scholarly journals On Gumbel limit for the length of reactive paths

2014 ◽  
Vol 15 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Yuri Bakhtin
Keyword(s):  
Limit Theorem ◽  
Scaling Limit ◽  
Two Dimensional ◽  
Exit Times ◽  
One Dimensional ◽  
Starting Point ◽  
Noise Limit

We give a new proof of the vanishing noise limit theorem for exit times of one-dimensional diffusions conditioned on exiting through a point separated from the starting point by a potential wall. We also prove a scaling limit for exit location in a model two-dimensional situation.

scholarly journals One-dimensional and two-dimensional dynamics of cubic maps

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Djellit Ilhem ◽  
Kara Amel
Keyword(s):  
Large Class ◽  
System Parameter ◽  
Two Dimensional ◽  
One Dimensional ◽  
Henon Maps ◽  
Hénon Maps ◽  
Starting Point ◽  
Good Starting Point ◽  
Polynomial Diffeomorphisms

We concentrate on the dynamics of one-dimensional and two-dimensional cubic maps, it describes how complex behaviors can possibly arise as a system parameter changes. This is a large class of diffeomorphisms which provide a good starting point for understanding polynomial diffeomorphisms with constant Jacobian and equivalent to a composition of generalized Hénon maps. Due to the theoretical and practical difficulties involved in the study, computers will presumably play a role in such efforts.

scholarly journals Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone

Logistics ◽  
2019 ◽  
Vol 3 (3) ◽  
pp. 17
Author(s):  
Todor Todorov
Keyword(s):  
Probability Density ◽  
Travel Time ◽  
Analytical Form ◽  
Two Dimensional ◽  
Travel Times ◽  
One Dimensional ◽  
Starting Point ◽  
Random Location ◽  
The Time Domain ◽  
Taxicab Geometry

Travel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way travel from a random to another random location. The probability density function (PDF) of the travelling time for a semi-random trip in a one-dimensional zone is expressed analytically for all possible locations of its starting point. The PDF of a random trip within the same zone is found as a marginal probability by considering all possible durations for such travel. Then the PDFs for the travel times of single command (SC) and dual command (DC) cycles are obtained by scaling the PDF for the travel time of a semi-random trip (for SC) and as the maximum travel time of two independent semi-random trips (for DC). PDFs for travel times in a two-dimensional service zone with taxicab geometry are calculated by considering the trip as a superposition of two one-dimensional trips. The PDFs for travel times of SC and DC cycles are calculated in the same way. Both the one-dimensional and the two-dimensional service zones are analyzed in the time domain without normalization. The PDFs for all travel times are expressed in an analytical form parameterized by the maximal possible travel time within the zone. The graphs of all PDFs are illustrated by numerical examples.

Rods, plates and shells

1968 ◽  
Vol 64 (3) ◽  
pp. 895-913 ◽  
Author(s):  
A. E. Green ◽  
N. Laws ◽  
P. M. Naghdi
Keyword(s):  
Continuum Mechanics ◽  
Three Dimensional ◽  
Elastic Rods ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Starting Point ◽  
Non Linear ◽  
Plates And Shells

AbstractWe discuss non-linear thermodynamical theories of rods and shells using the three-dimensional theory of classical continuum mechanics as a starting point. The three-dimensional theory is reduced to a two-dimensional theory for a shell, or plate, and a one-dimensional theory for a rod by employing an exact expansion for the displacement but an approximation for the temperature. For elastic rods and shells a method of approximation is suggested which brings the respective theories into correspondence with those of Green and Laws (1) and Green, Naghdi and Wain-wright(2).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

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