find a good approximation in the so-called tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern, which is already ruled out by the measurements, could be a very good starting point in order to describe the lepton mixing. In this paper I review both the flavour structures and then I present an explicit flavour model based on the discrete group S4, in which the PMNS mixing matrix is of the bimaximal form in first approximation and after it receives corrections which bring it in agreement with the data. The resulting spectrum of light neutrinos shows a moderate normal hierarchy and is compatible, within large ambiguities, with the constraints from leptogenesis as an explanation of the baryon asymmetry in the Universe.
On the geometry of discret Michell trusses
DEFF Research Database (Denmark)
Almegaard, Henrik
2011-01-01
given by Michell in 1904. A set of simple design rules are extracted and it is indicated how these rules can be used to construct discrete Michell truss geometries. A number of geometrical optimized discrete examples of known Michell trusses are presented and they meet these design rules very well.......This paper concerns design of two-dimensional minimum weight trusses with a limited number of bars and nodes, so called discrete Michell trusses. It is shown that the geometrical properties for such discrete systems found by Prager in 1978, is analogues to the properties for continuous systems...
Energy Technology Data Exchange (ETDEWEB)
Beane, S R; Detmold, W; Lin, H W; Luu, T C; Orginos, K; Parreno, A; Savage, M J; Torok, A; Walker-Loud, A
2011-07-01
The volume dependence of the octet baryon masses and relations among them are explored with Lattice QCD. Calculations are performed with nf = 2 + 1 clover fermion discretization in four lattice volumes, with spatial extent L ? 2.0, 2.5, 3.0 and 4.0 fm, with an anisotropic lattice spacing of b_s ? 0.123 fm in the spatial direction, and b_t = b_s/3.5 in the time direction, and at a pion mass of m_\\pi ? 390 MeV. The typical precision of the ground-state baryon mass determination is volume dependence of the masses, the Gell-Mann Okubo mass-relation, and of other mass combinations. A comparison with the predictions of heavy baryon chiral perturbation theory is performed in both the SU(2)L ? SU(2)R and SU(3)L ? SU(3)R expansions. Predictions of the three-flavor expansion for the hadron masses are found to describe the observed volume dependences reasonably well. Further, the ?N? axial coupling constant is extracted from the volume dependence of the nucleon mass in the two-flavor expansion, with only small modifications in the three-flavor expansion from the inclusion of kaons and eta's. At a given value of m?L, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at m_\\pi ? 140 MeV than at m_\\pi ? 390 MeV due to a coefficient that scales as ? m_\\pi^3. This is relevant for the design of future ensembles of lattice gauge-field configurations. Finally, the volume dependence of the pion and kaon masses are analyzed with two-flavor and three-flavor chiral perturbation theory.
A new class of group field theories for first order discrete quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Oriti, D [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD (Netherlands); Tlas, T [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)], E-mail: d.oriti@phys.uu.nl, E-mail: t.tlas@damtp.cam.ac.uk
2008-04-21
Group field theories, a generalization of matrix models for 2D gravity, represent a second quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of group field theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in first order variables. In the three-dimensional case, the corresponding discrete action is that of first order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Oriti, Daniele
2007-01-01
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF-theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum grav...
2007-09-19
for a city . Spatial attributes are used to define the spatial location and extent of spatial objects [35]. The spatial attributes of a spatial object...regarding both geometry and thematic differentiation. It can be used to model 2.5D data (e.g., digital terrain model), as well as 3D data ( walkable ...within a city , if the coverage area of a wireless antenna is considered to be the visible area, then the union of coverage areas of all the antennas in
Geometry intuitive, discrete, and convex : a tribute to László Fejes Tóth
Böröczky, Károly; Tóth, Gábor; Pach, János
2013-01-01
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Energy Technology Data Exchange (ETDEWEB)
Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)
1996-12-31
The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.
The stress statistics of the first pop-in or discrete plastic event in crystal plasticity
Derlet, P. M.; Maaß, R.
2016-12-01
The stress at which the first discrete plastic event occurs is investigated using extreme value statistics. It is found that the average of this critical stress is inversely related to the deforming volume, via an exponentially truncated power-law. This is demonstrated for the first pop-in event observed in experimental nano-indentation data as a function of the indenter volume, and for the first discrete plastic event seen in a dislocation dynamics simulation. When the underlying master distribution of critical stresses is assumed to be a power-law, it becomes possible to extract the density of discrete plastic events available to the crystal, and to understand the exponential truncation as a break-down of the asymptotic Weibull limit.
A minimal coupled fluid-discrete element model for bedload transport
Maurin, Raphael; Chareyre, Bruno; Frey, Philippe
2016-01-01
A minimal Lagragian two-phase model to study turbulent bedload transport focusing on the granular phase is presented, and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results s...
Discrete Averaging Relations for Micro to Macro Transition
Liu, Chenchen; Reina, Celia
2016-05-01
The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly under standard finite element discretizations, even if the stress field is discontinuous across elements and the standard proofs based on the divergence theorem are no longer suitable. The discrete averaging results are derived for the three classical types of boundary conditions (affine displacement, periodic and uniform traction boundary conditions) using the properties of the shape functions and the weak form of the microscopic equilibrium equations. The analytical proofs are further verified numerically through a simple finite element simulation of an irregular representative volume element undergoing large deformations. Furthermore, the proofs are extended to include the effects of body forces and inertia, and the results are consistent with those in the smooth continuum setting. This work provides a solid foundation to apply Hill's averaging relations in multiscale finite element methods without introducing an additional error in the scale transition due to the discretization.
A posteriori error estimator and AMR for discrete ordinates nodal transport methods
Energy Technology Data Exchange (ETDEWEB)
Duo, Jose I. [Westinghouse Electric Co., 4350 Northern Pike, Monroeville, PA 15146 (United States)], E-mail: duoji@westinghouse.com; Azmy, Yousry Y. [North Carolina State University, 1110 Burlington Lab., Raleigh, NC 27695-7909 (United States)], E-mail: yyazmy@ncsu.edu; Zikatanov, Ludmil T. [The Pennsylvania State University, 218 McAllister Bldg, University Park (United States)
2009-04-15
In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. In this regard, error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posteriori error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L{sub 2} error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of unknowns solved for to achieve prescribed solution accuracy in global L{sub 2} error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns.
DEFF Research Database (Denmark)
Hansen, Rico Hjerm; Hansen, Anders Hedegaard; Andersen, Torben Ole
2012-01-01
Efficient discrete force control of cylinders may be realised by having multi-chambered cylinders, where the pressure of the chambers are shifted between fixed pressure levels of a secondary controlled system. However, the pressure shifting on a volume where the dynamics of pressure propagation i...
DEFF Research Database (Denmark)
Hansen, Rico Hjerm; Hansen, Anders Hedegaard; Andersen, Torben Ole
2012-01-01
Efficient discrete force control of cylinders may be realised by having multi-chambered cylinders, where the pressure of the chambers are shifted between fixed pressure levels of a secondary controlled system. However, the pressure shifting on a volume where the dynamics of pressure propagation...
Discreteness of space from GUP in a weak gravitational field
Directory of Open Access Journals (Sweden)
Soumen Deb
2016-04-01
Full Text Available Quantum gravity effects modify the Heisenberg's uncertainty principle to a generalized uncertainty principle (GUP. Earlier work showed that the GUP-induced corrections to the Schrödinger equation, when applied to a non-relativistic particle in a one-dimensional box, led to the quantization of length. Similarly, corrections to the Klein–Gordon and the Dirac equations, gave rise to length, area and volume quantizations. These results suggest a fundamental granular structure of space. In this work, it is investigated how spacetime curvature and gravity might influence this discreteness of space. In particular, by adding a weak gravitational background field to the above three quantum equations, it is shown that quantization of lengths, areas and volumes continue to hold. However, it should be noted that the nature of this new quantization is quite complex and under proper limits, it reduces to cases without gravity. These results suggest that quantum gravity effects are universal.
Discrete Event Simulation of Patient Admissions to a Neurovascular Unit
Directory of Open Access Journals (Sweden)
S. Hahn-Goldberg
2014-01-01
Full Text Available Evidence exists that clinical outcomes improve for stroke patients admitted to specialized Stroke Units. The Toronto Western Hospital created a Neurovascular Unit (NVU using beds from general internal medicine, Neurology and Neurosurgery to care for patients with stroke and acute neurovascular conditions. Using patient-level data for NVU-eligible patients, a discrete event simulation was created to study changes in patient flow and length of stay pre- and post-NVU implementation. Varying patient volumes and resources were tested to determine the ideal number of beds under various conditions. In the first year of operation, the NVU admitted 507 patients, over 66% of NVU-eligible patient volumes. With the introduction of the NVU, length of stay decreased by around 8%. Scenario testing showed that the current level of 20 beds is sufficient for accommodating the current demand and would continue to be sufficient with an increase in demand of up to 20%.
Discreteness of space from GUP in a weak gravitational field
Energy Technology Data Exchange (ETDEWEB)
Deb, Soumen, E-mail: soumen.deb@uleth.ca [Theoretical Physics Group, Dept. of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada); Das, Saurya, E-mail: saurya.das@uleth.ca [Theoretical Physics Group, Dept. of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4 (Canada); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2016-04-10
Quantum gravity effects modify the Heisenberg's uncertainty principle to a generalized uncertainty principle (GUP). Earlier work showed that the GUP-induced corrections to the Schrödinger equation, when applied to a non-relativistic particle in a one-dimensional box, led to the quantization of length. Similarly, corrections to the Klein–Gordon and the Dirac equations, gave rise to length, area and volume quantizations. These results suggest a fundamental granular structure of space. In this work, it is investigated how spacetime curvature and gravity might influence this discreteness of space. In particular, by adding a weak gravitational background field to the above three quantum equations, it is shown that quantization of lengths, areas and volumes continue to hold. However, it should be noted that the nature of this new quantization is quite complex and under proper limits, it reduces to cases without gravity. These results suggest that quantum gravity effects are universal.
Institute of Scientific and Technical Information of China (English)
Feng Lixin; Jia Niannian
2007-01-01
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.
Switching between bistable states in a discrete nonlinear model with long-range dispersion
DEFF Research Database (Denmark)
Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth
1998-01-01
In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...
Discrete excitation of mode pulses using a diode-pumped solid-state digital laser
CSIR Research Space (South Africa)
Ngcobo, Sandile
2016-02-01
Full Text Available In this paper, we experimentally demonstrate novel method of generating discrete excitation of on-demand Lagaurre-Gaussian (LG) mode pulses, in a diode pumped solid-state digital laser. The digital laser comprises of an intra-cavity spatial light...
Botnan, Magnus Bakke
2011-01-01
We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.
Pathak, Harshavardhana S.; Shukla, Ratnesh K.
2016-08-01
A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to
Current Density and Continuity in Discretized Models
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Ensemble simulations with discrete classical dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2013-01-01
For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde...
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discrete integrable system and its integrable coupling
Institute of Scientific and Technical Information of China (English)
LI Zhu
2009-01-01
This paper derives new discrete integrable system based on discrete isospectral problem. It shows that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.
Type IIB orientifolds with discrete torsion
Karp, R L; Witten, Louis; Karp, Robert L; Witten, Louis
2001-01-01
We consider compact four-dimensional ${\\bf Z_N}\\times {\\bf Z_M}$ type IIB orientifolds, for certain values of $N$ and $M$. We allow the additional feature of discrete torsion and discuss the modification of the consistency conditions arising from tadpole cancellation. We point out the differences between the cases with and without discrete torsion.
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
Discrete Riccati equation solutions: Distributed algorithms
Directory of Open Access Journals (Sweden)
D. G. Lainiotis
1996-01-01
Full Text Available In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Nonlocality and discrete cellular methods in optics
Wijers, C.M.J.; Boeij, de P.L.
2001-01-01
A subdivision of space into discrete cells underlies the traditional discrete dipole model. This model presumes that only nonlocal electric interactions between cells govern the electromagnetic response of a condensed matter system. Apart from the case of simple dielectrics, this is not realistic. C
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to p
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; Schaft, van der A.J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to p
Interface discrete light bullets in waveguide arrays.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-08-01
We analyze spatiotemporal light localization at the interface separating two different periodic photonic lattices. We demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons propagating along the interface, including hybrid staggered-unstaggered discrete light bullets with tails belonging to spectral gaps of different types.
Discrete/PWM Ballast-Resistor Controller
King, Roger J.
1994-01-01
Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Conservative discretization of the Landau collision integral
Hirvijoki, Eero
2016-01-01
We describe a density, momentum, and energy conserving discretization of the nonlinear Landau collision integral. Our algorithm is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem.
Neutrino mass, mixing and discrete symmetries
Smirnov, Alexei Y
2013-01-01
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry $G_f$ to different residual symmetries $G_{\\ell}$ and $G_\
Quantum-like diffusion over discrete sets
Energy Technology Data Exchange (ETDEWEB)
Battaglia, Demian; Rasetti, Mario
2003-06-23
In the present Letter, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of a Schroedinger-like equation of motion, without need of any quantization procedure.
Kaiser, Mary Kister; Remington, Roger
1988-01-01
Spatial cognition is the ability to reason about geometric relationships in the real (or a metaphorical) world based on one or more internal representations of those relationships. The study of spatial cognition is concerned with the representation of spatial knowledge, and our ability to manipulate these representations to solve spatial problems. Spatial cognition is utilized most critically when direct perceptual cues are absent or impoverished. Examples are provided of how human spatial cognitive abilities impact on three areas of space station operator performance: orientation, path planning, and data base management. A videotape provides demonstrations of relevant phenomena (e.g., the importance of orientation for recognition of complex, configural forms). The presentation is represented by abstract and overhead visuals only.
Invariants of broken discrete symmetries
Kalozoumis, P.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...
Continuous Attributes Discretization Algorithm based on FPGA
Directory of Open Access Journals (Sweden)
Guoqiang Sun
2013-07-01
Full Text Available The paper addresses the problem of Discretization of continuous attributes in rough set. Discretization of continuous attributes is an important part of rough set theory because most of data that we usually gain are continuous data. In order to improve processing speed of discretization, we propose a FPGA-based discretization algorithm of continuous attributes making use of the speed advantage of FPGA. Combined attributes dependency degree of rough ret, the discretization system was divided into eight modules according to block design. This method can save much time of pretreatment in rough set and improve operation efficiency. Extensive experiments on a certain fighter fault diagnosis validate the effectiveness of the algorithm.
Handbook on modelling for discrete optimization
Pitsoulis, Leonidas; Williams, H
2006-01-01
The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Generalized exponential function and discrete growth models
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Discrete multiscale wavelet shrinkage and integrodifferential equations
Didas, S.; Steidl, G.; Weickert, J.
2008-04-01
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.
Odefy -- From discrete to continuous models
Directory of Open Access Journals (Sweden)
Wittmann Dominik M
2010-05-01
Full Text Available Abstract Background Phenomenological information about regulatory interactions is frequently available and can be readily converted to Boolean models. Fully quantitative models, on the other hand, provide detailed insights into the precise dynamics of the underlying system. In order to connect discrete and continuous modeling approaches, methods for the conversion of Boolean systems into systems of ordinary differential equations have been developed recently. As biological interaction networks have steadily grown in size and complexity, a fully automated framework for the conversion process is desirable. Results We present Odefy, a MATLAB- and Octave-compatible toolbox for the automated transformation of Boolean models into systems of ordinary differential equations. Models can be created from sets of Boolean equations or graph representations of Boolean networks. Alternatively, the user can import Boolean models from the CellNetAnalyzer toolbox, GINSim and the PBN toolbox. The Boolean models are transformed to systems of ordinary differential equations by multivariate polynomial interpolation and optional application of sigmoidal Hill functions. Our toolbox contains basic simulation and visualization functionalities for both, the Boolean as well as the continuous models. For further analyses, models can be exported to SQUAD, GNA, MATLAB script files, the SB toolbox, SBML and R script files. Odefy contains a user-friendly graphical user interface for convenient access to the simulation and exporting functionalities. We illustrate the validity of our transformation approach as well as the usage and benefit of the Odefy toolbox for two biological systems: a mutual inhibitory switch known from stem cell differentiation and a regulatory network giving rise to a specific spatial expression pattern at the mid-hindbrain boundary. Conclusions Odefy provides an easy-to-use toolbox for the automatic conversion of Boolean models to systems of ordinary
Discrete echo signal modeling of ultrasound imaging systems
Chen, Ming; Zhang, Cishen
2008-03-01
In this paper, a discrete model representing the pulse-tissue interaction in the medical ultrasound scanning and imaging process is developed. The model is based on discretizing the acoustical wave equation and is in terms of convolution between the input ultrasound pulses and the tissue mass density variation. Such a model can provide a useful means for ultrasound echo signal processing and imaging. Most existing models used for ultrasound imaging are based on frequency domain transform. A disadvantage of the frequency domain transform is that it is only applicable to shift-invariant models. Thus it has ignored the shift-variant nature of the original acoustic wave equation where the tissue compressibility and mass density distributions are spatial-variant factors. The discretized frequency domain model also obscures the compressibility and mass density representations of the tissue, which may mislead the physical understanding and interpretation of the image obtained. Moreover, only the classical frequency domain filtering methods have been applied to the frequency domain model for acquiring some tissue information from the scattered echo signals. These methods are non-parametric and require a prior knowledge of frequency spectra of the transmitted pulses. Our proposed model technique will lead to discrete, multidimensional, shift-variant and parametric difference or convolution equations with the transmitted pulse pressure as the input, the measurement data of the echo signals as the output, and functions of the tissue compressibility and mass density distributions as shift-variant parameters that can be readily identified from input-output measurements. The proposed model represents the entire multiple scattering process, and hence overcomes the key limitation in the current ultrasound imaging methods.
Cosmological Measures without Volume Weighting
Page, Don N
2008-01-01
Many cosmologists (myself included) have advocated volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all observations would be by momentary Boltzmann brains that arise very briefly as quantum fluctuations in the late universe when it has expanded to a huge size, so that our observations (too ordered for Boltzmann brains) would be highly atypical and unlikely. Here it is suggested that volume weighting may be a mistake. Volume averaging is advocated as an alternative. One consequence would be a loss of the argument for eternal inflation.
Succinct Sampling from Discrete Distributions
DEFF Research Database (Denmark)
Bringmann, Karl; Larsen, Kasper Green
2013-01-01
We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x_1,...,x_n, the task is to build a data structure that allows sampling i with probability proportional to x_i. The classic solution is Walker's alias method that takes, when implemented...... on a Word RAM, O(n) preprocessing time, O(1) expected query time for one sample, and n(w+2 lg n+o(1)) bits of space. Using the terminology of succinct data structures, this solution has redundancy 2n lg n+o(n) bits, i.e., it uses 2n lg n+o(n) bits in addition to the information theoretic minimum required...... requirement of the classic solution for a fundamental sampling problem, on the other hand, they provide the strongest known separation between the systematic and non-systematic case for any data structure problem. Finally, we also believe our upper bounds are practically efficient and simpler than Walker...
Succinct Sampling from Discrete Distributions
DEFF Research Database (Denmark)
Bringmann, Karl; Larsen, Kasper Green
2013-01-01
We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x_1,...,x_n, the task is to build a data structure that allows sampling i with probability proportional to x_i. The classic solution is Walker's alias method that takes, when implemented...... on a Word RAM, O(n) preprocessing time, O(1) expected query time for one sample, and n(w+2 lg n+o(1)) bits of space. Using the terminology of succinct data structures, this solution has redundancy 2n lg n+o(n) bits, i.e., it uses 2n lg n+o(n) bits in addition to the information theoretic minimum required...... in redundancy by a factor of Omega(log n) over the alias method for r = n, even though the alias method is not systematic. Moreover, we complement our data structure with a lower bound showing that this trade-off is tight for systematic data structures. In the non-systematic case, in which the input numbers may...
A life-like virtual cell membrane using discrete automata.
Broderick, Gordon; Ru'aini, Melania; Chan, Eugene; Ellison, Michael J
2005-01-01
A framework is presented that captures the discrete and probabilistic nature of molecular transport and reaction kinetics found in a living cell as well as formally representing the spatial distribution of these phenomena. This particle or agent-based approach is computationally robust and complements established methods. Namely it provides a higher level of spatial resolution than formulations based on ordinary differential equations (ODE) while offering significant advantages in computational efficiency over molecular dynamics (MD). Using this framework, a model cell membrane has been constructed with discrete particle agents that respond to local component interactions that resemble flocking or herding behavioural cues in animals. Results from simulation experiments are presented where this model cell exhibits many of the characteristic behaviours associated with its biological counterpart such as lateral diffusion, response to osmotic pressure gradients, membrane growth and cell division. Lateral diffusion rates and estimates for the membrane modulus of elasticity derived from these simple experiments fall well within a biologically relevant range of values. More importantly, these estimates were obtained by applying a simple qualitative tuning of the model membrane. Membrane growth was simulated by injecting precursor molecules into the proto-cell at different rates and produced a variety of morphologies ranging from a single large cell to a cluster of cells. The computational scalability of this methodology has been tested and results from benchmarking experiments indicate that real-time simulation of a complete bacterial cell will be possible within 10 years.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2007-01-01
@@ Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft φ4 potential but also in hard φ4 potential and K4 chains. The measurements of compact-like discrete breathers' core in soft and hard φ4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers' core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice.
DEFF Research Database (Denmark)
Thomsen, Bodil Marie Stavning
2011-01-01
The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations.......The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations....
DEFF Research Database (Denmark)
2011-01-01
The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations.......The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations....
Higher dimensional discrete Cheeger inequalities
Directory of Open Access Journals (Sweden)
Anna Gundert
2015-01-01
Full Text Available For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\\lambda(G \\leq h(G$, where $\\lambda(G$ is the second smallest eigenvalue of the Laplacian of a graph $G$ and $h(G$ is the Cheeger constant measuring the edge expansion of $G$. We are interested in generalizations of expansion properties to finite simplicial complexes of higher dimension (or uniform hypergraphs. Whereas higher dimensional Laplacians were introduced already in 1945 by Eckmann, the generalization of edge expansion to simplicial complexes is not straightforward. Recently, a topologically motivated notion analogous to edge expansion that is based on $\\mathbb{Z}_2$-cohomology was introduced by Gromov and independently by Linial, Meshulam and Wallach. It is known that for this generalization there is no direct higher dimensional analogue of the lower bound of the Cheeger inequality. A different, combinatorially motivated generalization of the Cheeger constant, denoted by $h(X$, was studied by Parzanchevski, Rosenthal and Tessler. They showed that indeed $\\lambda(X \\leq h(X$, where $\\lambda(X$ is the smallest non-trivial eigenvalue of the ($(k-1$-dimensional upper Laplacian, for the case of $k$-dimensional simplicial complexes $X$ with complete $(k-1$-skeleton. Whether this inequality also holds for $k$-dimensional complexes with non-com\\-plete$(k-1$-skeleton has been an open question.We give two proofs of the inequality for arbitrary complexes. The proofs differ strongly in the methods and structures employed,and each allows for a different kind of additional strengthening of the original result.
Lv, Yanlu; Cai, Chuangjian; Bai, Jing; Luo, Jianwen
2016-12-01
Traditional spectral imaging systems mainly rely on spatial scanning or spectral scanning methods to acquire spatial and spectral features. The acquisition is time-consuming and cannot fully satisfy the need of monitoring dynamic phenomenon and observing different structures of the specimen simultaneously. To overcome these barriers, we develop a video-rate simultaneous multispectral imaging system built with a spectral multiplexed volume holographic grating (VHG) and few optical components. Four spectral multiplexed volume holograms optimized for four discrete spectral bands (centered at 488 nm, 530 nm, 590 nm and 620 nm) are recorded into an 8×12 mm photo-thermal refractive glass. The diffraction efficiencies of all the holograms within the multiplexed VHG are greater than 80%. With the high throughout multiplexed VHG, the system can work with both reflection and fluorescence modes and allow simultaneous acquisition of spectral and spatial information with a single exposure. Imaging experiments demonstrate that the multispectral images of the target illuminated with white light source can be obtained. Fluorescence images of multiple fluorescence objects (two glass beads filled with 20 uL 1.0 mg/mL quantum dots solutions that emit 530 +/- 15 nm and 620 +/- 15 nm fluorescence, respectively) buried 3 mm below the surface of a tissue mimicking phantom are acquired. The results demonstrate that the system can provide complementary information in fluorescence imaging. The design diagram of the proposed system is given to explain the advantage of compactness and flexibility in integrating with other imaging platforms.
Hoffmann, Tim
1999-01-01
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schr\\"odinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izergin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.
Pan, Sung B.; Park, Rae-Hong
1997-12-01
A two-dimensional (2-D) very large scale integration (VLSI) architecture using a unified systolic array for fast computation of the discrete cosine transform (DCT), the discrete sine transform (DST), and the discrete Hartley transform (DHT) is proposed. The N-point discrete transform is decomposed into even- and odd-numbered frequency samples and they are computed independently at the same time. The proposed unified systolic array architecture can compute the DCT, the DST, and the DHT by defining different coefficient values specific for each transform. We also present another architecture for computation of the DHT, a modified version of the unified systolic array structure, which is faster than the unified architecture by a factor of 2. In addition, the proposed unified architecture can be employed for computation of the inverse DCT (IDCT), the inverse DST (IDST), and the inverse DHT (IDHT) with some modifications.
Hairs of discrete symmetries and gravity
Directory of Open Access Journals (Sweden)
Kang Sin Choi
2017-06-01
Full Text Available Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
Discrete continuous-phase superresolving filters.
Zhou, Sumei; Zhou, Changhe
2004-12-01
A new type of phase-only superresolving pupil filter with a discrete continuous-phase profile is presented that is a combination of discrete multilevel-phase modulation and continuous-phase modulation. This type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003). Therefore, with regard to the superresolution effect, this type of filter deserves study for practical applications. More importantly, the diffraction performance of this type of filter can explain the effect of a discrete-phase filter illuminated with a continuous wave front, whose superresolving performance cannot be analyzed with previous superresolution methods.
Discrete flavour symmetries from the Heisenberg group
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Discrete Flavour Symmetries from the Heisenberg Group
Floratos, E G
2015-01-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PSL_2(p)$ groups which contain the phenomenologically interesting cases.
Hairs of discrete symmetries and gravity
Choi, Kang Sin; Kim, Jihn E.; Kyae, Bumseok; Nam, Soonkeon
2017-06-01
Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
On Discrete Differential Geometry in Twistor Space
2011-01-01
In this paper we introduce a discrete integrable system generalizing the discrete (real) cross-ratio system in $S^4$ to complex values of a generalized cross-ratio by considering $S^4$ as a real section of the complex Pl\\"ucker quadric, realized as the space of two-spheres in $S^4.$ We develop the geometry of the Pl\\"ucker quadric by examining the novel contact properties of two-spheres in $S^4,$ generalizing classical Lie geometry in $S^3.$ Discrete differential geometry aims to develop disc...
On Discreteness of the Hopf Equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete equation more accurate than the original equation. These model equations can either be conveniently discretized for producing novel numerical schemes or further analyzed to enrich the theory of nonlinear partial differential equations.
Bispen, Georgij; Lukáčová-Medvid'ová, Mária; Yelash, Leonid
2017-04-01
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M ≪ 1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization the finite volume approximation is used with the central and Rusanov/Lax-Friedrichs numerical fluxes for the linear and nonlinear subsystem, respectively. In the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small Mach number. We also analyze experimentally convergence rates in the singular limit when the Mach number tends to zero.
Level set discrete element method for three-dimensional computations with triaxial case study
Kawamoto, Reid; Andò, Edward; Viggiani, Gioacchino; Andrade, José E.
2016-06-01
In this paper, we outline the level set discrete element method (LS-DEM) which is a discrete element method variant able to simulate systems of particles with arbitrary shape using level set functions as a geometric basis. This unique formulation allows seamless interfacing with level set-based characterization methods as well as computational ease in contact calculations. We then apply LS-DEM to simulate two virtual triaxial specimens generated from XRCT images of experiments and demonstrate LS-DEM's ability to quantitatively capture and predict stress-strain and volume-strain behavior observed in the experiments.
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Simultaneous amplitude and phase modulation by a discrete phase-only filter.
Goto, Hiroomi; Konishi, Tsuyoshi; Itoh, Kazuyoshi
2009-03-01
We propose a simultaneous amplitude and phase modulation method by a discrete phase-only filter. The proposed amplitude-phase filter can be realized by a discrete phase modulation of the diffractive optical element as well as a continuous phase modulation of the liquid crystal spatial light modulator. The fabricated amplitude-phase filter that has the six phase modulation levels shows a transfer efficiency of 75% regardless of the polarization state of the incident light. By using the proposed amplitude-phase filter, we demonstrate a temporal waveform conversion from sech(2) to super-Gaussian, which requires both amplitude and phase modulations.
Energy Technology Data Exchange (ETDEWEB)
Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
Flach, S; MacKay, R S
1997-01-01
Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two- and three-dimensional lattices. We show that breather energies have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value. These findings could be important for the experimental detection of discrete breathers.
Comparing the Discrete and Continuous Logistic Models
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Memorized discrete systems and time-delay
Luo, Albert C J
2017-01-01
This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.
Local discrete symmetries from superstring derived models
Energy Technology Data Exchange (ETDEWEB)
Faraggi, A.E.
1996-10-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Running Parallel Discrete Event Simulators on Sierra
Energy Technology Data Exchange (ETDEWEB)
Barnes, P. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Jefferson, D. R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Comparing the Discrete and Continuous Logistic Models
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Local discrete symmetries from superstring derived models
Faraggi, Alon E.
1997-02-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Local discrete symmetries from superstring derived models
Faraggi, A E
1996-01-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non--Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Discrete Event Simulation: State of the Art
Eduard Babulak; Ming Wang
2010-01-01
Discrete event simulation technologies have been up and down as global manufacturing industries went through radical changes. The changes have created new problems, challenges and opportunities to the discrete event simulation. On manufacturing applications, it is no longer an isolated model but the distributed modeling and simulation along the supply-chain. In order to study the hybrid manufacturing systems, it is critical to have capability to model human performance with different level of...
Degrees of freedom in discrete geometry
Ariwahjoedi, Seramika; Rovelli, Carlo; Zen, Freddy P
2016-01-01
Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices using vectorial (differential form) and coordinate-free pictures, and a consistent procedure to couple particles of space, together with a method to calculate the degrees of freedom of the system of 'quanta' of space in the classical framework.
Survey on Discrete Surface Ricci Flow
Institute of Scientific and Technical Information of China (English)
Min Zhang; Wei Zeng; Ren Guo; Feng Luo; Xianfeng David Gu
2015-01-01
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures. Surface Ricci flow has been generalized to the discrete setting. This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis.
MESOSCOPIC ELECTRIC CIRCUITS WITH CHARGE DISCRETIZATION
2004-01-01
MESOSCOPIC ELECTRIC CIRCUITS WITH CHARGE DISCRETIZATION Nanoscience is a modern aspect of electronic engineering with significant projections for applications on new devices. This project allowed presenting an innovative language and a rigorous vision on aspects of nanoscience. The theory of quantum electrical circuits with discrete charge corresponds to the description (in simple terms) of some aspects of nanoscience. Our results gather aspects of quantum mechanics, electrical circuit...
Discrete Surface Modelling Using Partial Differential Equations.
Xu, Guoliang; Pan, Qing; Bajaj, Chandrajit L
2006-02-01
We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.
Quantum Measurement, Complexity and Discrete Physics
Leckey, Martin
2003-01-01
This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of the theory for a realist view of the quantum realm.
Center for Efficient Exascale Discretizations Software Suite
Energy Technology Data Exchange (ETDEWEB)
2017-08-30
The CEED Software suite is a collection of generally applicable software tools focusing on the following computational motives: PDE discretizations on unstructured meshes, high-order finite element and spectral element methods and unstructured adaptive mesh refinement. All of this software is being developed as part of CEED, a co-design Center for Efficient Exascale Discretizations, within DOE's Exascale Computing Project (ECP) program.
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Fast Generation of Discrete Random Variables
Directory of Open Access Journals (Sweden)
George Marsaglia
2004-07-01
Full Text Available We describe two methods and provide C programs for generating discrete random variables with functions that are simple and fast, averaging ten times as fast as published methods and more than five times as fast as the fastest of those. We provide general procedures for implementing the two methods, as well as specific procedures for three of the most important discrete distributions: Poisson, binomial and hypergeometric.
Polarization for arbitrary discrete memoryless channels
Sasoglu, Eren; Telatar, Emre; Arikan, Erdal
2009-01-01
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization. This method can be extended to channels of composite input alphabet sizes by decomposing such channels into a set of channels with prime input alphabet sizes. It is also shown that all discrete memoryless channels can...
Mohamed, Mamdouh S; Samtaney, Ravi
2015-01-01
A conservative discretization of incompressible Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the contraction operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second ord...
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Discrete Calculus as a Bridge between Scales
Degiuli, Eric; McElwaine, Jim
2012-02-01
Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310
Discrete differential geometry: the nonplanar quadrilateral mesh.
Twining, Carole J; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.
Theoretical Basics of Teaching Discrete Mathematics
Directory of Open Access Journals (Sweden)
Y. A. Perminov
2012-01-01
Full Text Available The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training.
Textbook of Semi-discrete Calculus
Shachar, Amir
2010-01-01
Ever since the early 1980's, computer scientists have been using an algorithm named "Summed Area Table", also known as "Integral Image". This algorithm was shown to provide a tremendous computational gain, since it fits precisely to the needs of discrete geometry researchers, due to its discrete nature. It was first introduced in 1984 by Crow, and was reintroduced to the computer vision community in 2001 by Viola and Jones. In 2007, Wang and his colleagues suggested a semi-discrete, semi-continuous formulation of an extension to this algorithm (discrete Green's theorem), and in this book it is suggested that a decisive parameter at the formulation of the theorem can be naturally defined via a simple pointwise operator. The main operator of this theory is defined by a mixture of the discrete and continuous, to form a semi discrete and efficient operator, given that one aims at classification of monotony. This approach to analyze the monotony of functions is hence suitable for computers (in order to save comput...
HEURISTIC DISCRETIZATION METHOD FOR BAYESIAN NETWORKS
Directory of Open Access Journals (Sweden)
Mariana D.C. Lima
2014-01-01
Full Text Available Bayesian Network (BN is a classification technique widely used in Artificial Intelligence. Its structure is a Direct Acyclic Graph (DAG used to model the association of categorical variables. However, in cases where the variables are numerical, a previous discretization is necessary. Discretization methods are usually based on a statistical approach using the data distribution, such as division by quartiles. In this article we present a discretization using a heuristic that identifies events called peak and valley. Genetic Algorithm was used to identify these events having the minimization of the error between the estimated average for BN and the actual value of the numeric variable output as the objective function. The BN has been modeled from a database of Bit’s Rate of Penetration of the Brazilian pre-salt layer with 5 numerical variables and one categorical variable, using the proposed discretization and the division of the data by the quartiles. The results show that the proposed heuristic discretization has higher accuracy than the quartiles discretization.
Finite-volume WENO scheme for viscous compressible multicomponent flows
Coralic, Vedran; Colonius, Tim
2014-01-01
We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358
Compact-like discrete breather and its stability in a discrete monatomic Klein-Gordon chain
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2008-01-01
This paper studies a discrete one-dimensional monatomie Klein-Gordon chain with only quartic nearest-neighbour interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient (β)of quartic on-site potential and the coupling constant (K4) of quartic interactive potential satisfy the given conditions,they are linearly stable.
Discrete integrable systems and deformations of associative algebras
Energy Technology Data Exchange (ETDEWEB)
Konopelchenko, B G [Dipartimento di Fisica, Universita del Salento and INFN, Sezione di Lecce, 73100 Lecce (Italy)], E-mail: konopel@le.infn.it
2009-10-30
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.
Directory of Open Access Journals (Sweden)
J. Thuburn
2014-05-01
Full Text Available A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV. The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
Perspectives on spatial data analysis
Rey, Sergio
2010-01-01
This book takes both a retrospective and prospective view of the field of spatial analysis by combining selected reprints of classic articles by Arthur Getis with current observations by leading experts in the field. Four main aspects are highlighted, dealing with spatial analysis, pattern analysis, local statistics as well as illustrative empirical applications. Researchers and students will gain an appreciation of Getis' methodological contributions to spatial analysis and the broad impact of the methods he has helped pioneer on an impressively broad array of disciplines including spatial epidemiology, demography, economics, and ecology. The volume is a compilation of high impact original contributions, as evidenced by citations, and the latest thinking on the field by leading scholars. This makes the book ideal for advanced seminars and courses in spatial analysis as well as a key resource for researchers seeking a comprehensive overview of recent advances and future directions in the field.
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
Modeling of asphalt by means of discrete element method – an initial study
DEFF Research Database (Denmark)
Feng, Huan; Hededal, Ole; Stang, Henrik
type of numerical simulation method which allows the finite displacement and rotation of discrete particles, making it an excellent tool to simulate the complex micro interaction between aggregate particles within an asphalt mixture, [3],[4] . In this research, PFC3D – a commercial DEM program...... of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples...
High-order solution methods for grey discrete ordinates thermal radiative transfer
Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.
2016-12-01
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge-Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
"Discrete" vacuum geometry as a tool for Dirac fundamental quantization of Minkowskian Higgs model
Lantsman, Leonid
2007-01-01
We demonstrate that assuming the "discrete" vacuum geometry in the Minkowskian Higgs model with vacuum BPS monopole solutions can justify the Dirac fundamental quantization of that model. The important constituent of this quantization is getting various rotary effects, including collective solid rotations inside the physical BPS monopole vacuum, and just assuming the "discrete" vacuum geometry seems to be that thing able to justify these rotary effects. More precisely, assuming the "discrete" geometry for the appropriate vacuum manifold implies the presence of thread topological defects (side by side with point hedgehog topological defects and walls between different topological domains) inside this manifold in the shape of specific (rectilinear) threads: gauge and Higgs fields located in the spatial region intimately near the axis $z$ of the chosen (rest) reference frame. This serves as the source of collective solid rotations proceeding inside the BPS monopole vacuum suffered the Dirac fundamental quantizat...
High-order solution methods for grey discrete ordinates thermal radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)
2016-12-15
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2013-01-01
Using numerical method,we investigate whether periodic,quasiperiodic,and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term.The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables,and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system.By introducing a periodic interaction into the linear interaction between the atoms,we achieve the coupling of two incommensurate frequencies for a single DB,and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system,too.
Hydrofracture Modeling Using Discrete Fracture Network in Barnett Shale
Yaghoubi, A.; Zoback, M. D.
2012-12-01
Shale gas has become an important source of unconventional reservoir in the united state over the past decade. Since the shale gas formations are impermeable, hydraulic fracturing from vertical and horizontal well are commonly approach to extract natural gas deposit from these unconventional sources. Hydraulic fracturing has been a successful and relatively inexpensive stimulation method for stimulation and enhances hydrocarbon recovery. Multistage hydro fracturing treatments in horizontal well creates a large stimulated reservoir volume. However, modeling hydraulic fracturing requires to prior knowledge of natural fracture network. This problem can be deal with Discrete Fracture network modeling. The objective of this study is first to model discrete fracture network and then simulate hydro-fracturing in five horizontal well of a case study in Barnett shale gas reservoir. In the case study, five horizontal wells have been drilled in Barnett shale gas reservoir in which each of them has 10 stages of hydro-fracturing stimulation. Of all five wells, just well C has a full comprehensive logging data. Fracture date detected using FMI image log of well C for building DFN model are associated with different sources of uncertainty; orientation, density and length. After building reservoir geomechanics model and detecting natural fracture form image log from well C, DFN model has built based on fracture parameters, orientation, intensity, shape size and permeability detected from image log and core data. Modeling hydrofractuing in five wells are consistent with critically stressed-fracture and micro-seismic events.
DEFF Research Database (Denmark)
2012-01-01
– 2006. The essays published here allow us to subdivide the field of spatial culture into five major domains, summarized in the titles of chapters in the book: ”Perception and Strategies: Architecture”, ”Politics and Poetics: Urban Spaces”, ”Movements and Cityscape: Textuality”, ”Crisis and Construction......Spatial Culture – A Humanities Perspective Abstract of introductory essay by Henrik Reeh Secured by alliances between socio-political development and cultural practices, a new field of humanistic studies in spatial culture has developed since the 1990s. To focus on links between urban culture...... and modern society is, however, an intellectual practice which has a much longer history. Already in the 1980s, the debate on the modern and the postmodern cited Paris and Los Angeles as spatio-cultural illustrations of these major philosophical concepts. Earlier, in the history of critical studies, the work...
Finite volume hydromechanical simulation in porous media.
Nordbotten, Jan Martin
2014-05-01
Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media.
Discrete Feature Model (DFM) User Documentation
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2008-06-15
This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this
Makedonska, Nataliia; Hyman, Jeffrey D.; Karra, Satish; Painter, Scott L.; Gable, Carl W.; Viswanathan, Hari S.
2016-08-01
The apertures of natural fractures in fractured rock are highly heterogeneous. However, in-fracture aperture variability is often neglected in flow and transport modeling and individual fractures are assumed to have uniform aperture distribution. The relative importance of in-fracture variability in flow and transport modeling within kilometer-scale field-scale fracture networks has been under a matter of debate for a long time because the flow in each single fracture is controlled not only by in-fracture variability but also by boundary conditions. Computational limitations have previously prohibited researchers from investigating the relative importance of in-fracture variability in flow and transport modeling within large-scale fracture networks. We address this question by incorporating internal heterogeneity of individual fractures into flow simulations within kilometer scale three-dimensional fracture networks, where fracture intensity, P32 (ratio between total fracture area and domain volume) is between 0.027 and 0.031 [1/m]. A recently developed discrete fracture network (DFN) simulation capability, dfnWorks, is used to generate DFNs that include in-fracture aperture variability represented by a stationary log-normal stochastic field with various correlation lengths and variances. The Lagrangian transport parameters, non-reacting travel time and cumulative retention, are calculated along particles streamlines. It is observed that due to local flow channeling early particle travel times are more sensitive to in-fracture variability than the tails of travel time distributions, where no significant effect of the in-fracture transmissivity variations and spatial correlation length is observed.
Discrete extrinsic curvatures and approximation of surfaces by polar polyhedra
Garanzha, V. A.
2010-01-01
Duality principle for approximation of geometrical objects (also known as Eu-doxus exhaustion method) was extended and perfected by Archimedes in his famous tractate “Measurement of circle”. The main idea of the approximation method by Archimedes is to construct a sequence of pairs of inscribed and circumscribed polygons (polyhedra) which approximate curvilinear convex body. This sequence allows to approximate length of curve, as well as area and volume of the bodies and to obtain error estimates for approximation. In this work it is shown that a sequence of pairs of locally polar polyhedra allows to construct piecewise-affine approximation to spherical Gauss map, to construct convergent point-wise approximations to mean and Gauss curvature, as well as to obtain natural discretizations of bending energies. The Suggested approach can be applied to nonconvex surfaces and in the case of multiple dimensions.
Truss topology optimization with discrete design variables by outer approximation
DEFF Research Database (Denmark)
Stolpe, Mathias
2015-01-01
Several variants of an outer approximation method are proposed to solve truss topology optimization problems with discrete design variables to proven global optimality. The objective is to minimize the volume of the structure while satisfying constraints on the global stiffness of the structure...... for classical outer approximation approaches applied to optimal design problems. A set of two- and three-dimensional benchmark problems are solved and the numerical results suggest that the proposed approaches are competitive with other special-purpose global optimization methods for the considered class...... of problems. Numerical comparisons indicate that the suggested outer approximation algorithms can outperform standard approaches suggested in the literature, especially on difficult problem instances. © 2014 Springer Science+Business Media New York....
Bayesian inference from count data using discrete uniform priors.
Comoglio, Federico; Fracchia, Letizia; Rinaldi, Maurizio
2013-01-01
We consider a set of sample counts obtained by sampling arbitrary fractions of a finite volume containing an homogeneously dispersed population of identical objects. We report a Bayesian derivation of the posterior probability distribution of the population size using a binomial likelihood and non-conjugate, discrete uniform priors under sampling with or without replacement. Our derivation yields a computationally feasible formula that can prove useful in a variety of statistical problems involving absolute quantification under uncertainty. We implemented our algorithm in the R package dupiR and compared it with a previously proposed Bayesian method based on a Gamma prior. As a showcase, we demonstrate that our inference framework can be used to estimate bacterial survival curves from measurements characterized by extremely low or zero counts and rather high sampling fractions. All in all, we provide a versatile, general purpose algorithm to infer population sizes from count data, which can find application in a broad spectrum of biological and physical problems.
Discrete Rogue waves in an array of waveguides
Efe, S
2015-01-01
We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue wave solution of the discrete nonlinear Schrodinger equation.
Geometric formulations and variational integrators of discrete autonomous Birkhoff systems
Institute of Scientific and Technical Information of China (English)
Liu Shi-Xing; Liu Chang; Guo Yong-Xin
2011-01-01
The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.
Positivity for Convective Semi-discretizations
Fekete, Imre
2017-04-19
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.
Novel genetic loci associated with hippocampal volume
D.P. Hibar (Derrek); H.H.H. Adams (Hieab); N. Jahanshad (Neda); G. Chauhan (Ganesh); J.L. Stein; E. Hofer (Edith); M.E. Rentería (Miguel); J.C. Bis (Joshua); A. Arias-Vásquez (Alejandro); Ikram, M.K. (M. Kamran); S. Desrivières (Sylvane); M.W. Vernooij (Meike); L. Abramovic; S. Alhusaini (Saud); N. Amin (Najaf); M. Andersson (Micael); K. Arfanakis (Konstantinos); B. Aribisala (Benjamin); N.J. Armstrong (Nicola J.); L. Athanasiu (Lavinia); T. Axelsson (Tomas); A.H. Beecham (Ashley); A. Beiser (Alexa); M. Bernard (Manon); S.H. Blanton (Susan H.); M.M. Bohlken (Marc M.); M.P.M. Boks (Marco); L.B.C. Bralten (Linda); A.M. Brickman (Adam M.); Carmichael, O. (Owen); M.M. Chakravarty (M. Mallar); Q. Chen (Qiang); C.R.K. Ching (Christopher); V. Chouraki (Vincent); G. Cuellar-Partida (Gabriel); F. Crivello (Fabrice); A. den Braber (Anouk); Doan, N.T. (Nhat Trung); S.M. Ehrlich (Stefan); S. Giddaluru (Sudheer); A.L. Goldman (Aaron L.); R.F. Gottesman (Rebecca); O. Grimm (Oliver); M.D. Griswold (Michael); T. Guadalupe (Tulio); Gutman, B.A. (Boris A.); J. Hass (Johanna); U.K. Haukvik (Unn); D. Hoehn (David); A.J. Holmes (Avram); M. Hoogman (Martine); D. Janowitz (Deborah); T. Jia (Tianye); Jørgensen, K.N. (Kjetil N.); N. Karbalai (Nazanin); D. Kasperaviciute (Dalia); S. Kim (Shinseog); M. Klein (Marieke); B. Kraemer (Bernd); P.H. Lee (Phil); D.C. Liewald (David C.); L.M. Lopez (Lorna); M. Luciano (Michelle); C. MacAre (Christine); Marquand, A.F. (Andre F.); M. Matarin (Mar); R. Mather; M. Mattheisen (Manuel); McKay, D.R. (David R.); Milaneschi, Y. (Yuri); S. Muñoz Maniega (Susana); K. Nho (Kwangsik); A.C. Nugent (Allison); P. Nyquist (Paul); Loohuis, L.M.O. (Loes M. Olde); J. Oosterlaan (Jaap); M. Papmeyer (Martina); Pirpamer, L. (Lukas); B. Pütz (Benno); A. Ramasamy (Adaikalavan); Richards, J.S. (Jennifer S.); S.L. Risacher (Shannon); R. Roiz-Santiañez (Roberto); N. Rommelse (Nanda); S. Ropele (Stefan); E.J. Rose (Emma); N.A. Royle (Natalie); T. Rundek (Tatjana); P.G. Sämann (Philipp); Saremi, A. (Arvin); C.L. Satizabal (Claudia L.); L. Schmaal (Lianne); N.J. Schork (Nicholas); Shen, L. (Li); J. Shin (Jean); Shumskaya, E. (Elena); A.V. Smith (Albert Vernon); R. Sprooten (Roy); V.M. Strike (Vanessa); A. Teumer (Alexander); D. Tordesillas-Gutierrez (Diana); R. Toro (Roberto); D. Trabzuni (Danyah); S. Trompet (Stella); D. Vaidya (Dhananjay); J. van der Grond (Jeroen); S. van der Lee (Sven); Van Der Meer, D. (Dennis); M.M.J. Van Donkelaar (Marjolein M. J.); K.R. van Eijk (Kristel); T.G.M. van Erp (Theo G.); Van Rooij, D. (Daan); E. Walton (Esther); L.T. Westlye (Lars); C.D. Whelan (Christopher); B.G. Windham (B Gwen); A.M. Winkler (Anderson); K. Wittfeld (Katharina); G. Woldehawariat (Girma); A. Björnsson (Asgeir); Wolfers, T. (Thomas); L.R. Yanek (Lisa); Yang, J. (Jingyun); A.P. Zijdenbos; M.P. Zwiers (Marcel); I. Agartz (Ingrid); L. Almasy (Laura); D. Ames (David); Amouyel, P. (Philippe); O.A. Andreassen (Ole A.); S. Arepalli (Sampath); A.A. Assareh; S. Barral (Sandra); M.E. Bastin (Mark); Becker, D.M. (Diane M.); J.T. Becker; D.A. Bennett (David A.); J. Blangero (John); H. van Bokhoven (Hans); D.I. Boomsma (Dorret); H. Brodaty (Henry); R.M. Brouwer (Rachel); H.G. Brunner; M. Buckner; J.K. Buitelaar (Jan); K. Bulayeva (Kazima); W. Cahn (Wiepke); V.D. Calhoun Vince D. (V.); D.M. Cannon (Dara); G. Cavalleri (Gianpiero); Cheng, C.-Y. (Ching-Yu); S. Cichon (Sven); M.R. Cookson (Mark); A. Corvin (Aiden); B. Crespo-Facorro (Benedicto); J.E. Curran (Joanne); M. Czisch (Michael); A.M. Dale (Anders); G.E. Davies (Gareth); A.J. de Craen (Anton); E.J.C. de Geus (Eco); P.L. de Jager (Philip); G.I. de Zubicaray (Greig); I.J. Deary (Ian J.); S. Debette (Stéphanie); C. DeCarli (Charles); N. Delanty; C. Depondt (Chantal); A.L. DeStefano (Anita); A. Dillman (Allissa); S. Djurovic (Srdjan); D.J. Donohoe (Dennis); D.A. Drevets (Douglas); Duggirala, R. (Ravi); M.D. Dyer (Matthew); C. Enzinger (Christian); S. Erk; T. Espeseth (Thomas); Fedko, I.O. (Iryna O.); Fernández, G. (Guillén); L. Ferrucci (Luigi); S.E. Fisher (Simon); D. Fleischman (Debra); I. Ford (Ian); M. Fornage (Myriam); T. Foroud (Tatiana); P.T. Fox (Peter); C. Francks (Clyde); Fukunaga, M. (Masaki); Gibbs, J.R. (J. Raphael); D.C. Glahn (David); R.L. Gollub (Randy); H.H.H. Göring (Harald H.); R.C. Green (Robert C.); O. Gruber (Oliver); V. Gudnason (Vilmundur); S. Guelfi (Sebastian); Håberg, A.K. (Asta K.); N.K. Hansell (Narelle); J. Hardy (John); C.A. Hartman (C.); Hashimoto, R. (Ryota); K. Hegenscheid (Katrin); J. Heinz (Judith); S. Le Hellard (Stephanie); D.G. Hernandez (Dena); D.J. Heslenfeld (Dirk); Ho, B.-C. (Beng-Choon); P.J. Hoekstra (Pieter); W. Hoffmann (Wolfgang); A. Hofman (Albert); F. Holsboer (Florian); G. Homuth (Georg); N. Hosten (Norbert); J.J. Hottenga (Jouke Jan); M.J. Huentelman (Matthew); H.H. Pol; Ikeda, M. (Masashi); Jack, C.R. (Clifford R.); S. Jenkinson (Sarah); R. Johnson (Robert); Jönsson, E.G. (Erik G.); J.W. Jukema; R. Kahn; Kanai, R. (Ryota); I. Kloszewska (Iwona); Knopman, D.S. (David S.); P. Kochunov (Peter); Kwok, J.B. (John B.); S. Lawrie (Stephen); H. Lemaître (Herve); X. Liu (Xinmin); D.L. Longo (Dan L.); O.L. Lopez (Oscar L.); S. Lovestone (Simon); Martinez, O. (Oliver); J.-L. Martinot (Jean-Luc); V.S. Mattay (Venkata S.); McDonald, C. (Colm); A.M. McIntosh (Andrew); McMahon, F.J. (Francis J.); McMahon, K.L. (Katie L.); P. Mecocci (Patrizia); I. Melle (Ingrid); Meyer-Lindenberg, A. (Andreas); S. Mohnke (Sebastian); Montgomery, G.W. (Grant W.); D.W. Morris (Derek W); T.H. Mosley (Thomas H.); T.W. Mühleisen (Thomas); B. Müller-Myhsok (B.); M.A. Nalls (Michael); M. Nauck (Matthias); T.E. Nichols (Thomas); W.J. Niessen (Wiro); M.M. Nöthen (Markus); L. Nyberg (Lars); Ohi, K. (Kazutaka); R.L. Olvera (Rene); R.A. Ophoff (Roel); M. Pandolfo (Massimo); T. Paus (Tomas); Z. Pausova (Zdenka); B.W.J.H. Penninx (Brenda); Pike, G.B. (G. Bruce); S.G. Potkin (Steven); B.M. Psaty (Bruce); S. Reppermund; M. Rietschel (M.); J.L. Roffman (Joshua); N. Seiferth (Nina); J.I. Rotter (Jerome I.); M. Ryten (Mina); Sacco, R.L. (Ralph L.); P.S. Sachdev (Perminder); A.J. Saykin (Andrew); R. Schmidt (Reinhold); Schmidt, H. (Helena); C.J. Schofield (Christopher); Sigursson, S. (Sigurdur); Simmons, A. (Andrew); A. Singleton (Andrew); S.M. Sisodiya (Sanjay); Smith, C. (Colin); J.W. Smoller; H. Soininen (H.); V.M. Steen (Vidar); D.J. Stott (David J.); J. Sussmann (Jessika); A. Thalamuthu (Anbupalam); A.W. Toga (Arthur W.); B. Traynor (Bryan); J.C. Troncoso (Juan); M. Tsolaki (Magda); C. Tzourio (Christophe); A.G. Uitterlinden (André); Hernández, M.C.V. (Maria C. Valdés); M.P. van der Brug (Marcel); A. van der Lugt (Aad); N.J. van der Wee (Nic); N.E.M. van Haren (Neeltje E.); D. van 't Ent (Dennis); M.J.D. van Tol (Marie-José); B.N. Vardarajan (Badri); B. Vellas (Bruno); D.J. Veltman (Dick); H. Völzke (Henry); H.J. Walter (Henrik); J. Wardlaw (Joanna); A.M.J. Wassink (Annemarie); M.E. Weale (Michael); Weinberger, D.R. (Daniel R.); Weiner, M.W. (Michael W.); Wen, W. (Wei); E. Westman (Eric); T.J.H. White (Tonya); Wong, T.Y. (Tien Y.); Wright, C.B. (Clinton B.); R.H. Zielke (Ronald H.); A.B. Zonderman; N.G. Martin (Nicholas); C.M. van Duijn (Cock); M.J. Wright (Margaret); W.T. Longstreth Jr; G. Schumann (Gunter); H.J. Grabe (Hans Jörgen); B. Franke (Barbara); L.J. Launer (Lenore); S.E. Medland (Sarah Elizabeth); S. Seshadri (Sudha); P.M. Thompson (Paul); M.K. Ikram (Kamran)
2017-01-01
textabstractThe hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpi
Novel genetic loci associated with hippocampal volume
Hibar, Derrek P; Adams, Hieab H H; Jahanshad, Neda; Chauhan, Ganesh; Stein, Jason L; Hofer, Edith; Renteria, Miguel E; Bis, Joshua C; Arias-Vasquez, Alejandro; Ikram, M Kamran; Desrivières, Sylvane; Vernooij, Meike W; Abramovic, Lucija|info:eu-repo/dai/nl/34549072X; Alhusaini, Saud; Amin, Najaf; Andersson, Micael; Arfanakis, Konstantinos; Aribisala, Benjamin S; Armstrong, Nicola J; Athanasiu, Lavinia; Axelsson, Tomas; Beecham, Ashley H; Beiser, Alexa; Bernard, Manon; Blanton, Susan H; Bohlken, Marc M; Boks, Marco P|info:eu-repo/dai/nl/286852071; Bralten, Janita; Brickman, Adam M; Carmichael, Owen; Chakravarty, M Mallar; Chen, Qiang; Ching, Christopher R K; Chouraki, Vincent; Cuellar-Partida, Gabriel; Crivello, Fabrice; Den Braber, Anouk; Doan, Nhat Trung; Ehrlich, Stefan; Giddaluru, Sudheer; Goldman, Aaron L; Gottesman, Rebecca F; Grimm, Oliver; Griswold, Michael E; Guadalupe, Tulio; Gutman, Boris A; Hass, Johanna; Haukvik, Unn K; Hoehn, David; Holmes, Avram J; Hoogman, Martine; Janowitz, Deborah; Jia, Tianye; Jørgensen, Kjetil N; Karbalai, Nazanin; Kasperaviciute, Dalia; Kim, Sungeun; Klein, Marieke; Kraemer, Bernd; Lee, Phil H; Liewald, David C M; Lopez, Lorna M; Luciano, Michelle; Macare, Christine; Marquand, Andre F; Matarin, Mar; Mather, Karen A; Mattheisen, Manuel; McKay, David R; Milaneschi, Yuri; Muñoz Maniega, Susana; Nho, Kwangsik; Nugent, Allison C; Nyquist, Paul; Loohuis, Loes M Olde; Oosterlaan, Jaap; Papmeyer, Martina; Pirpamer, Lukas; Pütz, Benno; Ramasamy, Adaikalavan; Richards, Jennifer S; Risacher, Shannon L; Roiz-Santiañez, Roberto; Rommelse, Nanda; Ropele, Stefan; Rose, Emma J; Royle, Natalie A; Rundek, Tatjana; Sämann, Philipp G; Saremi, Arvin; Satizabal, Claudia L; Schmaal, Lianne; Schork, Andrew J; Shen, Li; Shin, Jean; Shumskaya, Elena; Smith, Albert V; Sprooten, Emma; Strike, Lachlan T; Teumer, Alexander; Tordesillas-Gutierrez, Diana; Toro, Roberto; Trabzuni, Daniah; Trompet, Stella; Vaidya, Dhananjay; Van der Grond, Jeroen; Van der Lee, Sven J; Van der Meer, Dennis; Van Donkelaar, Marjolein M J; Van Eijk, Kristel R|info:eu-repo/dai/nl/344497569; Van Erp, Theo G M; Van Rooij, Daan; Walton, Esther; Westlye, Lars T; Whelan, Christopher D; Windham, Beverly G; Winkler, Anderson M; Wittfeld, Katharina; Woldehawariat, Girma; Wolf, Christiane; Wolfers, Thomas; Yanek, Lisa R; Yang, Jingyun; Zijdenbos, Alex; Zwiers, Marcel P; Agartz, Ingrid; Almasy, Laura; Ames, David; Amouyel, Philippe; Andreassen, Ole A; Arepalli, Sampath; Assareh, Amelia A; Barral, Sandra; Bastin, Mark E; Becker, Diane M; Becker, James T; Bennett, David A; Blangero, John; van Bokhoven, Hans; Boomsma, Dorret I; Brodaty, Henry; Brouwer, Rachel M|info:eu-repo/dai/nl/304811432; Brunner, Han G; Buckner, Randy L; Buitelaar, Jan K; Bulayeva, Kazima B; Cahn, Wiepke|info:eu-repo/dai/nl/250566370; Calhoun, Vince D; Cannon, Dara M; Cavalleri, Gianpiero L; Cheng, Ching-Yu; Cichon, Sven; Cookson, Mark R; Corvin, Aiden; Crespo-Facorro, Benedicto; Curran, Joanne E; Czisch, Michael; Dale, Anders M; Davies, Gareth E; De Craen, Anton J M; De Geus, Eco J C; De Jager, Philip L; De Zubicaray, Greig I; Deary, Ian J; Debette, Stéphanie; DeCarli, Charles; Delanty, Norman; Depondt, Chantal; DeStefano, Anita; Dillman, Allissa; Djurovic, Srdjan; Donohoe, Gary; Drevets, Wayne C; Duggirala, Ravi; Dyer, Thomas D; Enzinger, Christian; Erk, Susanne; Espeseth, Thomas; Fedko, Iryna O; Fernández, Guillén; Ferrucci, Luigi; Fisher, Simon E; Fleischman, Debra A; Ford, Ian; Fornage, Myriam; Foroud, Tatiana M; Fox, Peter T; Francks, Clyde; Fukunaga, Masaki; Gibbs, J Raphael; Glahn, David C; Gollub, Randy L; Göring, Harald H H; Green, Robert C; Gruber, Oliver; Gudnason, Vilmundur; Guelfi, Sebastian; Håberg, Asta K; Hansell, Narelle K; Hardy, John; Hartman, Catharina A; Hashimoto, Ryota; Hegenscheid, Katrin; Heinz, Andreas; Le Hellard, Stephanie; Hernandez, Dena G; Heslenfeld, Dirk J; Ho, Beng-Choon; Hoekstra, Pieter J; Hoffmann, Wolfgang; Hofman, Albert; Holsboer, Florian; Homuth, Georg; Hosten, Norbert; Hottenga, Jouke-Jan; Huentelman, Matthew; Pol, Hilleke E Hulshoff|info:eu-repo/dai/nl/142348228; Ikeda, Masashi; Jack, Clifford R; Jenkinson, Mark; Johnson, Robert; Jönsson, Erik G; Jukema, J Wouter; Kahn, René S|info:eu-repo/dai/nl/073778532; Kanai, Ryota; Kloszewska, Iwona; Knopman, David S; Kochunov, Peter; Kwok, John B; Lawrie, Stephen M; Lemaître, Hervé; Liu, Xinmin; Longo, Dan L; Lopez, Oscar L; Lovestone, Simon; Martinez, Oliver; Martinot, Jean-Luc; Mattay, Venkata S; McDonald, Colm; McIntosh, Andrew M; McMahon, Francis J; McMahon, Katie L; Mecocci, Patrizia; Melle, Ingrid; Meyer-Lindenberg, Andreas; Mohnke, Sebastian; Montgomery, Grant W; Morris, Derek W; Mosley, Thomas H; Mühleisen, Thomas W; Müller-Myhsok, Bertram; Nalls, Michael A; Nauck, Matthias; Nichols, Thomas E; Niessen, Wiro J; Nöthen, Markus M; Nyberg, Lars; Ohi, Kazutaka; Olvera, Rene L; Ophoff, Roel A; Pandolfo, Massimo; Paus, Tomas; Pausova, Zdenka; Penninx, Brenda W J H; Pike, G Bruce; Potkin, Steven G; Psaty, Bruce M; Reppermund, Simone; Rietschel, Marcella; Roffman, Joshua L; Romanczuk-Seiferth, Nina; Rotter, Jerome I; Ryten, Mina; Sacco, Ralph L; Sachdev, Perminder S; Saykin, Andrew J; Schmidt, Reinhold; Schmidt, Helena; Schofield, Peter R; Sigursson, Sigurdur; Simmons, Andrew; Singleton, Andrew; Sisodiya, Sanjay M; Smith, Colin; Smoller, Jordan W; Soininen, Hilkka; Steen, Vidar M; Stott, David J; Sussmann, Jessika E; Thalamuthu, Anbupalam; Toga, Arthur W; Traynor, Bryan J; Troncoso, Juan; Tsolaki, Magda; Tzourio, Christophe; Uitterlinden, Andre G; Hernández, Maria C Valdés; Van der Brug, Marcel; van der Lugt, Aad; van der Wee, Nic J A; Van Haren, Neeltje E M|info:eu-repo/dai/nl/271562161; van 't Ent, Dennis; Van Tol, Marie-Jose; Vardarajan, Badri N; Vellas, Bruno; Veltman, Dick J; Völzke, Henry; Walter, Henrik; Wardlaw, Joanna M; Wassink, Thomas H; Weale, Michael E; Weinberger, Daniel R; Weiner, Michael W; Wen, Wei; Westman, Eric; White, Tonya; Wong, Tien Y; Wright, Clinton B; Zielke, Ronald H; Zonderman, Alan B; Martin, Nicholas G; Van Duijn, Cornelia M; Wright, Margaret J; Longstreth, W T; Schumann, Gunter; Grabe, Hans J; Franke, Barbara; Launer, Lenore J; Medland, Sarah E; Seshadri, Sudha; Thompson, Paul M; Ikram, M Arfan
2017-01-01
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hi
Novel genetic loci associated with hippocampal volume
D.P. Hibar (Derrek); H.H.H. Adams (Hieab); N. Jahanshad (Neda); G. Chauhan (Ganesh); J.L. Stein; E. Hofer (Edith); M.E. Rentería (Miguel); J.C. Bis (Joshua); A. Arias-Vásquez (Alejandro); Ikram, M.K. (M. Kamran); S. Desrivières (Sylvane); M.W. Vernooij (Meike); L. Abramovic; S. Alhusaini (Saud); N. Amin (Najaf); M. Andersson (Micael); K. Arfanakis (Konstantinos); B. Aribisala (Benjamin); N.J. Armstrong (Nicola J.); L. Athanasiu (Lavinia); T. Axelsson (Tomas); A.H. Beecham (Ashley); A. Beiser (Alexa); M. Bernard (Manon); S.H. Blanton (Susan H.); M.M. Bohlken (Marc M.); M.P.M. Boks (Marco); L.B.C. Bralten (Linda); A.M. Brickman (Adam M.); Carmichael, O. (Owen); M.M. Chakravarty (M. Mallar); Q. Chen (Qiang); C.R.K. Ching (Christopher); V. Chouraki (Vincent); G. Cuellar-Partida (Gabriel); F. Crivello (Fabrice); A. den Braber (Anouk); Doan, N.T. (Nhat Trung); S.M. Ehrlich (Stefan); S. Giddaluru (Sudheer); A.L. Goldman (Aaron L.); R.F. Gottesman (Rebecca); O. Grimm (Oliver); M.D. Griswold (Michael); T. Guadalupe (Tulio); Gutman, B.A. (Boris A.); J. Hass (Johanna); U.K. Haukvik (Unn); D. Hoehn (David); A.J. Holmes (Avram); M. Hoogman (Martine); D. Janowitz (Deborah); T. Jia (Tianye); Jørgensen, K.N. (Kjetil N.); N. Karbalai (Nazanin); D. Kasperaviciute (Dalia); S. Kim (Shinseog); M. Klein (Marieke); B. Kraemer (Bernd); P.H. Lee (Phil); D.C. Liewald (David C.); L.M. Lopez (Lorna); M. Luciano (Michelle); C. MacAre (Christine); Marquand, A.F. (Andre F.); M. Matarin (Mar); R. Mather; M. Mattheisen (Manuel); McKay, D.R. (David R.); Milaneschi, Y. (Yuri); S. Muñoz Maniega (Susana); K. Nho (Kwangsik); A.C. Nugent (Allison); P. Nyquist (Paul); Loohuis, L.M.O. (Loes M. Olde); J. Oosterlaan (Jaap); M. Papmeyer (Martina); Pirpamer, L. (Lukas); B. Pütz (Benno); A. Ramasamy (Adaikalavan); Richards, J.S. (Jennifer S.); S.L. Risacher (Shannon); R. Roiz-Santiañez (Roberto); N. Rommelse (Nanda); S. Ropele (Stefan); E.J. Rose (Emma); N.A. Royle (Natalie); T. Rundek (Tatjana); P.G. Sämann (Philipp); Saremi, A. (Arvin); C.L. Satizabal (Claudia L.); L. Schmaal (Lianne); N.J. Schork (Nicholas); Shen, L. (Li); J. Shin (Jean); Shumskaya, E. (Elena); A.V. Smith (Albert Vernon); R. Sprooten (Roy); V.M. Strike (Vanessa); A. Teumer (Alexander); D. Tordesillas-Gutierrez (Diana); R. Toro (Roberto); D. Trabzuni (Danyah); S. Trompet (Stella); D. Vaidya (Dhananjay); J. van der Grond (Jeroen); S. van der Lee (Sven); Van Der Meer, D. (Dennis); M.M.J. Van Donkelaar (Marjolein M. J.); K.R. van Eijk (Kristel); T.G.M. van Erp (Theo G.); Van Rooij, D. (Daan); E. Walton (Esther); L.T. Westlye (Lars); C.D. Whelan (Christopher); B.G. Windham (B Gwen); A.M. Winkler (Anderson); K. Wittfeld (Katharina); G. Woldehawariat (Girma); A. Björnsson (Asgeir); Wolfers, T. (Thomas); L.R. Yanek (Lisa); Yang, J. (Jingyun); A.P. Zijdenbos; M.P. Zwiers (Marcel); I. Agartz (Ingrid); L. Almasy (Laura); D. Ames (David); Amouyel, P. (Philippe); O.A. Andreassen (Ole A.); S. Arepalli (Sampath); A.A. Assareh; S. Barral (Sandra); M.E. Bastin (Mark); Becker, D.M. (Diane M.); J.T. Becker; D.A. Bennett (David A.); J. Blangero (John); H. van Bokhoven (Hans); D.I. Boomsma (Dorret); H. Brodaty (Henry); R.M. Brouwer (Rachel); H.G. Brunner; M. Buckner; J.K. Buitelaar (Jan); K. Bulayeva (Kazima); W. Cahn (Wiepke); V.D. Calhoun Vince D. (V.); D.M. Cannon (Dara); G. Cavalleri (Gianpiero); Cheng, C.-Y. (Ching-Yu); S. Cichon (Sven); M.R. Cookson (Mark); A. Corvin (Aiden); B. Crespo-Facorro (Benedicto); J.E. Curran (Joanne); M. Czisch (Michael); A.M. Dale (Anders); G.E. Davies (Gareth); A.J. de Craen (Anton); E.J.C. de Geus (Eco); P.L. de Jager (Philip); G.I. de Zubicaray (Greig); I.J. Deary (Ian J.); S. Debette (Stéphanie); C. DeCarli (Charles); N. Delanty; C. Depondt (Chantal); A.L. DeStefano (Anita); A. Dillman (Allissa); S. Djurovic (Srdjan); D.J. Donohoe (Dennis); D.A. Drevets (Douglas); Duggirala, R. (Ravi); M.D. Dyer (Matthew); C. Enzinger (Christian); S. Erk; T. 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Wassink (Annemarie); M.E. Weale (Michael); Weinberger, D.R. (Daniel R.); Weiner, M.W. (Michael W.); Wen, W. (Wei); E. Westman (Eric); T.J.H. White (Tonya); Wong, T.Y. (Tien Y.); Wright, C.B. (Clinton B.); R.H. Zielke (Ronald H.); A.B. Zonderman; N.G. Martin (Nicholas); C.M. van Duijn (Cock); M.J. Wright (Margaret); W.T. Longstreth Jr; G. Schumann (Gunter); H.J. Grabe (Hans Jörgen); B. Franke (Barbara); L.J. Launer (Lenore); S.E. Medland (Sarah Elizabeth); S. Seshadri (Sudha); P.M. Thompson (Paul); M.K. Ikram (Kamran)
2017-01-01
textabstractThe hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpi
Performance Evaluation of Image Fusion Based on Discrete Cosine Transform
Directory of Open Access Journals (Sweden)
Ramkrishna Patil
2013-05-01
Full Text Available Discrete cosine transform (DCT is used for fusion of two different images and for image compression. Image fusion deals with creating an image by combining portions from other images to obtain an image in which all of the objects are in focus. Two multi focus images are used for image fusion. Different fusion algorithms are used and their performance is evaluated using evaluation metrics such as PSNR, SSIM, Spatial Frequency, Quality Index, Structural Content, Mean Absolute Error. Fusion performance is not good while using the algorithms with block size less than 64x64 and also the block size of 512x512. Contrast, amplitude and energy based image fusion algorithms performed well. The fused images are comparable with the reference image. Only the image size is considered but blurring percentage is not considered. These algorithms are very simple and might be suitable for real time applications
Snaking and isolas of localised states in bistable discrete lattices
Taylor, Chris; 10.1016/j.physleta.2010.10.010
2010-01-01
We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localised states is made possible by pinning to the underlying lattice; they do not exist in the equivalent continuum equation. In particular we address the existence of 'isolas': closed curves of solutions in the bifurcation diagram. Isolas appear for some non-periodic boundary conditions in one spatial dimension but seem to appear generically in two dimensions. We point out how features of the bifurcation diagram in 1D help to explain some (unintuitive) features of the bifurcation diagram in 2D.
Operadic quantization as a tool for discrete geometry
Paal, E.; Virkepu, J.
2014-09-01
The operadic Lax representations of the harmonic oscillator are used to construct the quantum counterparts of 3d real Lie algebras in the Bianchi classification. The Jacobi operators of these quantum algebras are studied. It is shown how the energy conservation is related to the Jacobi identity and how the quantization leads to an anomaly - the quantum violation of the Jacobi relations. By using the nonvanishing quantum Jacobi operators, the derivative quantum algebra for a triple of 3d real Lie algebras is defined. It is proposed that the derivative algebra is the 3d real Heisenberg algebra. From this it follows that in this model only the discrete values of the spatial coordinates are physically allowed.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Breaking discrete symmetries in the effective field theory of inflation
Energy Technology Data Exchange (ETDEWEB)
Cannone, Dario [Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova,Padova, I-35131 (Italy); INFN, Sezione di Padova,Padova, I-35131 (Italy); Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics,Pohang, 790-784 (Korea, Republic of); Department of Physics,Postech, Pohang, 790-784 (Korea, Republic of); Tasinato, Gianmassimo [Department of Physics, Swansea University,Swansea, SA2 8PP (United Kingdom)
2015-08-03
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.