Contributions of higher-order proximal distribution functions to solvent structure around proteins

2021 ◽  
Vol 155 (10) ◽  
pp. 104110
Author(s):  
Razie Yousefi ◽  
Gillian C. Lynch ◽  
Madeline Galbraith ◽  
B. Montgomery Pettitt
Keyword(s):  
Higher Order ◽  
Distribution Functions ◽  
Solvent Structure

scholarly journals Higher-order dissipation in the theory of homogeneous isotropic turbulence

2016 ◽  
Vol 803 ◽  
pp. 250-274 ◽  
Author(s):  
Norbert Peters ◽  
Jonas Boschung ◽  
Michael Gauding ◽  
Jens Henrik Goebbert ◽  
Reginald J. Hill ◽  
...  
Keyword(s):  
Source Term ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Higher Order ◽  
Distribution Functions ◽  
Order Structure ◽  
Source Terms ◽  
Homogeneous Isotropic Turbulence ◽  
Higher Order Moments ◽  
Even Order

The two-point theory of homogeneous isotropic turbulence is extended to source terms appearing in the equations for higher-order structure functions. For this, transport equations for these source terms are derived. We focus on the trace of the resulting equations, which is of particular interest because it is invariant and therefore independent of the coordinate system. In the trace of the even-order source term equation, we discover the higher-order moments of the dissipation distribution, and the individual even-order source term equations contain the higher-order moments of the longitudinal, transverse and mixed dissipation distribution functions. This shows for the first time that dissipation fluctuations, on which most of the phenomenological intermittency models are based, are contained in the Navier–Stokes equations. Noticeably, we also find the volume-averaged dissipation $\unicode[STIX]{x1D700}_{r}$ used by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) in the resulting system of equations, because it is related to dissipation correlations.

Higher order alignment tensors for continuum dislocation dynamics

2013 ◽  
Vol 1535 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Total Curvature ◽  
Higher Order ◽  
Distribution Functions ◽  
Dislocation Dynamics ◽  
Symmetric Tensors ◽  
Materials Modeling ◽  
Continuum Dislocation Dynamics ◽  
Alignment Tensors ◽  
Higher Order Tensors

ABSTRACTDislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

scholarly journals Dispersion chain of Vlasov equations

2022 ◽  
Vol 2022 (1) ◽  
pp. 013205
Author(s):  
E E Perepelkin ◽  
B I Sadovnikov ◽  
N G Inozemtseva ◽  
I I Aleksandrov
Keyword(s):  
Fluid Dynamics ◽  
Conservation Laws ◽  
Probability Density ◽  
Wigner Function ◽  
Higher Order ◽  
Distribution Functions ◽  
Tensor Form ◽  
Vlasov Equations

Abstract On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).

scholarly journals ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS

2018 ◽  
Vol 33 (1) ◽  
pp. 64-80 ◽  
Author(s):  
Idir Arab ◽  
Paulo Eduardo Oliveira
Keyword(s):  
Explicit Expression ◽  
Failure Rate ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Higher Order ◽  
Distribution Functions ◽  
Weibull Distributions ◽  
Stochastic Orderings ◽  
Definition Of ◽  
Relative Convexity

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

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