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N. Sánchez-Salas
Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. 9 UP Zacatenco, CP 07738, CDMX, Mexico

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Journal article
Published: 17 August 2021 in Physica A: Statistical Mechanics and its Applications
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This paper applies Langevin idea to describe the Brownian motion of a particle characterized by an Ornstein–Uhlenbeck-type process. The original and clever method proposed by Langevin is based on Newton’s second law plus a fluctuating force whose solution for the mean square displacement consists in separating the fluctuating force from his equation to obtain a deterministic equation for the relevant physical variable. In this work the Langevin original idea is applied to calculate the mean square velocity for a field free particle case; then it is extended for a charged particle in a constant magnetic field. In a similar way, the strategy is also applied to calculate the mean square displacement for a Brownian harmonic oscillator in the overdamped regime, and also when a magnetic field is present. In particular, it is shown in the field free case that Langevin’s original strategy leads to the same results as those obtained using the statistical properties of a Gaussian white noise. All the theoretical results are compared with both the numerical simulation of the Langevin equation, and numerical solution of the corresponding deterministic differential equations.

ACS Style

O. Contreras-Vergara; N. Lucero-Azuara; N. Sánchez-Salas; J.I. Jiménez-Aquino. Langevin original approach and Ornstein–Uhlenbeck-type processes. Physica A: Statistical Mechanics and its Applications 2021, 126349 .

AMA Style

O. Contreras-Vergara, N. Lucero-Azuara, N. Sánchez-Salas, J.I. Jiménez-Aquino. Langevin original approach and Ornstein–Uhlenbeck-type processes. Physica A: Statistical Mechanics and its Applications. 2021; ():126349.

Chicago/Turabian Style

O. Contreras-Vergara; N. Lucero-Azuara; N. Sánchez-Salas; J.I. Jiménez-Aquino. 2021. "Langevin original approach and Ornstein–Uhlenbeck-type processes." Physica A: Statistical Mechanics and its Applications , no. : 126349.

Journal article
Published: 04 January 2021 in Revista Mexicana de Física E
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The original strategy applied by Langevin to Brownian movement problem is used to solve the case of a free particle under a harmonic potential. Such straightforward strategy consists in separating the noise termin the Langevin equation in order to solve a deterministic equation associated with the Mean Square Displacement (MSD). In this work, to achieve our goal we first calculate the variance for the stochastic harmonic oscillator and then the MSD appears immediately. We study the problem in the damped and lightly damped cases and show that, for times greater than the relaxation time, Langevin's original strategy is quite consistent with the exact theoretical solutions reported by Chandrasekhar and Lemons, these latter obtained using the statistical properties of a Gaussian white noise. Our results for the MSDs are compared with the exact theoretical solutions as well as with the numerical simulation.

ACS Style

O. Contreras-Vergara; N. Lucero-Azuara; N. Sánchez-Salas; J. I. Jiménez-Aquino. Harmonic oscillator Brownian motion: Langevin approach revisited. Revista Mexicana de Física E 2021, 18, 97 -106.

AMA Style

O. Contreras-Vergara, N. Lucero-Azuara, N. Sánchez-Salas, J. I. Jiménez-Aquino. Harmonic oscillator Brownian motion: Langevin approach revisited. Revista Mexicana de Física E. 2021; 18 (1):97-106.

Chicago/Turabian Style

O. Contreras-Vergara; N. Lucero-Azuara; N. Sánchez-Salas; J. I. Jiménez-Aquino. 2021. "Harmonic oscillator Brownian motion: Langevin approach revisited." Revista Mexicana de Física E 18, no. 1: 97-106.

Accepted manuscript
Published: 15 January 2020 in European Journal of Physics
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In this work we present the original Langevin's method to study the Brownian motion of a charged particle across a constant magnetic field. Langevin's strategy allows transforming the Langevin equation into a deterministic one associated with Mean Square Displacement (MSD), whose solution is explicitly study in this work. We calculate the MSD for the $z$-axis, along which the magnetic field is allowed to point, in this direction, the solution is exactly the same proposed by Langevin. While, in the $x$-$y$ plane orthogonal to the magnetic field, the solution for the MSD is obtained with the validity of the Bohr-van Leuuwen theorem in thermal equilibrium.

ACS Style

Norberto Lucero-Azuara; Norma Sánchez-Salas; Jose Ines Jimenez-Aquino. Brownian motion across a magnetic field: Langevin approach revisited. European Journal of Physics 2020, 41, 035807 .

AMA Style

Norberto Lucero-Azuara, Norma Sánchez-Salas, Jose Ines Jimenez-Aquino. Brownian motion across a magnetic field: Langevin approach revisited. European Journal of Physics. 2020; 41 (3):035807.

Chicago/Turabian Style

Norberto Lucero-Azuara; Norma Sánchez-Salas; Jose Ines Jimenez-Aquino. 2020. "Brownian motion across a magnetic field: Langevin approach revisited." European Journal of Physics 41, no. 3: 035807.

Journal article
Published: 22 May 2019 in Physica A: Statistical Mechanics and its Applications
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The statistics of the first passage and nonlinear relaxation times are used to characterize the decay process of an unstable state for an electrically charged Brownian particle embedded in non-Markovian heat baths under the action of an external electric field. The relaxation process is described, in the overdamped regime, by a Generalized Langevin Equation (GLE) characterized by an arbitrary friction memory kernel, and a bistable potential profile. By applying the quasideterministic approach, the statistics of the mean first passage time is calculated through the exact analytical solution of the GLE with arbitrary memory kernel in the linear regime of the bistable potential. To characterize the relaxation process including the nonlinear contributions of the bistable potential, we use the specific Ornstein–Uhlenbeck friction memory kernel to exactly calculate the nonlinear statistics of the mean first passage time as well as the nonlinear relaxation time. Both characteristic times are applied for possible detection of weak signals in the unstable state decay process.

ACS Style

J.I. Jiménez-Aquino; N. Sánchez-Salas; L. Ramírez-Piscina; M. Romero-Bastida. Unstable state decay in non-Markovian heat baths and weak signals detection. Physica A: Statistical Mechanics and its Applications 2019, 529, 121493 .

AMA Style

J.I. Jiménez-Aquino, N. Sánchez-Salas, L. Ramírez-Piscina, M. Romero-Bastida. Unstable state decay in non-Markovian heat baths and weak signals detection. Physica A: Statistical Mechanics and its Applications. 2019; 529 ():121493.

Chicago/Turabian Style

J.I. Jiménez-Aquino; N. Sánchez-Salas; L. Ramírez-Piscina; M. Romero-Bastida. 2019. "Unstable state decay in non-Markovian heat baths and weak signals detection." Physica A: Statistical Mechanics and its Applications 529, no. : 121493.

Journal article
Published: 21 February 2018 in Journal of Non-Equilibrium Thermodynamics
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This paper presents a general property of endoreversible thermal engines known as the Semisum property previously studied in a finite-time thermodynamics context for a Curzon–Ahlborn (CA) engine but now extended to a simplified version of the CA engine studied by Agrawal in 2009 (A simplified version of the Curzon–Ahlborn engine, European Journal of Physics 30 (2009), 1173). By building the Ecological function, proposed by Angulo-Brown (An ecological optimization criterion for finite-time heat engines, Journal of Applied Physics 69 (1991), 7465–7469) in 1991, and considering two heat transfer laws an analytical expression is obtained for efficiency and power output which depends only on the heat reservoirs’ temperature. When comparing the existing efficiency values of real power plants and the theoretical efficiencies obtained in this work, it is observed that the Semisum property is satisfied. Moreover, for the Newton and the Dulong–Petit heat transfer laws the existence of the g function is demonstrated and we confirm that in a Carnot-type thermal engine there is a general property independent of the heat transfer law used between the thermal reservoirs and the working substance.

ACS Style

Ricardo T. Paéz-Hernández; Juan Carlos Chimal-Eguía; Norma Sánchez-Salas; Delfino Ladino-Luna. General Properties for an Agrawal Thermal Engine. Journal of Non-Equilibrium Thermodynamics 2018, 43, 131 -139.

AMA Style

Ricardo T. Paéz-Hernández, Juan Carlos Chimal-Eguía, Norma Sánchez-Salas, Delfino Ladino-Luna. General Properties for an Agrawal Thermal Engine. Journal of Non-Equilibrium Thermodynamics. 2018; 43 (2):131-139.

Chicago/Turabian Style

Ricardo T. Paéz-Hernández; Juan Carlos Chimal-Eguía; Norma Sánchez-Salas; Delfino Ladino-Luna. 2018. "General Properties for an Agrawal Thermal Engine." Journal of Non-Equilibrium Thermodynamics 43, no. 2: 131-139.

Journal article
Published: 22 November 2017 in Entropy
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This paper presents an analysis of a Curzon and Alhborn thermal engine model where both internal irreversibilities and non-instantaneous adiabatic branches are considered, operating with maximum ecological function and maximum power output regimes. Its thermodynamic properties are shown, and an analysis of its local dynamic stability is performed. The results derived are compared throughout the work with the results obtained previously for a case in which the adiabatic branches were assumed as instantaneous. The results indicate a better performance for thermodynamic properties in the model with instantaneous adiabatic branches, whereas there is an improvement in robustness in the case where non-instantaneous adiabatic branches are considered.

ACS Style

Ricardo T. Paéz-Hernández; Norma Sánchez-Salas; Juan C. Chimal-Eguía; Delfino Ladino-Luna. Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats. Entropy 2017, 19, 632 .

AMA Style

Ricardo T. Paéz-Hernández, Norma Sánchez-Salas, Juan C. Chimal-Eguía, Delfino Ladino-Luna. Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats. Entropy. 2017; 19 (11):632.

Chicago/Turabian Style

Ricardo T. Paéz-Hernández; Norma Sánchez-Salas; Juan C. Chimal-Eguía; Delfino Ladino-Luna. 2017. "Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats." Entropy 19, no. 11: 632.

Journal article
Published: 04 December 2015 in Entropy
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A recent work reported a local stability analysis of a thermo-economical model of an irreversible heat engine working under maximum power conditions. That work showed that after small perturbations to the working temperatures, the system decreases exponentially to the steady state characterized by two different relaxation times. This work extends the local stability analysis considering other performance regimes: the Maximum Efficient Power (MEP) and the Ecological Function (EF) regimes. The relaxation time was shown under different performance regimes as functions of the temperature ratio τ = T2/T1, with T1 > T2, the fractional fuel cost f and a lumped parameter R related to the internal irreversibilities degree. Under Maximum Efficient Power conditions the relaxation times are less than the relaxation times under both Maximum Ecological function and Maximum Power. At Maximum Power Efficient conditions, the model gives better stability conditions than for the other two regimes.

ACS Style

Marco A. Barranco-Jimenez; Norma Sanchez-Salas; Israel Reyes-Ramírez. Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes. Entropy 2015, 17, 8019 -8030.

AMA Style

Marco A. Barranco-Jimenez, Norma Sanchez-Salas, Israel Reyes-Ramírez. Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes. Entropy. 2015; 17 (12):8019-8030.

Chicago/Turabian Style

Marco A. Barranco-Jimenez; Norma Sanchez-Salas; Israel Reyes-Ramírez. 2015. "Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes." Entropy 17, no. 12: 8019-8030.

Journal article
Published: 17 December 2012 in Entropy
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This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT). Using an endoreversible Curzon–Ahlborn (CA) heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law) was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Müser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Müser engine performance were obtained.

ACS Style

Juan C. Chimal-Eguía; Norma Sánchez-Salas; Marco A. Barranco-Jiménez. A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria. Entropy 2012, 14, 2611 -2625.

AMA Style

Juan C. Chimal-Eguía, Norma Sánchez-Salas, Marco A. Barranco-Jiménez. A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria. Entropy. 2012; 14 (12):2611-2625.

Chicago/Turabian Style

Juan C. Chimal-Eguía; Norma Sánchez-Salas; Marco A. Barranco-Jiménez. 2012. "A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria." Entropy 14, no. 12: 2611-2625.

Journal article
Published: 08 February 2011 in Entropy
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In this work, we focused mainly in the analysis of stability of a non-endoreversible Curzon-Ahlborn engine working in an ecological regime. For comparison purposes we also include the Maximum Efficient Power (MEP) regime taking into account the engine time delays. When the system’s dynamic stability is compared with its thermodynamics properties (efficiency and power output), we find that the temperature ratio τ = T1/T2 represents a trade-off between stability and energetic properties. When we take the non-endoreversible case, τ can increases to values greater than R (where R is the non-endoreversible parameter) but not greater than one. We reformulate an important difference between this case and the other two, Maximum Power (MP) and MEP regime, in which τ = R. Finally, we demonstrated that the total time delay does not destabilize the steady state of system. It does not seem to play a role in the dynamic thermodynamic property trade-off.

ACS Style

Norma Sanchez-Salas; Juan C. Chimal-Eguia; Florencio Guzman-Aguilar. On the Dynamic Robustness of a Non-Endoreversible Engine Working in Different Operation Regimes. Entropy 2011, 13, 422 -436.

AMA Style

Norma Sanchez-Salas, Juan C. Chimal-Eguia, Florencio Guzman-Aguilar. On the Dynamic Robustness of a Non-Endoreversible Engine Working in Different Operation Regimes. Entropy. 2011; 13 (2):422-436.

Chicago/Turabian Style

Norma Sanchez-Salas; Juan C. Chimal-Eguia; Florencio Guzman-Aguilar. 2011. "On the Dynamic Robustness of a Non-Endoreversible Engine Working in Different Operation Regimes." Entropy 13, no. 2: 422-436.

Journal article
Published: 14 January 2011 in Entropy
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In the present paper, the thermoeconomic optimization of an irreversible solar-driven heat engine model has been carried out by using finite-time/finite-size thermodynamic theory. In our study we take into account losses due to heat transfer across finite time temperature differences, heat leakage between thermal reservoirs and internal irreversibilities in terms of a parameter which comes from the Clausius inequality. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be Dulong-Petit type and the heat transfer to the cold reservoir is assumed of the Newtonian type. In this work, the optimum performance and two design parameters have been investigated under two objective functions: the power output per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned two criteria of performance.

ACS Style

Marco A. Barranco-Jiménez; Norma Sanchez-Salas; Fernando Angulo-Brown. Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model. Entropy 2011, 13, 171 -183.

AMA Style

Marco A. Barranco-Jiménez, Norma Sanchez-Salas, Fernando Angulo-Brown. Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model. Entropy. 2011; 13 (1):171-183.

Chicago/Turabian Style

Marco A. Barranco-Jiménez; Norma Sanchez-Salas; Fernando Angulo-Brown. 2011. "Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model." Entropy 13, no. 1: 171-183.

Journal article
Published: 25 August 2009 in Entropy
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In the present paper, the thermoeconomic optimization of an endoreversible solardriven heat engine has been carried out by using finite-time/finite-size thermodynamic theory. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be the radiation type and the heat transfer to the cold reservoir is assumed the conduction type. In this work, the optimum performance and two design parameters have been investigated under three objective functions: the power output per unit total cost, the efficient power per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned three criteria of performance.

ACS Style

Marco A. Barranco-Jiménez; Norma Sánchez-Salas; Marco A. Rosales. Thermoeconomic Optimum Operation Conditions of a Solar-driven Heat Engine Model. Entropy 2009, 11, 443 -453.

AMA Style

Marco A. Barranco-Jiménez, Norma Sánchez-Salas, Marco A. Rosales. Thermoeconomic Optimum Operation Conditions of a Solar-driven Heat Engine Model. Entropy. 2009; 11 (3):443-453.

Chicago/Turabian Style

Marco A. Barranco-Jiménez; Norma Sánchez-Salas; Marco A. Rosales. 2009. "Thermoeconomic Optimum Operation Conditions of a Solar-driven Heat Engine Model." Entropy 11, no. 3: 443-453.