scholarly journals Warping Effects in Strongly Perturbed Metrics

Physics ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 665-678
Author(s):  
Marco Frasca ◽  
Riccardo Maria Liberati ◽  
Massimiliano Rossi
Keyword(s):  
General Relativity ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Symmetric Case ◽  
Einstein Equations ◽  
Time Dependent ◽  
Warp Factor ◽  
Leading Order ◽  
Numerical Examples

A technique devised some years ago permits us to develop a theory regarding a regime of strong perturbations. This translates into a gradient expansion that, at the leading order, can recover the Belinsky-Kalathnikov-Lifshitz solution for general relativity. We solve exactly the leading order Einstein equations in a spherical symmetric case, assuming a Schwarzschild metric under the effect of a time-dependent perturbation, and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

scholarly journals Warping Effects in Strongly Perturbed Metrics

2020 ◽  
Author(s):  
Marco Frasca ◽  
Riccardo Maria Liberati ◽  
Massimiliano Rossi
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Symmetric Case ◽  
Warp Factor ◽  
Leading Order ◽  
Gradient Expansion ◽  
Numerical Examples

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translate into a gradient expansion that, at the leading order, can recover the BKL solution. We solve exactly the leading order equations in a spherical symmetric case and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

A CLOSED-FORM SOLUTION OF THE EVOLUTION OPERATOR IN TWO-LEVEL SYSTEMS

1994 ◽  
Vol 08 (08n09) ◽  
pp. 505-508 ◽  
Author(s):  
XIAN-GENG ZHAO
Keyword(s):  
Closed Form ◽  
Lie Algebra ◽  
Evolution Operator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Two Level Systems ◽  
Special Case

It is demonstrated by using the technique of Lie algebra SU(2) that the problem of two-level systems described by arbitrary time-dependent Hamiltonians can be solved exactly. A closed-form solution of the evolution operator is presented, from which the results for any special case can be deduced.

Closed Form Solution for Time-dependent Enzyme Kinetics

1997 ◽  
Vol 187 (2) ◽  
pp. 207-212 ◽  
Author(s):  
S. Schnell ◽  
C. Mendoza
Keyword(s):  
Enzyme Kinetics ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

2000 ◽  
Vol 68 (2) ◽  
pp. 176-185 ◽  
Author(s):  
S. Candan ◽  
I. Elishakoff
Keyword(s):  
Closed Form ◽  
Infinite Number ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Benchmark Solutions

An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.

scholarly journals Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
M.-C. Casabán ◽  
J.-C. Cortés ◽  
B. García-Mora ◽  
L. Jódar
Keyword(s):  
Stochastic Process ◽  
Temperature Distribution ◽  
Numerical Solution ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mean Square ◽  
Random Boundary ◽  
Numerical Examples

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.

A Gas-Surface Interaction Model for Spatial and Time-Dependent Friction Coefficient in Reciprocating Contacts: Applications to Near-Frictionless Carbon

2005 ◽  
Vol 127 (1) ◽  
pp. 82-88 ◽  
Author(s):  
P. L. Dickrell ◽  
W. G. Sawyer ◽  
J. A. Heimberg ◽  
I. L. Singer ◽  
K. J. Wahl ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Closed Form ◽  
Closed Form Solution ◽  
Interaction Model ◽  
Nitrogen Atmosphere ◽  
Form Solution ◽  
Time Dependent ◽  
Series Expression ◽  
Dependent Model ◽  
Pin On Disk

A closed-form time- and position-dependent model for coverage, based on the adsorption of environmental contaminants and their removal through the pin contact, is developed for reciprocating contacts. The model employs an adsorption fraction and removal ratio to formulate a series expression for the entering coverage at any cycle and location on the wear track. A closed-form solution to the series expression is presented and compared to other coverage models developed for steady-state coverage for pin-on-disk contacts, reciprocating contacts, or the time-dependent center-point model for reciprocating contacts. The friction coefficient is based on the average coverage under the pin contact. The model is compared to position- and time-dependent data collected on near-frictionless carbon self-mated contacts on a reciprocating tribometer in a nitrogen atmosphere. There are many similarities between the model curves and the data, both in magnitude and trends. No new curve fitting was performed in this paper, with all needed parameters coming from previous models of average friction coefficient behavior.

scholarly journals Stochastic time-dependent enzyme kinetics: closed-form solution and transient bimodality

2020 ◽  
Author(s):  
James Holehouse ◽  
Augustinas Sukys ◽  
Ramon Grima
Keyword(s):  
Master Equation ◽  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Delta Function ◽  
Product Formation ◽  
Form Solution ◽  
Chemical Master Equation ◽  
Time Dependent ◽  
Enzyme Molecules

AbstractWe derive an approximate closed-form solution to the chemical master equation describing the Michaelis-Menten reaction mechanism of enzyme action. In particular, assuming that the probability of a complex dissociating into enzyme and substrate is significantly larger than the probability of a product formation event, we obtain expressions for the time-dependent marginal probability distributions of the number of substrate and enzyme molecules. For delta function initial conditions, we show that the substrate distribution is either unimodal at all times or else becomes bimodal at intermediate times. This transient bimodality, which has no deterministic counterpart, manifests when the initial number of substrate molecules is much larger than the total number of enzyme molecules and if the frequency of enzyme-substrate binding events is large enough. Furthermore, we show that our closed-form solution is different from the solution of the chemical master equation reduced by means of the widely used discrete stochastic Michaelis-Menten approximation, where the propensity for substrate decay has a hyperbolic dependence on the number of substrate molecules. The differences arise because the latter does not take into account enzyme number fluctuations while our approach includes them. We confirm by means of stochastic simulation of all the elementary reaction steps in the Michaelis-Menten mechanism that our closed-form solution is accurate over a larger region of parameter space than that obtained using the discrete stochastic Michaelis-Menten approximation.

scholarly journals A Closed-Form Solution of Photon States in Generic Gravitational Fields

2020 ◽  
Author(s):  
Xiaoping Hu
Keyword(s):  
General Relativity ◽  
Closed Form ◽  
A Priori ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dilation ◽  
Gravitational Fields ◽  
Special Cases ◽  
Photon States

This article first examines the solutions of two special cases of photon states (position, velocity, and frequency), which prove that the isotropy assumption underlies general relativity is invalid. As such, the geodesic methods used in general relativity cannot be used in general, though it may work in special cases. Then a method based on gravitational decomposition is proposed that solves the photon states in any gravitational fields in closed form. The solution does not even involve time t because time dilation is automatically covered in the decomposition solutions by a priori, proven solutions.

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