PDE: Hyperbolic form

2019 ◽  
pp. 109-136
Author(s):  
Bijan Kumar Bagchi
Keyword(s):  
Hyperbolic Form

A stochastic model for sand sorting in a wind-tunnel

1981 ◽  
Vol 13 (2) ◽  
pp. 282-297 ◽  
Author(s):  
O. Barndorff-Nielsen ◽  
J. N. Darroch
Keyword(s):  
Wind Tunnel ◽  
Stochastic Model ◽  
Single Particle ◽  
Hyperbolic Type ◽  
Size Distributions ◽  
Wind Tunnel Experiments ◽  
Stable Conditions ◽  
Hyperbolic Form ◽  
Experimental Findings

The wind exerts a sorting effect on particles of sands and, under certain stable conditions that occur frequently but whose nature is little understood, the sorting results in log-size distributions of the hyperbolic form, first noted by R. A. Bagnold. Here, for wind-tunnel experiments a stochastic model is constructed which exhibits a sorting effect deriving from the dependence of distance travelled on the size of the single particle. Under rather specific, experimentally testable assumptions the model reproduces log-size distributions which are of the hyperbolic type and show a variation with distance along the wind tunnel that accords with experimental findings of R. A. Bagnold.

scholarly journals Limits of canonical forms on towers of Riemann surfaces

2020 ◽  
Vol 2020 (764) ◽  
pp. 287-304
Author(s):  
Hyungryul Baik ◽  
Farbod Shokrieh ◽  
Chenxi Wu
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Type Theorem ◽  
Universal Cover ◽  
Canonical Forms ◽  
Classical Version ◽  
Galois Cover ◽  
Hyperbolic Form ◽  
Galois Covers ◽  
Hyperbolic Riemann Surface

AbstractWe prove a generalized version of Kazhdan’s theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence {\{S_{n}\rightarrow S\}} of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on {S_{n}}’s converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss–Bonnet-type theorem in the context of arbitrary infinite Galois covers.

scholarly journals Steady-state analysis for a class of hyperbolic systems with boundary inputs

2013 ◽  
Vol 23 (3) ◽  
pp. 295-310 ◽  
Author(s):  
Krzysztof Bartecki
Keyword(s):  
Steady State ◽  
Hyperbolic Systems ◽  
Hyperbolic Partial Differential Equations ◽  
Distributed Parameter ◽  
State Variables ◽  
Steady State Analysis ◽  
Tube Heat Exchanger ◽  
State Response ◽  
Hyperbolic Form ◽  
State Analysis

Abstract Results of a steady-state analysis performed for a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the system with two state variables and two boundary inputs, the analytical expressions for the steady-state distribution of the state variables are derived, both in the exponential and in the hyperbolic form. The influence of the location of the boundary inputs on the steady-state response is demonstrated. The considerations are illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

The influence of temperature and osmotic stress on the development and eclosion of hookworm eggs

1985 ◽  
Vol 59 (3) ◽  
pp. 217-224 ◽  
Author(s):  
Bernard E. Matthews
Keyword(s):  
Osmotic Stress ◽  
Development Time ◽  
Ionic Composition ◽  
Time Lapse ◽  
Ancylostoma Ceylanicum ◽  
Hatching Time ◽  
Ionic Changes ◽  
Hyperbolic Form ◽  
Increasing Temperature ◽  
Developmental Parameter

ABSTRACTTime lapse video micro recording techniques have been used to investigate the development and eclosion of Ancylostoma ceylanicum and A. tubaeforme eggs under a range of temperature and osmotic conditions. Over the range 15 to 35°C increasing temperature resulted in decreased development time, the hyperbolic form of the curve being similar to that found by other workers. The adoption of a developmental parameter to mark the start of timing provided more reproducible results than previously reported. Osmotic stress in the range 0·600 mOsM/kg provided by a number of inorganic salts and organic sugars increased hatching time but did not greatly reduce the percentage that hatched. There was no correlation between the ionic composition of the solution and its effect on the eggs. Solutions of EDTA, carbonates and iodides markedly reduced hatching. Behavioural studies of the pre-hatched larvae suggested that the eggs were permeable and susceptible to osmotic and ionic changes early in their development and well before they were ready to hatch. No appreciable differences were found between the two species of hookworm investigated.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

Effect of Temperature Dependent Properties on the Applicability of the Heat Conduction Equations for Rapid Heat Deposition Applications

2016 ◽  
Author(s):  
John G. Michopoulos ◽  
Andrew Birnbaum ◽  
Athanasios P. Iliopoulos
Keyword(s):  
Differential Equation ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Proper Form ◽  
Heat Deposition ◽  
Hyperbolic Form ◽  
Parabolic Form ◽  
Temperature Dependent Properties

Despite significant efforts examining the suitability of the proper form of the heat transfer partial differential equation (PDE) as a function of the time scale of interest (e.g. seconds, picoseconds, femtoseconds, etc.), very little work has been done to investigate the millisecond-microsecond regime. This paper examines the differences between the parabolic and one of the hyber-bolic forms of the heat conduction PDE that govern the thermal energy conservation on these intermediate timescales. Emphasis is given to the types of problems where relatively fast heat flux deposition is realized. Specifically, the classical parabolic form is contrasted against the lesser known Cattaneo-Vernotte hyperbolic form. A comparative study of the behavior of these forms over various pulsed conditions are applied at the center of a rectangular plate. Further emphasis is given to the variability of the solutions subject to constant or temperature-dependent thermal properties. Additionally, two materials, Al-6061 and refractory Nb1Zr, with widely varying thermal properties, were investigated.

scholarly journals Black hole initial data by numerical integration of the parabolic–hyperbolic form of the constraints

2021 ◽  
Author(s):  
Anna Nakonieczna ◽  
Łukasz Nakonieczny ◽  
István Rácz
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Initial Data ◽  
Fourth Order ◽  
Main Part ◽  
Strong Field ◽  
Method Of Lines ◽  
Time Integration ◽  
The Method Of Lines ◽  
Hyperbolic Form

The parabolic–hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is fourth-order accurate (in the spatial directions) while “time”-integration is made by using the method of lines with a fourth-order order accurate Runge–Kutta scheme. The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors is determined by comparing numerically and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations. The main part of our investigations is, however, centered on the construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content. Remarkably, the applied new method is unprecedented in that it allows to construct initial data for highly boosted and spinning black holes, essentially for the full physical allowed ranges of these parameters. In addition, the use of the evolutionary form of the constraints is free from applying any sort of boundary conditions in the strong field regime.

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