51 resultados para Classical hydraulic jump


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We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

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Predictions of two popular closed-form models for unsaturated hydraulic conductivity (K) are compared with in situ measurements made in a sandy loam field soil. Whereas the Van Genuchten model estimates were very close to field measured values, the Brooks-Corey model predictions were higher by about one order of magnitude in the wetter range. Estimation of parameters of the Van Genuchten soil moisture characteristic (SMC) equation, however, involves the use of non-linear regression techniques. The Brooks-Corey SMC equation has the advantage of being amenable to application of linear regression techniques for estimation of its parameters from retention data. A conversion technique, whereby known Brooks-Corey model parameters may be converted into Van Genuchten model parameters, is formulated. The proposed conversion algorithm may be used to obtain the parameters of the preferred Van Genuchten model from in situ retention data, without the use of non-linear regression techniques.

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The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.

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The objective of this work is to develop a systematic methodology for describing hand postures and grasps which is independent of the kinematics and geometry of the hand model which in turn can be used for developing a universal referencing scheme. It is therefore necessary that the scheme be general enough to describe the continuum of hand poses. Indian traditional classical dance form, “Bharathanatyam”, uses 28 single handed gestures, called “mudras”. A Mudra can be perceived as a hand posture with a specific pattern of finger configurations. Using modifiers, complex mudras could be constructed from relatively simple mudras. An adjacency matrix is constructed to describe the relationship among mudras. Various mudra transitions can be obtained from the graph associated with this matrix. Using this matrix, a hierarchy of the mudras is formed. A set of base mudras and modifiers are used for describing how one simple posture of hand can be transformed into another relatively complex one. A canonical set of predefined hand postures and modifiers can be used in digital human modeling to develop standard hand posture libraries.

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Using the fact the BTZ black hole is a quotient of AdS(3) we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. We show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop. The Landau-Lifshitz equations from the spin chain can also be identified with the sigma model equations of motion.

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This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

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An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant $\chi =\mu /\hslash $ of the dimensions of a reciprocal length, $\mu $ being the meson mass, and as $\chi \rightarrow $ 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10$^{9}$ eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p$^{4}$/E$^{2}$ (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E $\sim $ 3$\cdot $5$\mu $, its value at this point being 3 $\times $ 10$^{-26}$ cm.$^{2}$, after which it decreases rapidly, becoming proportional to E$^{-2}$ at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E $\gtrsim $ 3$\mu $. The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3$\cdot $5$\mu $. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3$\mu $. Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.

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Hydraulic conductivity of fine-grained soils has assumed greater importance in waste disposal facilities. It is necessary to understand better the factors controlling hydraulic conductivity of fine-grained soils which are used as liners in waste disposal facilities. Hydraulic Conductivity study with ten soils with two fluids having extreme dielectric constants(epsilon) namely water and CCl4 has shown that intrinsic permeability (K) increases drastically with decrease in epsilon. These changes are attributed to the significant reduction in the thickness of diffuse double layer which in turn mainly dependent on the epsilon of the permeant. Hydraulic Conductivity with water of each pair of soils having nearly same liquid limit but different plasticity properties is found to be vastly different, but found to correlate well with shrinkage index, defined as difference between the liquid and the shrinkage limits. Also the ratio Kccl(4)/K-w is found to significantly increase with the increase in the shrinkage index.

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The orientational relaxation dynamics of water confined between mica surfaces is investigated using molecular dynamics simulations. The study illustrates the wide heterogeneity that exists in the dynamics of water adjacent to a strongly hydrophilic surface such as mica. Analysis of the survival probabilities in different layers is carried out by normalizing the corresponding relaxation times with bulk water layers of similar thickness. A 10-fold increase in the survival times is observed for water directly in contact with the mica surface and a non-monotonic variation in the survival times is observed moving away from the mica surface to the bulk-like interior. The orientational relaxation time is highest for water in the contact layer, decreasing monotonically away from the surface. In all cases the ratio of the relaxation times of the 1st and 2nd rank Legendre polynomials of the HH bond vector is found to lie between 1.5 and 1.9 indicating that the reorientational relaxation in the different water layers is governed by jump dynamics. The orientational dynamics of water in the contact layer is particularly novel and is found to undergo distinct two-dimensional hydrogen bond jump reorientational dynamics with an average waiting time of 4.97 ps. The waiting time distribution is found to possess a long tail extending beyond 15 ps. Unlike previously observed jump dynamics in bulk water and other surfaces, jump events in the mica contact layer occur between hydrogen bonds formed by the water molecule and acceptor oxygens on the mica surface. Despite slowing down of the water orientational relaxation near the surface, life-times of water in the hydration shell of the K ion are comparable to that observed in bulk salt solutions. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4717710]

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Motion analysis is very essential in sport activities to enhance the performance of an athlete and to ensure the correctness of regimes. Expensive methods of motion analysis involving the use of sophisticated technology has led to limited application of motion analysis in sports. Towards this, in this paper we have integrated a low-cost method for motion analysis using three axis accelerometer, three axis magnetometer and microcontroller which are very accurate and easy to use. Seventeen male subjects performed two experiments, standing short jumps and long jumps over a wide range of take-off angles. During take-off and landing the acceleration and angles at different joints of the body are recorded using accelerometers and magnetometers, and the data is captured using Lab VIEW software. Optimum take-off angle in these jumps are calculated using the recorded data, to identify the optimum projection angle that maximizes the distance achieved in a jump. The results obtained for optimum take off angle in short jump and long jump is in agreement with those obtained using other methodologies and theoretical calculations assuming jump to be a projectile motion. The impact force (acceleration) is also analysed and is found to progressively decrease from foot to neck.

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We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

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The current study analyzes the leachate distribution in the Orchard Hills Landfill, Davis Junction, Illinois, using a two-phase flow model to assess the influence of variability in hydraulic conductivity on the effectiveness of the existing leachate recirculation system and its operations through reliability analysis. Numerical modeling, using finite-difference code, is performed with due consideration to the spatial variation of hydraulic conductivity of the municipal solid waste (MSW). The inhomogeneous and anisotropic waste condition is assumed because it is a more realistic representation of the MSW. For the reliability analysis, the landfill is divided into 10 MSW layers with different mean values of vertical and horizontal hydraulic conductivities (decreasing from top to bottom), and the parametric study is performed by taking the coefficients of variation (COVs) as 50, 100, 150, and 200%. Monte Carlo simulations are performed to obtain statistical information (mean and COV) of output parameters of the (1) wetted area of the MSW, (2) maximum induced pore pressure, and (3) leachate outflow. The results of the reliability analysis are used to determine the influence of hydraulic conductivity on the effectiveness of the leachate recirculation and are discussed in the light of a deterministic approach. The study is useful in understanding the efficiency of the leachate recirculation system. (C) 2013 American Society of Civil Engineers.