Time-Dependent Non-Linear Closed-Form Solution of Cable Trusses

2009 ◽  
Author(s):  
S. Kmet ◽  
Z. Kokorudova
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Non Linear

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.

Strain fields in cracked bodies under antiplane shear for a generalised non-hardening material law

2019 ◽  
Vol 24 (10) ◽  
pp. 3125-3135
Author(s):  
M Zappalorto
Keyword(s):  
Closed Form ◽  
Large Strain ◽  
Closed Form Solution ◽  
Form Solution ◽  
Antiplane Shear ◽  
Elastic Behaviour ◽  
Strain Fields ◽  
Hardening Material ◽  
Hardening Law ◽  
Non Linear

An exact, closed form, solution is derived for the non-linear stress distribution in a cracked body under antiplane shear deformation. A generalised, non work-hardening, law is introduced to describe the material behaviour, and the stress and strain fields are derived in closed form. Such a new generalised material law includes the effect of a new parameter, a, which allows the transition from the ideally elastic behaviour (low strain regime) to the pure non-linear behaviour (large strain regime) to be modulated. A discussion is carried out on the features of the new solution and on the behaviour of stresses and strains close to and far away from the crack tip.

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.

Pipeline Walking due to Temperature Transient: Enhanced Analytical Calculations

2020 ◽  
Author(s):  
Daniel Carneiro ◽  
Renata Carvalhal
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Transient Temperature ◽  
Temperature Profiles ◽  
Linear Temperature ◽  
Temperature Front ◽  
Non Linear ◽  
Closed Form Analytical Solution ◽  
Remarkable Agreement

Abstract Pipeline walking induced by transient temperature profiles as the pipeline heats up is assessed. Firstly, an integrated, closed-form solution is given for a problem for which only an ‘incremental’ solution was available [1]. This involves a short pipeline unrestrained at both ends subject to a linearly ramping temperature front. Secondly, the range of validity of this solution is significantly extended, whilst still presenting it in closed-form. Results are compared with previously published FEA results, presenting remarkable agreement. The closed-form analytical solution is then compared with FEA of more realistic transients (non-linear temperature front). Results show that the linear simplification can introduce excessive conservatism. The FEA results are then examined, and the reason for the excessive conservatism is found to be associated to early expansion of the cold end, which is not observed with the simplified linear front. A simplified incremental solution for non-linear transients is proposed. This is shown to be simple and effective in improving prediction for the range over which where the closed form solution is most conservative.

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.

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