The Boltzmann function as an embedded property of Liouville's equation

1990 ◽  
Vol 23 (9) ◽  
pp. L427-L432 ◽  
Author(s):  
M C Tapp
Keyword(s):  
Boltzmann Function ◽  
Liouville’S Equation

scholarly journals Hyperbolic three-string vertex

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Atakan Hilmi Fırat
Keyword(s):  
Boundary Value Problem ◽  
Conservation Laws ◽  
Riemann Surfaces ◽  
Higher Order ◽  
Local Coordinates ◽  
Pants Decomposition ◽  
Fuchsian Equation ◽  
String Amplitudes ◽  
Hyperbolic Riemann Surfaces ◽  
Liouville’S Equation

Abstract We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

1999 ◽  
Vol 13 (02) ◽  
pp. 161-189
Author(s):  
C. SYROS
Keyword(s):  
Quantum Mechanics ◽  
Radiation Spectrum ◽  
Black Body ◽  
Boltzmann Distribution ◽  
Black Body Radiation ◽  
Planck Constant ◽  
Klein Gordon ◽  
Energy Variable ◽  
Liouville’S Theorem ◽  
Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

Experimental Study on Fracture Toughness of Q460C the High-Strength Construction Steel at Low Temperature

2011 ◽  
Vol 71-78 ◽  
pp. 890-897 ◽  
Author(s):  
Yuan Qing Wang ◽  
Yun Lin ◽  
Yan Nian Zhang ◽  
Yong Jiu Shi
Keyword(s):  
Low Temperature ◽  
High Strength ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Three Point Bending ◽  
Function Fitting ◽  
Ductile Brittle Transition Temperature ◽  
Boltzmann Function ◽  
Fracture Appearance ◽  
Crack Tip Opening

Three point bending tests were carried out on 14mm-thick Q460C the high-strength structural steel at low temperature, and scanning electronic microscope of the fracture appearance was analyzed. The results showed that the obvious feature of brittle mechanism was shown on the three point bending specimen fracture whose testing took place at -40°C. And the crack tip opening displacement value of Q460C steel, which was less than that of Q235 steel, Q345 steel and Q390 steel at low temperature, tended to decrease with respect to the temperature reduction. Moreover, a Boltzmann function fitting analysis was applied to the experimental data, and the ductile-brittle transition temperature and the changing regularity were obtained.

CENTRALITY DEPENDENCE OF NUCLEAR MODIFICATION FACTOR IN Au+Au COLLISIONS AT $\sqrt{s_{NN}}=200~{\rm GeV}$

2007 ◽  
Vol 22 (19) ◽  
pp. 1381-1389 ◽  
Author(s):  
W. C. XIANG ◽  
D. C. ZHOU
Keyword(s):  
Model Calculation ◽  
Centrality Dependence ◽  
Nuclear Modification Factor ◽  
Surface Emission ◽  
Nuclear Modification ◽  
Boltzmann Function ◽  
Modification Factor ◽  
Phenix Data

Centrality dependence of nuclear modification factor at high pT above 4 GeV /c is studied in nucleus–nucleus collisions at [Formula: see text]. We find that the centrality dependence of the nuclear modification factor can be factorized as a Boltzmann function F(b). Comparing our model calculation with PHENIX data, we further confirm that the high pT spectrum of particles is dominated by surface emission.

scholarly journals Voltage-gated transient currents in bovine adrenal fasciculata cells. I. T-type Ca2+ current.

1993 ◽  
Vol 102 (2) ◽  
pp. 217-237 ◽  
Author(s):  
B Mlinar ◽  
B A Biagi ◽  
J J Enyeart
Keyword(s):  
Time Constant ◽  
Low Voltage ◽  
Zona Fasciculata ◽  
Patch Clamp Technique ◽  
Time Constants ◽  
Voltage Gated ◽  
Wide Range ◽  
Boltzmann Function ◽  
Voltage Dependent ◽  
Ca2 Channels

The whole cell version of the patch clamp technique was used to identify and characterize voltage-gated Ca2+ channels in enzymatically dissociated bovine adrenal zona fasciculata (AZF) cells. The great majority of cells (84 of 86) expressed only low voltage-activated, rapidly inactivating Ca2+ current with properties of T-type Ca2+ current described in other cells. Voltage-dependent activation of this current was fit by a Boltzmann function raised to an integer power of 4 with a midpoint at -17 mV. Independent estimates of the single channel gating charge obtained from the activation curve and using the "limiting logarithmic potential sensitivity" were 8.1 and 6.8 elementary charges, respectively. Inactivation was a steep function of voltage with a v1/2 of -49.9 mV and a slope factor K of 3.73 mV. The expression of a single Ca2+ channel subtype by AZF cells allowed the voltage-dependent gating and kinetic properties of T current to be studied over a wide range of potentials. Analysis of the gating kinetics of this Ca2+ current indicate that T channel activation, inactivation, deactivation (closing), and reactivation (recovery from inactivation) each include voltage-independent transitions that become rate limiting at extreme voltages. Ca2+ current activated with voltage-dependent sigmoidal kinetics that were described by an m4 model. The activation time constant varied exponentially at test potentials between -30 and +10 mV, approaching a voltage-independent minimum of 1.6 ms. The inactivation time constant (tau i) also decreased exponentially to a minimum of 18.3 ms at potentials positive to 0 mV. T channel closing (deactivation) was faster at more negative voltages; the deactivation time constant (tau d) decreased from 8.14 +/- 0.7 to 0.48 +/- 0.1 ms at potentials between -40 and -150 mV. T channels inactivated by depolarization returned to the closed state along pathways that included two voltage-dependent time constants. tau rec-s ranged from 8.11 to 4.80 s when the recovery potential was varied from -50 to -90 mV, while tau rec-f decreased from 1.01 to 0.372 s. At potentials negative to -70 mV, both time constants approached minimum values. The low voltage-activated Ca2+ current in AZF cells was blocked by the T channel selective antagonist Ni2+ with an IC50 of 20 microM. At similar concentrations, Ni2+ also blocked cortisol secretion stimulated by adrenocorticotropic hormone. Our results indicate that bovine AZF cells are distinctive among secretory cells in expressing primarily or exclusively T-type Ca2+ channels.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals A Validation Study on the Simultaneous Quantification of Multiple Wine Aroma Compounds with Static Headspace-Gas Chromatography-Ion Mobility Spectrometry (SHS-GC-IMS)

2021 ◽  
Author(s):  
Wenyao Zhu ◽  
Frank Benkwitz ◽  
Bahareh Sarmadi ◽  
Paul Kilmartin
Keyword(s):  
Gas Chromatography ◽  
Ion Mobility Spectrometry ◽  
Ion Mobility ◽  
Aroma Compounds ◽  
Headspace Gas Chromatography ◽  
Static Headspace ◽  
Simultaneous Quantification ◽  
Static Headspace Gas Chromatography ◽  
Boltzmann Function ◽  
Headspace Gas

A new quantitative method based on static headspace−gas chromatography−ion mobility spectrometry (SHS−GC−IMS) is proposed, which enables the simultaneous quantification of multiple aroma compounds in wine. The method was first evaluated for its stability and the necessity of using internal standards as a quality control measure. The two major hurdles in applying GC-IMS in quantification studies, namely, non-linearity and multiple ion species, were also investigated using the Boltzmann function and generalized additive model (GAM) as potential solutions. Metrics characterizing the model performance, including root mean squared error, bias, limit of detection, limit of quantification, repeatability, reproducibility, and recovery were investigated. Both non-linear fitting methods, Boltzmann function and GAM, were able to return desirable analytical outcomes with an acceptable range of error. Potential pitfalls that would cause inaccurate quantification i.e., effects of ethanol content and competitive ionization, were also discussed. The performance of the SHS-GC-IMS method was subsequently compared against a currently established method, namely, GC-MS, using actual wine samples. These findings provide an initial validation of a GC-IMS-based quantification method, as well as a starting point for further enhancing the analytical scope of GC-IMS.

Comparative analysis of methods for studying soot sediments at fire places

2021 ◽  
Vol 94 ◽  
pp. 34-49
Author(s):  
A. Yu. Medvedev ◽  
◽  
Yu. N. Belshina ◽  
Keyword(s):  
Electrical Resistance ◽  
Morphological Analysis ◽  
Molecular Spectroscopy ◽  
Component Composition ◽  
Photochemical Reactions ◽  
Laboratory Methods ◽  
Qualitative And Quantitative ◽  
Temperature Conditions ◽  
Boltzmann Function ◽  
Quantitative Indicators

Introduction. Smokes are aerosols that contain sublimating substances and condensing vapors, as well as products of chemical and photochemical reactions. In addition to solid and liquid particles, they contain gaseous products of both complete and incomplete decomposition during combustion process, as well as nitrogen and the remains of unreacted oxygen during combustion. The aerosol substance of smoke that has settled on any surface is called soot, which often acts as an object of fire-technical expertise, and the aggregate of soot particles that form zones of various configurations is called smokiness. Goals and objectives. The aim of the work is to study soot and its components for the development of a comprehensive methodology for the study of fires in determining both the focus and the cause of the fire, as well as the pathways of the spread of hazardous factors of fire at different stages of fire development. The main task of the work is to determine the dependence of the qualitative and quantitative indicators of soot and its component composition on the temperature conditions of combustion of various materials in order to establish the conditions for the course of a fire. Research methods. Field and laboratory methods for the study of soot are considered. Field methods include visual analysis of soot deposits (identifying the configuration of soot, color and intensity of the soot layer) and measuring the electrical resistance of the soot layer using a field contact probe. Laboratory methods include the method of microscopic morphological analysis, the method of thermal analysis, molecular spectroscopy and gas chromatography, which are indirect and direct methods for studying extracted organic components of soot. Results and its discussion. The modern methods of research of soot are analyzed. A scheme of laboratory methods is proposed. It allows carry out full morphological analysis, to evaluate the behavior of soot components during heating and composition of extracted components for solving the problems of studying fires. Regression dependences of the content of bituminous components on the logarithm of the electrical resistance of the soot layer were obtained, which showed that, regardless of the type of combustible material, a transition zone is observed on them, in which, with a relatively small change in electrical resistance, a significant increase in the content of bituminous components is observed. Conclusion. The paper considers an comprehensive approach to the study of extractable components of soot. The obtained dependences of the qualitative and quantitative indicators of soot and its component composition on the temperature conditions of combustion of various materials will improve the quality and level of reliability of information in the study of fires in order to determine the focus and cause of a fire, as well as the ways of spreading hazardous factors of a fire at different stages of its development. Key words: smoke, soot, extractable organic compounds, bitumen components, soot layer electrical resistance, molecular spectroscopy, Boltzmann function, fire investigation.

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