scholarly journals Statistical Thermodynamics of Economic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Hernando Quevedo ◽  
María N. Quevedo
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Probability Distribution ◽  
Statistical Physics ◽  
Mean Value ◽  
Economic Systems ◽  
Macroeconomic Variables ◽  
Multiplicative Systems ◽  
The Mean ◽  
Linear And Nonlinear

We formulate the thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic variables, and their determination is reduced to the computation of the partition function, starting from an arbitrary function. Explicit hypothetical examples are given which include linear and nonlinear economic systems as well as multiplicative systems such as those dominated by a Pareto law distribution. It is shown that the macroeconomic variables can be drastically changed by choosing the microeconomic variables in an appropriate manner. We propose to use the formalism of phase transitions to study severe changes of macroeconomic variables.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Effect of stiffness taper in aseismic design

1960 ◽  
Vol 50 (4) ◽  
pp. 537-552
Author(s):  
G. N. Bycroft
Keyword(s):  
Probability Distribution ◽  
Mean Value ◽  
Aseismic Design ◽  
Linear Shear ◽  
The Mean ◽  
Stiffness Distribution

ABSTRACT An investigation is made of the effect of changing the stiffness distribution up the height of a linear shear framed structure when subjected to idealized earthquake motions. The mean value of the largest strains arising in successive earthquakes is determined together with the associated probability distribution. It appears that the chances of finding a strain value greater than twice the mean are very small.

On estimating the mean energy of sea waves from the highest waves in a record

1958 ◽  
Vol 247 (1248) ◽  
pp. 22-48 ◽  
Keyword(s):  
Probability Distribution ◽  
Standard Error ◽  
Random Variable ◽  
Ocean Waves ◽  
Mean Value ◽  
Sea Waves ◽  
Mutual Correlation ◽  
Narrow Spectrum ◽  
Asymptotic Formulae ◽  
The Mean

An analysis is made of the probability distribution of the largest values attained by a stationary random variable f ( t ) over a period of time containing several oscillations. Exact computations are made and asymptotic formulae are derived for the expectation and standard error of the first, second and third greatest maxima in terms of √ m 0 , the r. m. s. deviation of f ( t ) about its mean value, on the assumption that successive waves are uncorrelated; an analysis is also made of the corrections necessary to allow for mutual correlation when f ( t ) has a narrow spectrum. The results are applied to measurements from a 24 h record of ocean waves containing some 10000 oscillations.

scholarly journals Bounding the Partition Function of Spin-Systems

10.37236/1098 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
David J. Galvin
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Probability Distribution ◽  
Statistical Physics ◽  
Hard Core ◽  
Spin Systems ◽  
Normalizing Constant ◽  
Graph Homomorphisms ◽  
Hard Core Model ◽  
Regular Bipartite Graph

With a graph $G=(V,E)$ we associate a collection of non-negative real weights $\bigcup_{v\in V}\{\lambda_{i,v}:1\leq i \leq m\} \cup \bigcup_{uv \in E} \{\lambda_{ij,uv}:1\leq i \leq j \leq m\}.$ We consider the probability distribution on $\{f:V\rightarrow\{1,\ldots,m\}\}$ in which each $f$ occurs with probability proportional to $\prod_{v \in V}\lambda_{f(v),v}\prod_{uv \in E}\lambda_{f(u)f(v),uv}$. Many well-known statistical physics models, including the Ising model with an external field and the hard-core model with non-uniform activities, can be framed as such a distribution. We obtain an upper bound, independent of $G$, for the partition function (the normalizing constant which turns the assignment of weights on $\{f:V\rightarrow\{1,\ldots,m\}\}$ into a probability distribution) in the case when $G$ is a regular bipartite graph. This generalizes a bound obtained by Galvin and Tetali who considered the simpler weight collection $\{\lambda_i:1 \leq i \leq m\} \cup \{\lambda_{ij}:1 \leq i \leq j \leq m\}$ with each $\lambda_{ij}$ either $0$ or $1$ and with each $f$ chosen with probability proportional to $\prod_{v \in V}\lambda_{f(v)}\prod_{uv \in E}\lambda_{f(u)f(v)}$. Our main tools are a generalization to list homomorphisms of a result of Galvin and Tetali on graph homomorphisms and a straightforward second-moment computation.

On the conditional expected value of contributions from a renewal process

1966 ◽  
Vol 3 (2) ◽  
pp. 464-480 ◽  
Author(s):  
M. F. James
Keyword(s):  
Probability Distribution ◽  
Cross Sections ◽  
Renewal Process ◽  
Mean Value ◽  
Distribution Functions ◽  
Total Contribution ◽  
Probability Distribution Functions ◽  
General Terms ◽  
The Mean ◽  
Neutron Cross Sections

The problem discussed in this paper arose from the study of the effects of unresolved resonances on neutron cross-sections, but it is considered here in more general terms.Events in a modified renewal process occur at successive intervals x1, x2, …, and the ith event has associated with it a parameter Γi. The random variables xi and Γi are all independent, and their probability distribution functions are known. Each event contributes to two quantities F(u) and G(v) measured at u and v respectively. The value of the total contribution of all events to G(v) is assumed to be known from observation: this paper gives formulae for the mean value of F(u) conditional on this known value of G(v).

On the conditional expected value of contributions from a renewal process

1966 ◽  
Vol 3 (02) ◽  
pp. 464-480
Author(s):  
M. F. James
Keyword(s):  
Probability Distribution ◽  
Cross Sections ◽  
Renewal Process ◽  
Mean Value ◽  
Distribution Functions ◽  
Total Contribution ◽  
Probability Distribution Functions ◽  
General Terms ◽  
The Mean ◽  
Neutron Cross Sections

The problem discussed in this paper arose from the study of the effects of unresolved resonances on neutron cross-sections, but it is considered here in more general terms. Events in a modified renewal process occur at successive intervals x 1, x 2, …, and the ith event has associated with it a parameter Γ i . The random variables xi and Γ i are all independent, and their probability distribution functions are known. Each event contributes to two quantities F(u) and G(v) measured at u and v respectively. The value of the total contribution of all events to G(v) is assumed to be known from observation: this paper gives formulae for the mean value of F(u) conditional on this known value of G(v).

Magnetic Phase Transitions in the Lattice Ising Model

2013 ◽  
Vol 718-720 ◽  
pp. 166-171 ◽  
Author(s):  
Petr Dmitrievich Andriushchenko ◽  
Konstantin Valentinovich Nefedev
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Percolation Theory ◽  
Cluster Size ◽  
Magnetic Phase ◽  
Percolation Cluster ◽  
Mean Value ◽  
Magnetic Phase Transitions ◽  
Lattice Systems ◽  
The Mean

In this paper we consider an approach, which allows the research of order-disorder transitionin lattice systems (with any distribution of the exchange integrals) in the frame of Ising model. Anew order parameters, which can give a description of a phase transitions, are found. The commondefinition of such order parameter is the mean value of percolation cluster size. Percolation clusterincludes spins in ground state. The transition from absolute disorder to correlated phase could bestudied with using of percolation theory methods.

The entropy excess and moment of inertia excess ratio with inclusion of statistical pairing fluctuations

2014 ◽  
Vol 23 (03) ◽  
pp. 1450015 ◽  
Author(s):  
R. Razavi ◽  
V. Dehghani
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Moment Of Inertia ◽  
Bcs Model ◽  
Statistical Fluctuations ◽  
Nuclear Temperature ◽  
Pairing Fluctuations ◽  
The Mean

The entropy excess of 163 Dy compared to 162 Dy as a function of nuclear temperature have been investigated using the mean value Bardeen–Cooper–Schrieffer (BCS) method based on application of the isothermal probability distribution function to take into account the statistical fluctuations. Then, the spin cut-off excess ratio (moment of inertia excess ratio) introduced by Razavi [Phys. Rev. C88 (2013) 014316] for proton and neutron system have been obtained and are compared with their corresponding data on the BCS model. The results show that the overall agreement between the BCS model and mean value BCS method is satisfactory and the mean value BCS model reduces fluctuations and washes out singularities. However, the expected constant value in the entropy excess is not reproduced by the mean value BCS method.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

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