110,121 research outputs found
Radial distribution functions of water: Models vs experiments
No full textWe study the temperature behavior of the first four peaks of the oxygen-oxygen radial distribution function of water, simulated by the TIP4P/2005, MB-pol, TIP5P, and SPC/E models and compare to experimental X-ray diffraction data, including a new measurement which extends down to 235 K [H. Pathak et al., J. Chem. Phys. 150, 224506 (2019)]. We find the overall best agreement using the MB-pol and TIP4P/2005 models. We observe, upon cooling, a minimum in the position of the second shell simulated with TIP4P/2005 and SPC/E potentials, located close to the temperature of maximum density. We also calculated the two-body entropy and the contributions coming from the first, second, and outer shells to this quantity. We show that, even if the main contribution comes from the first shell, the contribution of the second shell can become important at low temperature. While real water appears to be less ordered at short distance than obtained by any of the potentials, the different water potentials show more or less order compared to the experiments depending on the considered length-scale
Fixed and coincidence points of hybrid mappings
No full textsummary:The purpose of this note is to provide a substantial improvement and appreciable generalizations of recent results of Beg and Azam; Pathak, Kang and Cho; Shiau, Tan and Wong; Singh and Mishra
Sleep apnea and cardiac arrhythmia: a timely wake-up call!
No full textRajeev K. Pathak, Rajiv Mahajan, Dennis H. Lau, Prashanthan Sander
Uniform Ray Description for the PO Scattering by Vertices in Curved Surface With Curvilinear Edges and Relatively General Boundary Conditions
No full textA new high-frequency analysis is presented for the scattering by vertices in a curved surface with curvilinear edges and relatively general boundary conditions, under the physical optics (PO) approximation. Both, impenetrable (e. g., impedance surface, coated conductor) as well as transparent thin sheet materials (e. g., thin dielectric, or frequency selective surface) are treated, via their Fresnel reflection and transmission coefficients. The PO scattered field is cast in a uniform theory of diffraction (UTD) ray format and comprises geometrical optics, edge and vertex diffracted rays. The contribution of this paper is twofold. First, we derive PO-based edge and vertex diffraction coefficients for sufficiently thin but relatively arbitrary materials, while in the literature most of the results (especially for vertex diffraction) are valid only for perfectly conducting objects. Second, the shadow boundary transitional behavior of edge and vertex diffracted fields is rigorously derived for the curved geometry case, as a function of various geometrical parameters such as the local radii of curvature of the surface, of its edges and of the incident ray wavefront. For edge diffracted rays, such a transitional behavior is found to be the same as that obtained heuristically in the original UTD. For vertex diffracted rays, the PO-based transitional behavior is a novel result providing offers clues to generalize a recent UTD solution for a planar vertex to treat the present curved vertex problem. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description
Prevention and regressive effect of weight-loss and risk factor modification on atrial fibrillation: the reverse-AF study - authors' reply
No full textAbstract not availableMelissa E. Middeldorp, Rajeev K. Pathak, Dennis H. Lau and Prashanthan Sander
A UTD Diffraction Coefficient for a Corner Formed by Truncation of Edges in an Otherwise Smooth Curved Surface
No full textA uniform geometrical theory of diffraction for vertices formed by truncated curved wedges
No full textA uniform geometrical theory of diffraction (UTD) ray analysis is developed for analyzing the problem of electromagnetic (EM) scattering by vertices at the tip of a pyramid formed by curved surfaces with curvilinear edges when illuminated by an arbitrarily polarized astigmatic wavefront. The UTD vertex diffraction coefficient involves various geometrical parameters such as the local radii of curvature of the faces of the pyramid, of its edges, and of the incident ray wavefront, and it is able to compensate for those discontinuities of the field predicted by the UTD for edges (i.e., geometrical optics (GO) combined with the UTD edge diffracted rays) occurring when an edge diffraction point lies at the tip or vertex. This provides an effective engineering tool able to describe the field scattered by truncated edges in curved surfaces within a UTD framework, as required in modern ray-based codes. Some numerical examples highlight the accuracy and the effectiveness of the proposed UTD ray solution for vertex diffraction
The Uniform Geometrical Theory of Diffraction and Some of Its Applications
No full textKeller introduced his Geometrical Theory of Diffraction (GTD) in the 1950s. The Geometrical Theory of Diffraction development was revolutionary, in that it explained the phenomena of wave diffraction entirely in terms of rays for the first time, via a systematic generalization of Fermat's principle. In its original form, the Geometrical Theory of Diffraction exhibited singularities at and near ray-shadow boundaries and caustics. For practical applications, it is necessary to patch up the Geometrical Theory of Diffraction in such regions. Uniform asymptotic high-frequency methods overcome the failure of the Geometrical Theory of Diffraction inside those regions, and outside those regions they generally reduce to the Geometrical Theory of Diffraction. One such highly developed approach happens to be the Uniform Geometrical Theory of Diffraction (UTD). The present article focuses on some key Uniform Geometrical Theory of Diffraction developments in a semi-historical fashion, with a few typical applications to illustrate the power and utility of the Geometrical Theory of Diffraction/Uniform Geometrical Theory of Diffraction concept to solve practical problems
Uniform Asymptotic Evaluation of Surface Integrals With Polygonal Integration Domains in Terms of UTD Transition Functions
No full textThe field scattered by a scattering body or by an aperture in the free space (or in an unbounded homogenous medium) can be described in terms of a double integral. In this paper we show how a canonical integral on a polygonal domain, with a constant amplitude function and a quadratic phase variation, can be exactly expressed in terms of special functions, namely Fresnel integrals and generalized Fresnel integrals. This exact reduction represents a paradigm for deriving a new asymptotic evaluation for a more general integral. This new asymptotic uniform integral evaluation is expressed in the format of the uniform geometrical theory of diffraction which is convenient for numerical computations
A NEW UTD BASED RELATION BETWEEN MODIFIED PAULI-CLEMMOW AND VAN DER WAERDEN METHODS FOR ASYMPTOTIC EVALUATION OF WEDGE DIFFRACTION INTEGRALS
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