scholarly journals Entropy-Time Relationship in an Isochoric Adiabatic System

2021 ◽  
Author(s):  
Francisco Ros
Keyword(s):  
Differential Equation ◽  
Thermodynamic Equilibrium ◽  
Fundamental Equation ◽  
Maximal Entropy ◽  
Maximum Point ◽  
Minimal Action ◽  
Time Differential ◽  
Thermodynamic Variables ◽  
Internal Volume ◽  
First Time

Abstract The fundamental equation that connects the magnitudes entropy and time has been found out by static thermodynamics for the first time: dS/S = dVI/V0 = kdτ, VI internal volume. Constant k also equals dT/Tdτ and is an individual characteristic for each isochoric adiabatic system in evolution. The constancy of k does not hold for a nonisochoric adiabatic system. In such manner time is introduced in the frame of thermodynamic variables as a genuine magnitude. The theoretically deduced entropy-time differential equation is empirically upheld by Newton cooling law. It was found in connection with an a priory, uncritical notion of thermodynamic equilibrium that irreversible heat capacity (CIR = TΔS/ΔT) drawing near to thermodynamic equilibrium is an indicator for the equilibrium. CIR is alike to statistical Boltzmann H in the approach to thermodynamic equilibrium, and the undisclosed connection of H with temperature is presented. The integrated entropy-time equation was modified by rotation of the coordinate axes to fulfill the necessary thermodynamic condition that pertinent irreversible heat (QIR = TΔS) is smaller than reversible heat (dQ = TdS), which is not embodied in the primitive S-τ differential equation. This thermodynamically indispensable rotation gives rise to an otherwise naive maximal entropy and an entropy-time maximum point. The transformation conveys a contraction of both entropy and time and is in agreement with the principle of minimal action.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

Ultrasensitive Electrochemical Determination of Phosphate in water by Hydrophilic TiO2 modified Glassy Carbon Electrodes

2021 ◽  
Author(s):  
Yan Jin ◽  
Tong QI ◽  
Yuqing Ge ◽  
Jin Chen ◽  
Li juan Liang ◽  
...  
Keyword(s):  
Differential Pulse Voltammetry ◽  
Glassy Carbon ◽  
Differential Pulse ◽  
Electrochemical Determination ◽  
Carbon Electrodes ◽  
Glassy Carbon Electrodes ◽  
Time Differential ◽  
Pulse Voltammetry ◽  
First Time

In this paper, ultrasensitive electrochemical determination of phosphate in water is achieved by hydrophilic TiO2 modified glassy carbon electrodes for the first time. Differential pulse voltammetry (DPV) method is proposed...

scholarly journals On a new structure of the pantograph inclusion problem in the Caputo conformable setting

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sabri T. M. Thabet ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Differential Equation ◽  
Inclusion Problem ◽  
Integral Conditions ◽  
Lower Semi ◽  
First Time ◽  
Existence Criteria

Abstract In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville conformable integral conditions. To achieve this aim, we establish our main results in some cases including the lower semi-continuous, the upper semi-continuous and the Lipschitz set-valued maps. Eventually, the last part of the present research is devoted to proposing two numerical simulative examples to confirm the consistency of our findings.

How Crystals Form from a Cloud of Atoms

2011 ◽  
Vol 675-677 ◽  
pp. 3-7
Author(s):  
Peter Häussler ◽  
Martin Stiehler
Keyword(s):  
Structure Formation ◽  
Fundamental Equation ◽  
Structural Features ◽  
Local Order ◽  
Total System ◽  
Angular Momenta ◽  
General Dynamics ◽  
Bloch’S Theorem ◽  
The Given ◽  
First Time

Structure formation, the condensation of a cloud of atoms to a crystal is still not well understood. Disordered sytems (amorphous/liquid) should be in the center of this research, they are the precursors of any crystal. We consider elementary systems, as well as binary, or ternary amorphous alloys, irrespective whether they are metallically, covalently or ionically bonded and describe the process of structure formation in the formal language of thermodynamics but, as far as we know for the first time, by an extended version (general dynamics), based on the complete Gibbs fundamental equation, applied to internal subsystems. Major structural features evolve from global resonances between formerly independent internal subsystems by exchanging momenta and angular momenta, both accompanied by energy. By this they adjust mutually their internal features and create spherical-periodic structural order at medium-range distances. Under the given external constraints the resonances get optimized by selforganization. Global resonances of the type considered have clearly to be distinguished from local resonances between individual ions (described by quantum chemistry) forming local order. The global resonances cause anti-bonding (non-equilibrium) as well as bonding (equilibrium) states of the coupled total system, occupying the latter to form new structurally extended order. The transition to equilibrium creates entropy which itself leaves the system together with energy. At resonance the energetical splitting between the bonding and anti-bonding state is largest, the creation of entropy and the decrease of the total energy therefore, too. The crystal, finally, evolves by additionally optimizing a resonance based on angular momentum, and the additional adjustments of the local resonances to the global ones, theoretically done by applying Bloch’s theorem.

scholarly journals The ruin problem for a Wiener process with state-dependent jumps

2020 ◽  
Vol 16 (1) ◽  
pp. 13-23
Author(s):  
M. Lefebvre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Jump Diffusion ◽  
Moment Generating Function ◽  
Continuous Part ◽  
State Dependent ◽  
The Moment ◽  
First Time

AbstractLet X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

scholarly journals Solutions de similitude d'un jeu différentiel stochastique

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Similarity Solutions ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Controlled Processes ◽  
International Audience ◽  
First Time

International audience A two-dimensional controlled stochastic process defined by a set of stochastic differential equations is considered. Contrary to the most frequent formulation, the control variables appear only in the infinitesimal variances of the process, rather than in the infinitesimal means. The differential game ends the first time the two controlled processes are equal or their difference is equal to a given constant. Explicit solutions to particular problems are obtained by making use of the method of similarity solutions to solve the appropriate partial differential equation. On considère un processus stochastique commandé bidimensionnel défini par un ensemble d'équations différentielles stochastiques. Contrairement à la formulation la plus fréquente, les variables de commande apparaissent dans les variances infinitésimales du processus, plutôt que dans les moyennes infinitésimales. Le jeu différentiel prend fin lorsque les deux processus sont égaux ou que leur différence est égale à une constante donnée. Des solutions explicites à des problèmes particuliers sont obtenues en utilisant la méthode des similitudes pour résoudre l'équation aux dérivées partielles appropriée.

The Nuclear Quadrupole Interaction of 204mPb in Cadmium Monitored by γ–γ –Perturbed Angular Correlations

2002 ◽  
Vol 57 (6-7) ◽  
pp. 586-590 ◽  
Author(s):  
W. Tröger ◽  
M. Dietrich ◽  
J. P. Araujo ◽  
J. G. Correia ◽  
H. Haas
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Plane Waves ◽  
Nuclear Quadrupole Interaction ◽  
Full Potential ◽  
Angular Correlations ◽  
Time Differential ◽  
On Line ◽  
First Time

For the first time the nuclear probe 204mPb was produced at the on-line isotope separator ISOLDE at CERN and used for time differential perturbed angular correlation experiments. The electric field gradient of 204mPb at room temperature in Cd metal was determined to be = 19(1) 1021 V/m2. Ab initio-calculations of the electric field gradient for the impurities Pt to Bi in cadmium were performed with the full-potential linearized augmented plane waves code WIEN97 to interpret this result. For Au, Hg and Pb, where experimental results are now available, these agree with the calculations within 10 %.

scholarly journals Carbon and oxygen in metal-poor halo stars

2019 ◽  
Vol 622 ◽  
pp. L4 ◽  
Author(s):  
A. M. Amarsi ◽  
P. E. Nissen ◽  
M. Asplund ◽  
K. Lind ◽  
P. S. Barklem
Keyword(s):  
Chemical Evolution ◽  
Thermodynamic Equilibrium ◽  
Local Thermodynamic Equilibrium ◽  
Galactic Chemical Evolution ◽  
Elemental Abundances ◽  
Halo Stars ◽  
Effective Temperatures ◽  
Population Iii Stars ◽  
Hydrodynamic Effects ◽  
First Time

Carbon and oxygen are key tracers of the Galactic chemical evolution; in particular, a reported upturn in [C/O] towards decreasing [O/H] in metal-poor halo stars could be a signature of nucleosynthesis by massive Population III stars. We reanalyse carbon, oxygen, and iron abundances in 39 metal-poor turn-off stars. For the first time, we take into account 3D hydrodynamic effects together with departures from local thermodynamic equilibrium (LTE) when determining both the stellar parameters and the elemental abundances, by deriving effective temperatures from 3D non-LTE Hβ profiles, surface gravities from Gaia parallaxes, iron abundances from 3D LTE Fe II equivalent widths, and carbon and oxygen abundances from 3D non-LTE C I and O I equivalent widths. We find that [C/Fe] stays flat with [Fe/H], whereas [O/Fe] increases linearly up to 0.75 dex with decreasing [Fe/H] down to −3.0 dex. Therefore [C/O] monotonically decreases towards decreasing [C/H], in contrast to previous findings, mainly because the non-LTE effects for O I at low [Fe/H] are weaker with our improved calculations.

Application of Ambarzumian’s Method to Radiant Interchange in a Rectangular Cavity

1974 ◽  
Vol 96 (2) ◽  
pp. 191-196 ◽  
Author(s):  
A. L. Crosbie ◽  
T. R. Sawheny
Keyword(s):  
Differential Equation ◽  
Heat Flux ◽  
Integral Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Integral Equation ◽  
Initial Conditions ◽  
Rectangular Cavity ◽  
Wide Range ◽  
First Time

Ambarzumian’s method had been used for the first time to solve a radiant interchange problem. A rectangular cavity is defined by two semi-infinite parallel gray surfaces which are subject to an exponentially varying heat flux, i.e., q = q0 exp(−mx). Instead of solving the integral equation for the radiosity for each value of m, solutions for all values of m are obtained simultaneously. Using Ambarzumian’s method, the integral equation for the radiosity is first transformed into an integro-differential equation and then into a system of ordinary differential equations. Initial conditions required to solve the differential equations are the H functions which represent the radiosity at the edge of the cavity for various values of m. This H function is shown to satisfy a nonlinear integral equation which is easily solved by iteration. Numerical results for the H function and radiosity distribution within the cavity are presented for a wide range of m values.

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