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In this Brief Communication, we examine in detail the motion of light particles—or dense gas bubbles—rising under gravity in a cellular flow. We follow the methodology of Maxey [Phys. Fluids 30, 1915 (1987)], and we examine a range of parameters not fully discussed in the past, corresponding to particles lighter and yet more inertial than the surrounding fluid if the added mass effect is considered. We observe a nonmonotonic behavior of the particle rise velocity, which exhibits a maximum for density of the particles only slightly smaller than the density of the fluid. The maximum value of the average rise velocity corresponding to the “optimum” density is several times (more than 40) higher than those obtained for small density changes around the optimum. The occurrence of this maximum is due to the combined effects of particle inertia and fluid added mass, which segregate the rising particles into specific, fast pathlines where the local fluid velocity adds to the particle gravitational velocity. A plot covering particle rise velocity for this range—not covered by the analysis of Maxey—is provided. [ABSTRACT FROM AUTHOR]

In the preceding paper [A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos J. Chem. Phys. (in press)] we introduced wavelet-accelerated Monte Carlo (WAMC), a coarse-graining methodology based on the wavelet transform, as a method for sampling polymer chains. In the present paper, we extend our analysis to consider excluded-volume effects by studying self-avoiding chains. We provide evidence that the coarse-grained potentials developed using the WAMC method obey phenomenological scaling laws, and use simple physical arguments for freely jointed chains to motivate these laws. We show that coarse-grained self-avoiding random walks can reproduce results obtained from simulations of the original, more-detailed chains to a high degree of accuracy, in orders of magnitude less time. [ABSTRACT FROM AUTHOR]

A generalized enthalpy based equation of state, which includes thermal electron excitations explicitly, is formulated from simple considerations. Its application to obtain Hugoniot of materials needs simultaneous evaluation of pressure-volume curve and temperature, the latter requiring solution of a differential equation. The errors involved in two recent papers [Huayun et al., J. Appl. Phys. 92, 5917 (2002); 92, 5924 (2002)], which employed this approach, are brought out and discussed. In addition to developing the correct set of equations, the present work also provides a numerical method to implement this approach. Constant pressure specific heat of ions and electrons and ionic enthalpy parameter, needed for applications, are calculated using a three component equation of state. The method is applied to porous Cu with different initial porosities. Comparison of results with experimental data shows good agreement. It is found that temperatures along the Hugoniot of porous materials are significantly modified due to electronic effects. [ABSTRACT FROM AUTHOR]

Anharmonicities of vibrational modes allow controlling state-to-state transitions and encoding quantum information bits into vibrational eigenstates. Resonances between different transitions hinder the control. In this paper all resonances that can occur in a two-qubit system are identified and studied. Computational experiments are carried out using optimal control theory and numerical propagation of vibrational wave packets. Useful insight is obtained into the mechanisms of negative effect of these resonances onto the control tasks. A set of general criteria is derived for evaluation of candidate molecules for practical realization of vibrational two-qubit system. Several simple strategies for avoiding such resonances by choosing suitable vibrational characteristics (mode frequencies and anharmonicities) are proposed. [ABSTRACT FROM AUTHOR]

Recently, we developed an efficient free energy simulation technique, the simulated scaling (SS) method [H. Li et al., J. Chem. Phys. 126, 024106 (2007)], in the framework of generalized ensemble simulations. In the SS simulations, random walks in the scaling parameter space are realized so that both phase space overlap sampling and conformational space sampling can be simultaneously enhanced. To flatten the distribution in the scaling parameter space, in the original SS implementation, the Wang–Landau recursion was employed due to its well-known recursion capability. In the Wang–Landau recursion based SS free energy simulation scheme, at the early stage, recursion efficiencies are high and free energy regions are quickly located, although at this stage, the errors of estimated free energy values are large; at the later stage, the errors of estimated free energy values become smaller, however, recursions become increasingly slow and free energy refinements require very long simulation time. In order to robustly resolve this efficiency problem during free energy refinements, a hybrid recursion strategy is presented in this paper. Specifically, we let the Wang–Landau update method take care of the early stage recursion: the location of target free energy regions, and let the adaptive reweighting method take care of the late stage recursion: the refinements of free energy values. As comparably studied in the model systems, among three possible recursion procedures, the adaptive reweighting recursion approach is the least favorable one because of its low recursion efficiency during free energy region locations; and compared to the original Wang–Landau recursion approach, the proposed hybrid recursion technique can be more robust to guarantee free energy simulation efficiencies. [ABSTRACT FROM AUTHOR]

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105, 585 (2003); Annu. Rev. Phys. Chem. 58, 113 (2007)] emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential ΔG=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in PdPC, respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by “dissociation constants,” which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule that cannot be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein that can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon. [ABSTRACT FROM AUTHOR]

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same “weak order two” accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms. [ABSTRACT FROM AUTHOR]

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more “fast” reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the “Next Reaction” variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we investigate theoretically the effect of an external electric field on the rate constant of steady-state bulk diffusion-controlled reactions. We generalize previously derived results for isotropic diffusion in the absence of interparticle interaction [J. Chem. Phys. 87, 4622 (1987)] to the case where translational diffusion is anisotropic. A frequently occurring situation of transverse isotropy where Dx=Dy≠Dz is considered in detail. We derive the first-order expansion for the reaction rate constant in terms of the electric field strength E, k(E)=k(0) (1+1/2εγ), where γ=k(0)/4πRD⊥, ε=qER/kBT, q is the charge, R is the contact distance, and D⊥ is the transverse diffusion coefficient. Numerical calculations show that this first-order expansion works well in the whole range of applicability of the Nernst–Einstein relation, i.e., for ε<1. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their "physical" counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories. [ABSTRACT FROM AUTHOR]

Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim of this paper is to present a variant (obtained via a weighted residual approach) of the averaged one-dimensional model derived by Stewart et al. ["Local and global instabilities of flow in a flexible-walled channel," Eur. J. Mech. B/Fluids 28, 541-557 (2009)]. The asymptotic expansions for small Reynolds numbers of these two models, compared to the exact solution obtained from the lubrication approach, reveal some quantitative difference, even at higher Reynolds numbers. Qualitatively, the two models give similar results at least at a linear level. It is shown that for relatively low membrane tension (T), there are distinct regions in the (T, R) parameter space where steady bifurcating flows may occur. These flows can also be observed at vanishingly small Reynolds numbers combined with relatively high membrane tension. At sufficiently high T and R, the bifurcating flow is rather time periodic. A weakly nonlinear analysis is then performed in both cases leading to the derivation of evolution equations for the amplitudes of the bifurcating flows. The amplitude equations show that the saddle node bifurcation has a transcritical character while the Hopf bifurcation is either subcritical or supercritical, depending both on the mode number and membrane tension. [ABSTRACT FROM AUTHOR]

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFSPML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation. [ABSTRACT FROM AUTHOR]

This paper presents an empirical linear equation to predict peak pressure level of anthropogenic impulsive signals based on its correlation with the sound exposure level. The regression coefficients are shown to be weakly dependent on the environmental characteristics but governed by the source type and parameters. The equation can be applied to values of the sound exposure level predicted with a numerical model, which provides a significant improvement in the prediction of the peak pressure level. Part I presents the analysis for airgun arrays signals, and Part II considers the application of the empirical equation to offshore impact piling noise. [ABSTRACT FROM AUTHOR]

In this paper, we construct a reciprocal transformation for the Geng-Xue equation and show that, with help of this transformation, we relate the first negative flow of the modified Boussinesq hierarchy to the Geng-Xue equation. Furthermore, we analyze the construction of conserved quantities and present new ones. [ABSTRACT FROM AUTHOR]

A magnetic field is defined by the property that its divergence is zero in a threedimensional oriented Riemannian manifold. Each magnetic field generates amagnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, (M³, g). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and Bmagnetic curves. [ABSTRACT FROM AUTHOR]

In the paper, fractional differential inclusions with the Jumarie derivative are studied. We discuss the existence and uniqueness of a solution to such problems. Our study relies on standard variational methods. [ABSTRACT FROM AUTHOR]

In this paper we carry out a complete classification of the Lie point symmetry groups associated with the quadratic Liénard type equation, x+f(x)x2+g(x)=0, where f(x) and g(x) are arbitrary functions of x. The symmetry analysis gets divided into two cases, (i) the maximal (eight parameter) symmetry group and (ii) non-maximal (three, two, and one parameter) symmetry groups. We identify the most general form of the quadratic Liénard equation in each of these cases. In the case of eight parameter symmetry group, the identified general equation becomes linearizable as well as isochronic. We present specific examples of physical interest. For the non-maximal cases, the identified equations are all integrable and include several physically interesting examples such as the Mathews-Lakshmanan oscillator, particle on a rotating parabolic well, etc. We also analyse the underlying equivalence transformations. [ABSTRACT FROM AUTHOR]

In this paper, we analyze qualitative properties of the first multi-symplectic scheme for two-dimensional Maxwell's equations. We prove that the scheme is unconditionally stable and convergent, non-dissipative, and divergence-free. The numerical dispersion relation of the scheme is shown to converge to the exact dispersion relation of the Maxwell equations. We also present some numerical results to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective numerical method for solving nonlinear Volterra partial integro-differential equations. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function as the 'memory' of system. Radial basis functions and finite difference method as the main techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some examples are demonstrated to describe the method. Numerical results confirm the validity and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

The detection of localized defects such as cracks and corrosion in pipes using guided elastic waves is now an established non-destructive testing procedure. However, the prediction of guided wave excitation and scattering in pipes is a complex three-dimensional (3D) problem with many parameters that can generally only be solved using numerical methods. In many important industrial applications, the diameter of a pipe is much larger than wall thickness. In this case an approximate theory is applicable, when a pipe is considered as an unwrapped isotropic plate. In this paper, a technique for obtaining pipe mode amplitudes in terms of the solution to the forced 3D problem on a plate is presented. The same principle is extended to relate guided wave scattering from defects in plates to scattered circumferential modal amplitudes from defects in pipe. This is of practical benefit as the scattering of guided waves by defects in a plate is a much simpler problem than that in a pipe, and one that, in some cases, can be solved using analytical methods. Results are shown that illustrate the application of the method to reflection from through-thickness circumferential cracks in pipes. [ABSTRACT FROM AUTHOR]

When a global model is attempted from experimental data, some preprocessing might be required. Therefore it is only natural to wonder what kind of effects the preprocessing might have on the modeling procedure. This concern is manifested in the form of recurrent frequently asked questions, such as “how does the preprocessing affect the underlying dynamics?” This paper aims at providing answers to important questions related to (i) data interpolation, (ii) data smoothing, (iii) data-estimated derivatives, (iv) model structure selection, and (v) model validation. The answers provided will hopefully remove some of those doubts and one shall be more confident not only on global modeling but also on various data analyses which may be also dependent on data preprocessing. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new ten-point multisymplectic scheme for the regularized long-wave equation from its Bridges’ multisymplectic form. The new scheme is an explicit scheme in the sense that it does not need iteration. We discuss some properties of the new scheme. The performance and the efficiency of the new scheme are illustrated by solving several test examples. The obtained results are presented and compared with previous methods. Numerical results indicate that the multisymplectic scheme cannot only obtain satisfied solutions for the regularized long-wave equation but also keep three invariants of motion which are evaluated to determine the conservation properties of the algorithm very well. [ABSTRACT FROM AUTHOR]

This paper concerns linear instabilities of incompressible flow along a rotating pipe when the disturbances are inviscid. The inviscid spectrum comprises an infinite number of eigenmodes, and significant complications arise from (i) switching in the identity of the most unstable mode and (ii) the existence of distinguished parameter limits in which some or all of the modes acquire special scalings. Nevertheless, we show that in one sense all the instabilities form a single ordered family, which we term a center-mode family, by applying an asymptotic theory recently developed for the trailing line vortex flow. We give complete computed neutral curves (stability boundaries) over a wide range of Rossby numbers, as well as contour plots of maximum growth rate. We find that the numerical calculations are in good agreement with the asymptotic theory and correctly recover previous results, including the limits of very large and very small Rossby number. There is some disagreement, however, with published results on the neutral curve at finite Rossby number. We show that this disagreement results from the intricate nature of the spectrum, which possesses two different types of neutral mode with two distinguished scalings. [ABSTRACT FROM AUTHOR]

An analytical solution is presented in this paper to investigate the control mechanism and modal characteristics of finite periodic and irregular ribbed plates. Peak responses of a finite periodic ribbed plate were examined where they were grouped into two sets of propagation zones according to the coupling mechanism at beam/plate interfaces. Details of modal characteristics in pass bands of the periodic ribbed plate were elucidated and the control mechanism was discussed. Modes in each pass band that are governed by shear force couplings were characterized by one of the beam flexural modes whose modal responses could be represented approximately by those of the corresponding orthotropic plate modes. Modes in the second set of pass bands were found to retain the resonance frequencies of the corresponding modes of the unribbed base plate. Higher order orthotropic plate modes were also identified, which could not be grouped into any pass bands defined by the classical periodic theory. The control mechanism leading to vibration confinement in disordered and irregular ribbed plates was also discussed. It was found that beam spacing irregularity attributes to localization of the group of modes associated with flexural wave couplings but not the group of modes associated with moment couplings. [ABSTRACT FROM AUTHOR]

Microscopic models with anomalous diffusion, which include the Comb model and its generalization for the finite width of the backbone, have been considered in this paper. The physical mechanisms of the subdiffusion random walks have been established. The first comes from the permanent return of the diffusing particle to the initial point of the diffusion due to “effective reducing” of the dimensionality of the considered system to the quasi-one-dimensional system. This physical mechanism has been obtained in the Comb model and in the model with a strip. The second mechanism of the subdiffusion is connected with random capture on the traps of diffusing particles and their ensuing random release from the traps. It has been shown that these different mechanisms of subdiffusion have been described by the different generalized diffusion equations of fractional order. The solutions of these different equations have been obtained, and the physical sense of the fractional order generalized equations has been discussed. [ABSTRACT FROM AUTHOR]

High-amplitude pressure oscillations in solid propellant rocket motor combustion chambers display nonlinear effects including: (1) limit cycle behavior in which the fluctuations may dwell for a considerable period of time near their peak amplitude, (2) elevated mean chamber pressure (DC shift), and (3) a triggering amplitude above which pulsing will cause an apparently stable system to transition to violent oscillations. Along with the obvious undesirable vibrations, these features constitute the most damaging impact of combustion instability on system reliability and structural integrity. The physical mechanisms behind these phenomena and their relationship to motor geometry and physical parameters must, therefore, be fully understood if instability is to be avoided in the design process, or if effective corrective measures must be devised during system development. Predictive algorithms now in use have limited ability to characterize the actual time evolution of the oscillations, and they do not supply the motor designer with information regarding peak amplitudes or the associated critical triggering amplitudes. A pivotal missing element is the ability to predict the mean pressure shift; clearly, the designer requires information regarding the maximum chamber pressure that might be experienced during motor operation. In this paper, a comprehensive nonlinear combustion instability model is described that supplies vital information. The central role played by steep-fronted waves is emphasized. The resulting algorithm provides both detailed physical models of nonlinear instability phenomena and the critically needed predictive capability. In particular, the origin of the DC shift is revealed. [ABSTRACT FROM AUTHOR]

Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The name “implicit LES” is used for approaches that merge the SGS model and numerical discretization. In this paper, the implicit SGS modeling environment provided by the adaptive local deconvolution method is extended to LES of passive-scalar mixing. The resulting adaptive advection algorithm is discussed with respect to its numerical and turbulence-theoretical background. We demonstrate that the new method allows for reliable predictions of the turbulent transport of passive scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. [ABSTRACT FROM AUTHOR]

Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of D. G. Hurley and G. Keady [J. Fluid Mech. 351, 119 (1997)]. The width of the wave beams is determined by competition between forcing and viscous smoothing, and hydrodynamic screening of the steep part of the topography extends the cylinder’s horizontal length scale. Beyond the weak forcing regime, harmonic waves of frequency nΩ (with integer n>1 and nΩ

It is known that the wavelength of the ripples on icicles in nature is of the centimeter scale. Such study on morphological instability of ice-water interface during ice growth from flowing supercooled water film with one side being a free surface has recently been made [K. Ueno, Phys. Rev. E 68, 021603 (2003)]. This is the first theoretical study taking into account the influence of the shape of the water-air surface on the growth condition of infinitesimal disturbances of the ice-water interface. A simpler formula to determine the wavelength of the ripples than that in the previous paper is derived. It seems that the wavelength of ripples is insensitive to the water supply rates, diameters of the icicles, and surrounding air temperatures. The details of dependence of the wavelength of ripples on these parameters are investigated. [ABSTRACT FROM AUTHOR]

This paper reports results of an analytical and experimental investigation of the laminar flow in a parallel-plate microchannel with ultrahydrophobic top and bottom walls. The walls are fabricated with microribs and cavities that are oriented parallel to the flow direction. The channel walls are modeled in an idealized fashion, with the shape of the liquid-vapor meniscus approximated as flat. An analytical model of the vapor cavity flow is employed and coupled with a numerical model of the liquid flow by matching the local liquid and vapor phase velocity and shear stress at the interface. The numerical predictions show that the effective slip length and the reduction in the classical friction factor-Reynolds number product increase with increasing relative cavity width, increasing relative cavity depth, and decreasing relative microrib/cavity module length. Comparisons were also made between the zero shear interface model and the liquid-vapor cavity coupled model. The results illustrate that the zero shear interface model underpredicts the overall flow resistance. Further, the deviation between the two models was found to be significantly larger for increasing values of both the relative rib/cavity module width and the cavity fraction. The trends in the frictional pressure drop predictions are in good agreement with experimental measurements made at similar conditions, with greater deviation observed at increasing size of the cavity fraction. Based on the numerical predictions, an expression is proposed in which the friction factor-Reynolds number product may be estimated in terms of the important variables. [ABSTRACT FROM AUTHOR]

A relatively small number of mathematically simple maps and flows are routinely used as examples of low-dimensional chaos. These systems typically have a number of parameters that are chosen for historical or other reasons. This paper addresses the question of whether a different choice of these parameters can produce strange attractors that are significantly more chaotic (larger Lyapunov exponent) or more complex (higher dimension) than those typically used in such studies. It reports numerical results in which the parameters are adjusted to give either the largest Lyapunov exponent or the largest Kaplan-Yorke dimension. The characteristics of the resulting attractors are displayed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectra of asymmetric spike solutions to the Gierer-Meinhardt system. It has previously been shown that the spectra of such solutions may be determined by finding the generalized eigenvalues of matrices, which are determined by the positions of the spikes and various parameters from the system. We will examine the spectra of asymmetric solutions near the point at which they bifurcate off of a symmetric branch. We will confirm that all such solutions are unstable in a neighborhood of the bifurcation point and we derive an explicit expression for the leading order terms of the critical eigenvalues. [ABSTRACT FROM AUTHOR]

In the paper, we adapt our previous formalism for a mathematical treatment of branes to include processes, specifically the Kondo flow for Wess-Zumino-Witten (WZW) branes. In this framework, we give the precise mathematical definitions and formulate a mathematical conjecture relating WZW branes to nonequivariant twisted K theory in the case of the group SU(n). We also discuss regularization of the Kondo flow, thereby giving a first step toward proving our conjecture. [ABSTRACT FROM AUTHOR]

In this paper, a theoretical model is described and demonstrated that serves as a useful tool for understanding K-shell radiating Z-pinch plasma behavior. Such understanding requires a self-consistent solution to the complete nonlocal thermodynamic equilibrium kinetics and radiation transport in order to realistically model opacity effects and the high-temperature state of the plasma. For this purpose, we have incorporated into the MACH2 two-dimensional magnetohydrodynamic (MHD) code [R. E. Peterkin et al., J. Comput. Phys. 140, 148 (1998)] an equation of state, called the tabular collisional radiative equilibrium (TCRE) model [J. W. Thornhill et al., Phys. Plasmas 8, 3480 (2001)], that provides reasonable approximations to the plasma’s opacity state. MACH2 with TCRE is applied toward analyzing the multidimensional implosion behavior that occurred in Decade Quad (DQ) [D. Price et al., Proceedings of the 12th IEEE Pulsed Power Conference, Monterey, CA, edited by C. Stallings and H. Kirbie (IEEE, New York, 1999), p. 489] argon gas puff experiments that employed a 12 cm diameter nozzle with and without a central gas jet on axis. Typical peak drive currents and implosion times in these experiments were ∼6 MA and ∼230 ns. By using Planar Laser Induced Fluorescence measured initial density profiles as input to the calculations, the effect these profiles have on the ability of the pinch to efficiently produce K-shell emission can be analyzed with this combined radiation-MHD model. The calculated results are in agreement with the experimental result that the DQ central-jet configuration is superior to the no-central-jet experiment in terms of producing more K-shell emission. These theoretical results support the contention that the improved operation of the central-jet nozzle is due to the better suppression of instabilities and the higher-density K-shell radiating conditions that the central-jet configuration promotes. When we applied the model toward projecting argon K-shell yield behavior for Sandia National Laboratories’ ZR machine (∼25 MA peak drive currents, ∼100 ns implosion times) [D. McDaniel et al., Proceedings of the 5th International Conference on Dense Z-Pinches, Albuquerque, NM, 2002, edited by J. Davis, C. Deeney, and N. R. Pereira (American Institute of Physics, New York, 2002), Vol. 651, p. 23] for experiments that utilize the 12 cm diameter central-jet nozzle configuration, it predicts over 1 MJ of K-shell emission is attainable. [ABSTRACT FROM AUTHOR]

In this paper, we give a condition on the bicharacteristic which guarantees the global existence of the mild solution to the Boltzmann equation with an external force for the hard-sphere model and potentials with angular cutoff in infinite vacuum. This generalizes the previous results to the case when the force can have arbitrary strength. The constructive condition on the bicharacteristic is used to obtain the pointwise estimates on the collision operator so that the global existence comes from the contraction mapping theorem. [ABSTRACT FROM AUTHOR]

The Poincaré equation, a second-order partial differential equation describing wave motions in a rotating spheroid of arbitrary eccentricity satisfying a certain set of the boundary condition, is studied. A new polynomial as the general solution of the Poincaré equation in spheroidal geometry is found for the first time. The paper focuses on some unusual and intriguing mathematical properties of the new Poincaré polynomial. The possible completeness of the set of eigenfunctions of the Poincaré equation in the form of the new polynomial is also discussed. The new Poincaré polynomial would provide a powerful basis for the mathematical analysis in many important geophysical and astrophysical problems. [ABSTRACT FROM AUTHOR]

An effective method of chaotification via time-delay feedback for a simple finite-dimensional continuous-time autonomous system is made rigorous in this paper. Some mathematical conditions are derived under which a nonchaotic system can be controlled to become chaotic, where the chaos so generated is in a rigorous mathematical sense of Li–Yorke in terms of the Marotto theorem. Numerical simulations are given to verify the theoretical analysis. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new characterization for global hyperbolicity is given. The concept of cosmological time function and its regularity was considered by Anderson et al. ['The cosmological time function,' Class. Quantum Grav. 15, 309 (1998)] and it was proved that if the cosmological time function of (M, g) is regular then it is globally hyperbolic. In this paper it is proved that if (M, g) is globally hyperbolic then there is a smooth function Ω > 0 such that the cosmological time function of (M, Ωg) is regular. It is also proved that the cosmological time function of Friedman-Robertson-Walker spacetime ((a, b) × f H, -dt2 + f h), a, b < ∞, is regular and in addition the regularity of cosmological time function for this kind of spacetimes is stable in Lor(M). [ABSTRACT FROM AUTHOR]

Average trapping time (ATT) is central in the trapping problem since it is a key indicator characterizing the efficiency of the problem. Previous research has provided the scaling of a lower bound of the ATT for random walks in general networks with a deep trap. However, it is still not well understood in which networks this minimal scaling can be reached. Particularly, explicit quantitative results for ATT in such networks, even in a specific network, are lacking, in spite that such networks shed light on the design for optimal networks with the highest trapping efficiency. In this paper, we study the trapping problem taking place on a hierarchical scale-free network with a perfect trap. We focus on four representative cases with the immobile trap located at the root, a peripheral node, a neighbor of the root with a single connectivity, and a farthest node from the root, respectively. For all the four cases, we obtain the closed-form formulas for the ATT, as well as its leading scalings. We show that for all the four cases of trapping problems, the dominating scalings of ATT can reach the predicted minimum scalings. This work deepens the understanding of behavior of trapping in scale-free networks, and is helpful for designing networks with the most efficient transport process. [ABSTRACT FROM AUTHOR]

This paper comments on a recent paper by Yu and Cao [Chaos, 16, 023119 (2006)]. We find that the theorem in this paper is incorrect by numerical simulations. The consequence of the incorrectness is analyzed as well. [ABSTRACT FROM AUTHOR]

Multi-axis measurement of motion is indispensable for characterization of dynamic systems and control of motion stages. This paper presents an optical beam deflection-based measurement system to simultaneously measure three-axis out-of-plane motion of both micro- and macro-scale targets. Novel strategies are proposed to calibrate the sensitivities of the measurement system. Subsequently the measurement system is experimentally realized and calibrated. The system is employed to characterize coupled linear and angular motion of a piezo-actuated stage. The measured motion is shown to be in agreement with theoretical expectation. Next, the high bandwidth of the measurement system has been showcased by utilizing it to measure coupled two-axis transient motion of a Radio Frequency Micro-Electro-Mechanical System switch with a rise time of about 60 μs. Finally, the ability of the system to measure out-of-plane angular motion about the second axis has been demonstrated by measuring the deformation of a micro-cantilever beam. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 < α < 2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems. [ABSTRACT FROM AUTHOR]

In this paper, we compute the Leibniz homology of the Galilei algebra. [ABSTRACT FROM AUTHOR]

In this paper, we give a classification of finite dimensional indecomposable modules of the Schrödinger algebra. [ABSTRACT FROM AUTHOR]

In Bayın's paper [J. Math. Phys. 53, 042105 (2012)], he claims to prove the consistency of the purported piece-wise solutions to the fractional Schrödinger equation for an infinite square well. However, his calculation uses standard contour integral techniques despite the absence of an analytic integrand. The correct calculation is presented and supports our earlier work proving that the purported piece-wise solutions do not solve the fractional Schrödinger equation for an infinite square well [M. Jeng, S.-L.-Y. Xu, E. Hawkins, and J. M. Schwarz, J. Math. Phys. 51, 062102 (2010)]. [ABSTRACT FROM AUTHOR]

In this paper, we characterize bounded ancient solutions to the time-dependent Stokes system with zero boundary value in various domains, including the half-space. [ABSTRACT FROM AUTHOR]

Lions, Temam, and Wang in ['Problème à frontière libre pour les modèles couplés de l'océan et de l'atmosphère,' Acad. Sci., Paris, C. R. 318(12), 1165-1171 (1994)] introduced a free surface model for the primitive equations of the ocean. In this paper, we establish the local well-posedness of the model with analytic initial data. [ABSTRACT FROM AUTHOR]