scholarly journals Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
A. Palermo ◽  
M. Buzzegoli ◽  
F. Becattini
Keyword(s):  
Polarization Vector ◽  
Formal Series ◽  
Spin Density Matrix ◽  
Dirac Field ◽  
Energy Tensor ◽  
Mean Values ◽  
Pure Rotation ◽  
Special Cases ◽  
Equilibrium Distributions ◽  
Fermionic Case

Abstract We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which lead to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (2) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

On several static cylindrically symmetric solutions of the Einstein equations

2016 ◽  
Vol 31 (11) ◽  
pp. 1650068
Author(s):  
Sergey Grigoryev ◽  
Arkadiy Leonov
Keyword(s):  
Einstein Equations ◽  
Massless Scalar ◽  
Energy Tensor ◽  
Massless Scalar Field ◽  
Stress Energy Tensor ◽  
Perfect Fluid Solution ◽  
Cylindrically Symmetric ◽  
Special Cases ◽  
Stress Energy ◽  
Barotropic Equation

We study the Einstein equations in the static cylindrically symmetric case with the stress–energy tensor of the form [Formula: see text], where [Formula: see text] is an unknown function and [Formula: see text], [Formula: see text], [Formula: see text] are arbitrary real constants ([Formula: see text] is assumed to be nonzero). The stress–energy tensor of this form includes as special cases several well-known solutions, such as the perfect fluid solution with the barotropic equation of state, the solution with the static electric field and the solution with the massless scalar field. We solve the Einstein equations with this stress–energy tensor and study some properties of the obtained metric.

scholarly journals Studying Recorded lightning over Iraq for Period 1998-2011

2018 ◽  
Vol 28 (3) ◽  
pp. 1
Author(s):  
Lena Mohammed Abbas
Keyword(s):  
Relative Humidity ◽  
Sea Level ◽  
Vertical Velocity ◽  
Mean Value ◽  
Sea Level Pressure ◽  
Mean Sea Level ◽  
Mean Values ◽  
Level Pressure ◽  
Special Cases ◽  
The Hours

This research studies distribution of thunderstorm in Iraq for the period (1998-2011), the result showed that  the largest regions which had been hit by lightning stroke were between latitude (35-36◦)E and longitude (45-46◦)N, and April was the most frequent of lightning occurrence, also the results showed  that the number of flashes of most lightning cases were between (50-100) with higher number of flashes for some special cases. The studying of meteorological parameters which accompanied thunderstorm formation such as (Mean sea level pressure, Lifting index, relative humidity and Vertical velocity) illustrates the values of mean sea level pressure were increased during the hours after lightning occurrence comparing with their values before and at the time of lightning occurrence and their monthly mean value much greater than that recorded at the time of lightning occurrence, in addition the values of lifting index were negative at the time of lightning occurrence that refer to instability whereas their monthly average showed positive values. The values of relative humidity were greater at lightning recorded time at the three levels (500, 700, 1000)mb and also through the hours before and after this time comparing with their monthly mean. Vertical velocity values were negative for the three levels at the time of lightning occurrence that is referring to upward motion which is necessary for thundercloud initiation, and their monthly mean values were mostly negative at (500, 700)mb whereas were positive at the surface level

scholarly journals Maximum-Entropy Based Estimates of Stress and Strain in Thermoelastic Random Heterogeneous Materials

2020 ◽  
Vol 141 (2) ◽  
pp. 321-348
Author(s):  
Maximilian Krause ◽  
Thomas Böhlke
Keyword(s):  
Maximum Entropy ◽  
Heterogeneous Materials ◽  
Entropy Method ◽  
Distribution Functions ◽  
Internal Stresses ◽  
Field Methods ◽  
Common Procedure ◽  
Full Field ◽  
Mean Values ◽  
Special Cases

Abstract Mean-field methods are a common procedure for characterizing random heterogeneous materials. However, they typically provide only mean stresses and strains, which do not always allow predictions of failure in the phases since exact localization of these stresses and strains requires exact microscopic knowledge of the microstructures involved, which is generally not available. In this work, the maximum entropy method pioneered by Kreher and Pompe (Internal Stresses in Heterogeneous Solids, Physical Research, vol. 9, 1989) is used for estimating one-point probability distributions of local stresses and strains for various classes of materials without requiring microstructural information beyond the volume fractions. This approach yields analytical formulae for mean values and variances of stresses or strains of general heterogeneous linear thermoelastic materials as well as various special cases of this material class. Of these, the formulae for discrete-phase materials and the formulae for polycrystals in terms of their orientation distribution functions are novel. To illustrate the theory, a parametric study based on Al-Al2O3 composites is performed. Polycrystalline copper is considered as an additional example. Through comparison with full-field simulations, the method is found to be particularly suited for polycrystals and materials with elastic contrasts of up to 5. We see that, for increasing contrast, the dependence of our estimates on the particular microstructures is increasing, as well.

Geometrical measures of the smoothness of random functions

1976 ◽  
Vol 13 (01) ◽  
pp. 86-95
Author(s):  
Paul Switzer
Keyword(s):  
Euclidean Space ◽  
Random Function ◽  
Mean Values ◽  
Random Functions ◽  
Local Averaging ◽  
Special Cases ◽  
The Mean ◽  
Isotropic Random

For stationary isotropic random functions on a Euclidean space, we characterize and compare the mean values of certain geometric measures of the smoothness of realizations. In particular we examine mean properties of the contours and gradients of the random function, and the effect of local averaging on smoothness in special cases.

BOUNDARY CONDITIONS IN THE MECHANICS OF FIELDS

1952 ◽  
Vol 30 (6) ◽  
pp. 684-698
Author(s):  
S. M. Neamtan ◽  
E. Vogt
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Vector Fields ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Second Order ◽  
Dirac Field ◽  
Energy Tensor ◽  
Complex Scalar ◽  
Set Up

A variational principle has been set up for the description of relativistic fields with the aid of Lagrangians involving second order derivatives of the field functions. This constitutes a generalization of the usual formulation in that, besides the boundary conditions usually imposed, it admits also linear homogeneous boundary conditions. The formulation has been developed for the complex scalar and complex vector fields. The variational principle then yields not only the wave equations but also the allowed boundary conditions. A Hamiltonian and equations of motion in canonical form can be set up. A symmetric stress–energy tensor and a charge–current vector are defined, yielding the usual conservation equations. For the vector field, π4 is not identically zero; also the Lorentz condition arises out of the variational principle and does not have to be separately imposed. For the Dirac field an extension to Lagrangians with second order derivatives is not possible, but for this field also the variational principle yields the allowed boundary conditions.

scholarly journals A systematic treatment of moving axes in hydrodynamics

1949 ◽  
Vol 196 (1045) ◽  
pp. 285-300 ◽  
Keyword(s):  
Heat Transfer ◽  
Tropical Cyclones ◽  
Equations Of Motion ◽  
Rate Of Change ◽  
Energy Tensor ◽  
Mathematical Form ◽  
Tensor Calculus ◽  
Systematic Treatment ◽  
The Earth ◽  
Special Cases

A method is developed for transforming the equations of hydrodynamics to a system of curvilinear co-ordinates in motion relative to fixed axes using the tensor-calculus and without employing Coriolis’s theorem .The basic entity is the kinetic metric, a four-dimensional quadratic form defined through the kinetic energy of unit mass of fluid.The mechanics of special relativity are used to obtain, by approximation in terms of 1/ c 2 , where c is the velocity of light, the classical formulae.The equations of motion in terms of the energy-tensor, the four-dimensional vorticity-tensor and the˙ velocity-components are successively obtained and the equation of continuity is shown to be independent (in mathematical form) of the motion of the co-ordinate-system . This property holds also for the equation of heat-transfer in a non-viscous fluid. Applications are made to the case of local Cartesian and local cylindrical polar co-ordinates on the Earth ’s surface. Formulae for the rate of change of vorticity due to Helmholtz and to Petterssen, respectively, are obtained as special cases and Sawyer’s theory of tropical cyclones is also discussed.

Geometrical measures of the smoothness of random functions

1976 ◽  
Vol 13 (1) ◽  
pp. 86-95 ◽  
Author(s):  
Paul Switzer
Keyword(s):  
Euclidean Space ◽  
Random Function ◽  
Mean Values ◽  
Random Functions ◽  
Local Averaging ◽  
Special Cases ◽  
The Mean ◽  
Isotropic Random

For stationary isotropic random functions on a Euclidean space, we characterize and compare the mean values of certain geometric measures of the smoothness of realizations. In particular we examine mean properties of the contours and gradients of the random function, and the effect of local averaging on smoothness in special cases.

scholarly journals THE RENORMALIZED LOCALLY COVARIANT DIRAC FIELD

2014 ◽  
Vol 26 (01) ◽  
pp. 1330012 ◽  
Author(s):  
JOCHEN ZAHN
Keyword(s):  
Background Field ◽  
Field Method ◽  
Dirac Field ◽  
Energy Tensor ◽  
Stress Energy ◽  
Background Field Method ◽  
The One ◽  
Definition Of ◽  
Background Fields ◽  
Group Flow

The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.

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