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PubMed2002

Large clusters in supercritical percolation.

The statistical behavior of the size of large finite clusters in supercritical percolation on a finite lattice is investigated (below the critical dimension of the space d(c)=6). For this purpose, an approximate system of ordinary differential equations for a number of finite clusters is obtained. The correlation between the critical exponents zeta that determine the cluster decay law (ln n(s) approximately -s(zeta)) and the surface of clusters is shown. It is found that for clusters without self-intersections having a maximal surface zeta=1. For clusters with a small number of self-intersections zeta=1-eta. Here eta is a function depending on the ratio of the surface area of a cluster to its size, which tends to zero, when the surface tends to a maximum. For compact clusters with a minimum or near-minimum surface area, the first correction to the cluster decay law above percolation threshold (ln n(s) approximately -s((d-1)/d)) has been found on the basis of the drop model and the derived system of equations. The predictions are tested numerically on two- and three-dimensional lattices by Monte Carlo simulations. The results of the work allow one to conclude that above the percolation threshold majority of large clusters are compact and that the cluster surface is the main factor affecting its behavior in supercritical percolation.

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PubMed2003

Torus breakdown in noninvertible maps.

We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L(0) coincides with the eigendirection corresponding to vanishing eigenvalue for the noninvertible map. Further parameter changes lead typically to the generation of loops (self-intersections of the invariant manifolds) followed by the transformation of the torus into a complex chaotic set.

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PubMed2004

Efficient acceleration of electrons with counterpropagating intense laser pulses in vacuum and underdense plasma.

We propose that efficient acceleration of electrons in vacuum and underdense plasmas by an intense laser pulse can be triggered in the presence of another counterpropagating or intersecting laser pulse. This mechanism works when the laser fields exceed some threshold amplitudes for stochastic motion of electrons, as found in single-electron dynamics. Particle-in-cell simulations confirm that electron heating and acceleration in the case with two counterpropagating laser pulses can be much more efficient than with one laser pulse only. Two different diagnoses show that the increased heating and acceleration are caused mainly by direct laser acceleration rather than by plasma waves. In plasma at moderate densities such as a few percent of the critical density and when the underdense plasma region is large enough, the Raman backscattered and side-scattered waves can grow to a sufficiently high level to serve as the second counterpropagating or intersecting pulse and trigger the electron stochastic motion. As a result, even with a single intense laser pulse only in plasma, electrons can be accelerated to an energy level much higher than the corresponding laser ponderomotive potential.

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PubMed2004

Statistical mechanics of fluids adsorbed in planar wedges: finite contact angle.

I consider the statistical mechanics of inhomogeneous fluids applied to fluids adsorbed in planar wedges. Exact results are described that belong to an infinite subset of models defined as the intersection of any two identical semi-infinite planar wall-fluid potentials. This geometry is interesting as a generic example of adsorption onto structured interfaces and of interfacial phase transitions controlled by the substrate geometry. Previously described virial theorems are extended to the case of a general wall-fluid model. This enables the consideration of wedge filling when Young's contact angle far from the wedge apex is finite. The virial theorems generate two important relations: the wedge sum rules. The first sum rule links the interfacial free energy far from the wedge apex to the structure induced at the apex. The second sum rule links the free energy of the apex region to the structure induced by the apex. When Young's contact angle at the wedge walls is finite these relations further yield an exact result for the macroscopic contact angle in terms of the nanoscopic structure at the three-phase contact line (the intersection of the liquid-vapor surface with a wedge wall): the contact angle sum rule. These exact results are of direct relevance to computer simulation studies of adsorbed films. In addition, they take on special significance in the vicinity of continuous interfacial phase transitions: an approach to complete filling and the filling transition at bulk liquid-vapor coexistence.

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PubMed2004

Characteristics of vehicular traffic flow at a roundabout.

We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated and the delay experienced by the traffic at each individual street is evaluated. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalization schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic-light signalization schemes.

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PubMed2004

Scattering off two oscillating disks: dilute chaos.

We investigate the role of the unstable periodic orbits and their manifolds in the dynamics of a time-dependent two-dimensional scattering system. As a prototype we use two oscillating disks on the plane with the oscillation axes forming an angle theta. The phase space of the system is five dimensional and it possesses a variety of families of unstable periodic orbits (UPOs) with intersecting manifolds. We perform numerical experiments to probe the structure of distinct scattering functions, in one and two dimensions, near the location of the UPOs. We find that the corresponding manifolds occur only in a very particular and localized way in the high-dimensional phase space. As a consequence the underlying fractal structure is ubiquitous only in higher-dimensional, e.g., two-dimensional, scattering functions. Both two-dimensional and one-dimensional scattering functions are dominated by seemingly infinite sequences of discontinuities characterized by small values of the magnitude of the projectile's outgoing velocity. These peaks accumulate toward the phase-space locations of the UPOs, with a rate which monotonically depends on the corresponding instability exponent. They represent the intersections of the set of the initial conditions with invariant sets of larger dimensionality embedded in the phase space of the system, which are not directly related with the UPOs. We adopt the term "dilute chaos" to characterize these phenomenological aspects of the scattering dynamics.

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PubMed2005

Interplay of entropic and memory effects in diffusion of methane in silicalite zeolites.

The role of entropic effects in methane distribution and transport in silicalite zeolites is studied using molecular dynamics in the limit of infinite dilution or small loading. Diffusive behavior and its anisotropy is assessed as a function of temperature where we find both an Arrhenius regime above 250 K and deviations thereof below such temperature. Using a previous probabilistic model, geometrical correlations or memory effects are evidenced and are shown to be enhanced as temperature is reduced. Deviations from Arrhenius behavior are concomitant with entropic effects. We find that, the preference of methane towards presence at intersections or channel centers changes at a threshold temperature. A discrete transition is found from a channel-center preferred phase, at low temperatures, versus an intersection preferred phase at high temperatures with evidence of hysteresis effects. Such entropic effects are also reflected, in diffusive transport, as non-Arrhenius-type behavior. A model based on accessible volume as a function of energy agrees with the simulated transition lending new insight into zeolite cavity design.

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PubMed2006

Scale invariance in road networks.

We study the topological and geographic structure of the national road networks of the United States, England, and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2< or = alpha < or =2.4, and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent and the fractal dimensions governing the placement of roads and intersections.

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PubMed2006

Deconstructing the energy landscape: constraint-based algorithms for folding heteropolymers.

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a geometrical chain constraint and a threshold constraint on the contact energy. A dynamical system is then defined in terms of the projections to these constraint sets, such that its fixed points solve the set intersection problem. We present results for two off-lattice hydrophobic-polar models: one with only rotameric degrees of freedom, and one proposed by Stillinger [Phys. Rev. E 48, 1469 (1993)] with flexible bond angles. Our phase retrieval inspired algorithm is competitive with more established algorithms and even finds lower-energy folds for one of the longer polymer chains.

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PubMed2000

Born-oppenheimer approximation near level crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.

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PubMed2004

Possible spin-tripletf-wave pairing due to disconnected fermi surfaces in NaxCoO2.yH2O.

We propose that the spin-triplet pairing mechanism due to disconnected Fermi surfaces proposed in our previous study [Phys. Rev. B 63, 174507 (2001)]] may be at work in a recently discovered superconductor NaxCoO2.yH2O. We introduce a single band effective model that takes into account the pocketlike Fermi surfaces along with the van Hove singularity near the K point found in the band calculation results. Applying the fluctuation exchange method and solving the linearized Eliashberg equation, the most dominant pairing is found to have spin-triplet f-wave symmetry, where the nodes of the gap function do not intersect the pocket Fermi surfaces. The presence of finite Tc is suggested in sharp contrast to cases when the gap nodes intersect the Fermi surface.

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PubMed2006

Some algebraic properties of crystallographic sublattices.

In this article, a number of the results relevant to the concept of sublattices of a basic crystallographic lattice are reviewed, emphasizing particularly previously unpublished work on the algebraic aspects. A three-dimensional geometric lattice L can be considered as an infinite Abelian group under addition. A sublattice S of L, which is also three-dimensional, is a subgroup of L such that the finite quotient group, G approximately equals L/S, is an Abelian group of order the index of S in L. The sublattice itself in its standard form is represented by an upper triangular matrix. The index of the sublattice is given by the determinant of this matrix. It is first noted that a sublattice described by an arbitrary basis set in L may be converted to this standard form. Next the sublattice is expressed as the intersection of a set of sublattices of individual index a power of a distinct prime, i.e. S(n = p(a)(1)p(b)(2)...) = S(1)(p(a)(1)[cap]S(2)(p(b)(2)...[cap]... = [bigcap](i)S(i)(p(alpha(i)), where p(1), p(2) etc. are prime numbers and n = Pi(i)p(alpha)(i) is the Euclidean factorization of n. This decomposition is important because it corresponds to the Sylow decomposition of the corresponding quotient group G approximately equals (i)[sign: see text] A(p)(i). It is also useful to be able to carry out two commutative binary operations on sublattices of L; these are to find their common sublattice of lowest index in L, which is their intersection S(cap) = S(a)(m)[cap]S(b)(n) and their common superlattice of highest index in L, given by S(< >) = , where < > indicates the span of the sublattices.

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PubMed1994

Principles and design feasibility of a Doppler ultrasound intravascular volumetric flowmeter.

A new Doppler ultrasound intravascular method is described for the measurement of volumetric flow. Based on the principles described by Hottinger and Meindl [15], it uses a novel semispherical transducer mounted at the tip of a catheter, which generates sample volumes in the form of a thin semispherical shell. Volumetric flow is calculated by using the average velocity determined from the received Doppler spectrum and the area of intersection of a sample volume that completely intersects flow across the vessel. Although a catheter-size transducer was not developed, a larger version was tested using an in vitro steady flow model. Maximum average flow error was limited to 9% for steady flows of 2 to 7 L/min. This error is believed to be a result of the nonuniform intensity generated by the prototype transducer, as well as slight variations in the received power, rather than any fundamental limitations of the flow measurement method itself. Since this study has verified the design principles and feasibility of this new approach, we believe that more detailed experimental investigations are warranted.

Adult↗

PubMed1990

An algorithm for 3-D automatic movement detection by means of standard TV cameras.

An algorithm for the computation of 3-D coordinates (space intersection) of marked points on a moving subject surveyed by a couple of TV cameras is presented herein. It has been designed in order to meet the requirements of routinary analysis in biomechanic laboratories. 3-D geometrical arrangement of the TV cameras (space resection) is obtained by means of a method which is based on an iterative least-squares estimation and requires little time for calibration operations; 3-D coordinates are computed by means of a fast geometrical intersection algorithm. The whole algorithm has been extensively used in different laboratories and results on its reliability and accuracy are reported.

Algorithms↗

PubMed2006

Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected].

We present research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models--one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical each with their respective prolate spheroidal and cylindrical parameter assignment regimes. These choices were made based on the typical shape of the left ventricle. For each frame starting with end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent nonrigid registration of the biventricular model at end-diastole to all later time frames. After registration of the model to all later time points, the registered NURBS models are temporally lofted in order to create a comprehensive four-dimensional NURBS model. From the lofted model, we can extract three-dimensional myocardial deformation fields and corresponding Lagrangian and Eulerian strain maps which are local measures of nonrigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian NURBS models with the cylindrical and prolate spheroidal parameter assignments outperform their counterparts in predicting normal strain. The decreased complexity associated with the Cartesian model with the cylindrical parameter assignment prompted its use for subsequent calculations. Lagrangian strains in three canine data, a normal human, and a patient with history of myocardial infarction are presented. Eulerian strains for the normal human data are also included.

Algorithms↗

PubMed2006

Neural networks for continuous online learning and control.

This paper proposes a new hybrid neural network (NN) model that employs a multistage online learning process to solve the distributed control problem with an infinite horizon. Various techniques such as reinforcement learning and evolutionary algorithm are used to design the multistage online learning process. For this paper, the infinite horizon distributed control problem is implemented in the form of real-time distributed traffic signal control for intersections in a large-scale traffic network. The hybrid neural network model is used to design each of the local traffic signal controllers at the respective intersections. As the state of the traffic network changes due to random fluctuation of traffic volumes, the NN-based local controllers will need to adapt to the changing dynamics in order to provide effective traffic signal control and to prevent the traffic network from becoming overcongested. Such a problem is especially challenging if the local controllers are used for an infinite horizon problem where online learning has to take place continuously once the controllers are implemented into the traffic network. A comprehensive simulation model of a section of the Central Business District (CBD) of Singapore has been developed using PARAMICS microscopic simulation program. As the complexity of the simulation increases, results show that the hybrid NN model provides significant improvement in traffic conditions when evaluated against an existing traffic signal control algorithm as well as a new, continuously updated simultaneous perturbation stochastic approximation-based neural network (SPSA-NN). Using the hybrid NN model, the total mean delay of each vehicle has been reduced by 78% and the total mean stoppage time of each vehicle has been reduced by 84% compared to the existing traffic signal control algorithm. This shows the efficacy of the hybrid NN model in solving large-scale traffic signal control problem in a distributed manner. Also, it indicates the possibility of using the hybrid NN model for other applications that are similar in nature as the infinite horizon distributed control problem.

Algorithms↗

PubMed2004

Effective multiresolution arc segmentation: algorithms and performance evaluation.

Arc segmentation plays an important role in the process of graphics recognition from scanned images. The GREC arc segmentation contest shows there is a lot of room for improvement in this area. This paper proposes a multiresolution arc segmentation method based on our previous seeded circular tracking algorithm which largely depends on the OOPSV model. The newly-introduced multiresolution paradigm can handle arcs/circles with large radii well. We describe new approaches for arc seed detection, arc localization, and arc verification, making the proposed method self-contained and more efficient. Moreover, this paper also brings major improvement to the dynamic adjustment algorithm of circular tracking to make it more robust. A systematic performance evaluation of the proposed method has been conducted using the third-party evaluation tool and test images obtained from the GREC arc segmentation contests. The overall performance over various arc angles, arc lengths, line thickness, noises, arc-arc intersections, and arc-line intersections has been measured. The experimental results and time complexity analyses on real scanned images are also reported and compared with other approaches. The evaluation result demonstrates the stable performance and the significant improvement on processing large arcs/circles of the MAS method.

Algorithms↗

PubMedDate not supplied

A method to generate soft shadows using a layered depth image and warping.

We present an image-based method for propagating area light illumination through a Layered Depth Image (LDI) to generate soft shadows from opaque and nonrefractive transparent objects. In our approach, using the depth peeling technique, we render an LDI from a reference light sample on a planar light source. Light illumination of all pixels in an LDI is then determined for all the other sample points via warping, an image-based rendering technique, which approximates ray tracing in our method. We use an image-warping equation and McMillan's warp ordering algorithm to find the intersections between rays and polygons and to find the order of intersections. Experiments for opaque and nonrefractive transparent objects are presented. Results indicate our approach generates soft shadows fast and effectively. Advantages and disadvantages of the proposed method are also discussed.

Algorithms↗