Orazio Muscato, Giovanni Nastasi, Vittorio Romano, Giorgia Vitanza
The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys., vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys., vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.
这项工作的主要目的是优化量子漂移扩散模型（QDD）（V. Romano, M. Torrisi, and R. Tracinà, "Approximate solutions to the quantum drift-diffusion model of semiconductors," J. Math. Phys.48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, "Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model," SIAM J. Appl.物理》，第 148 卷，第 353-386 页，2012 年）与玻尔兹曼-维格纳输运方程（BWTE）（O. Muscato，"Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode," J. Comput.电子学》，第 20 卷，第 2062-2069 页，2021 年）使用签名蒙特卡罗方法求解（M. Nedjalkov、H. Kosina、S. Selberherr、C. Ringhofer 和 D. K. Ferry，《小型半导体器件中维格纳-玻尔兹曼传输的统一粒子方法》，《物理评论 B》，第 70 卷，第 115-319 页，2004 年）。研究了一种高非平衡态情况：由砷化镓（GaAs）制成的共振隧道二极管（RTD）中的电子传输，其中有两个砷化镓势垒。分析了应用于 RTD 的合适电压偏置范围。我们发现，当施加的偏压较低或适中时，QDD 模型与 BWTE 之间的一致性可以接受，阈值约为 0.225 V，长度为 150 nm。在更高的偏置电压下，我们预计 QDD 模型会失去准确性。
{"title":"Optimized quantum drift diffusion model for a resonant tunneling diode","authors":"Orazio Muscato, Giovanni Nastasi, Vittorio Romano, Giorgia Vitanza","doi":"10.1515/jnet-2023-0059","DOIUrl":"https://doi.org/10.1515/jnet-2023-0059","url":null,"abstract":"The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” <jats:italic>J. Math. Phys.</jats:italic>, vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” <jats:italic>SIAM J. Appl. Math.</jats:italic>, vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” <jats:italic>J. Stat. Phys.</jats:italic>, vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” <jats:italic>J. Comput. Electron</jats:italic>., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” <jats:italic>Phys. Rev. B</jats:italic>, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"156 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139544113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The modeling and understanding of micro- and nano-scale transport processes have raised increasing attention and extensive investigation during the past decades. In this mini-review, we aim to summarize our recent progress on the non-equilibrium thermodynamics of micro- and nano-scale flow and heat transfer. Special emphasis is put on the entropy generation at the interface, which plays a dominant role at small scale due to the strong non-equilibrium nature of particle-boundary interaction. We also prove the thermodynamic compatibility of both the macroscopic hydrodynamic equation and the non-equilibrium boundary conditions from the perspective of bulk and interfacial entropy generations respectively, as supported by the kinetic theory of microscopic particles. The present review will contribute to a clearer elaboration of thermodynamics at micro/nano-scale and its statistical mechanical demonstration, and thus will promote its further development in the future.
{"title":"Thermodynamics of micro- and nano-scale flow and heat transfer: a mini-review","authors":"Yangyu Guo, Moran Wang","doi":"10.1515/jnet-2023-0060","DOIUrl":"https://doi.org/10.1515/jnet-2023-0060","url":null,"abstract":"The modeling and understanding of micro- and nano-scale transport processes have raised increasing attention and extensive investigation during the past decades. In this mini-review, we aim to summarize our recent progress on the non-equilibrium thermodynamics of micro- and nano-scale flow and heat transfer. Special emphasis is put on the entropy generation at the interface, which plays a dominant role at small scale due to the strong non-equilibrium nature of particle-boundary interaction. We also prove the thermodynamic compatibility of both the macroscopic hydrodynamic equation and the non-equilibrium boundary conditions from the perspective of bulk and interfacial entropy generations respectively, as supported by the kinetic theory of microscopic particles. The present review will contribute to a clearer elaboration of thermodynamics at micro/nano-scale and its statistical mechanical demonstration, and thus will promote its further development in the future.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"52 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139522556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The development of non-Fourier heat conduction models is encouraged by the invalidity of Fourier’s law to explain heat conduction in ultrafast or ultrasmall systems. The production of negative entropy will result from the combination of traditional nonequlibrium thermodynamics and non-Fourier heat conduction models. To resolve this paradox, extended irreversible thermodynamics (EIT) introduces a new state variable. However, real dynamics variables like force and momentum are still missing from nonequilibrium thermodynamics and EIT’s generalized force and generalized flux. Heat has both mass and energy, according to thermomass theory and Einstein’s mass-energy relation. The generalized heat conduction model containing non-Fourier effects was established by thermomass gas model. The thermomass theory reshapes the concept of the generalized force and flux, temperature, and entropy production in nonequilibrium thermodynamics and revisits the assumption for the linear regression of the fluctuations in Onsager reciprocal relation. The generalized heat conduction model based on thermomass theory has been used to study thermal conductivity, thermoelectric effect, and thermal rectification effect in nanosystems.
由于傅里叶定律无法解释超快或超小系统中的热传导，因此非傅里叶热传导模型的发展受到了鼓励。传统的非平衡热力学和非傅里叶热传导模型的结合将产生负熵。为了解决这一矛盾，扩展不可逆热力学（EIT）引入了一个新的状态变量。然而，非平衡热力学和 EIT 的广义力和广义通量中仍然缺少力和动量等实际动力学变量。根据热质理论和爱因斯坦的质能关系，热具有质量和能量。热质气体模型建立了包含非傅里叶效应的广义热传导模型。热质理论重塑了非平衡热力学中广义力和通量、温度和熵产生的概念，并重新审视了昂萨格倒易关系中波动线性回归的假设。基于热质理论的广义热传导模型已被用于研究纳米系统中的热导率、热电效应和热整流效应。
{"title":"Revisit nonequilibrium thermodynamics based on thermomass theory and its applications in nanosystems","authors":"Renjie Hua, Yuan Dong","doi":"10.1515/jnet-2023-0094","DOIUrl":"https://doi.org/10.1515/jnet-2023-0094","url":null,"abstract":"The development of non-Fourier heat conduction models is encouraged by the invalidity of Fourier’s law to explain heat conduction in ultrafast or ultrasmall systems. The production of negative entropy will result from the combination of traditional nonequlibrium thermodynamics and non-Fourier heat conduction models. To resolve this paradox, extended irreversible thermodynamics (EIT) introduces a new state variable. However, real dynamics variables like force and momentum are still missing from nonequilibrium thermodynamics and EIT’s generalized force and generalized flux. Heat has both mass and energy, according to thermomass theory and Einstein’s mass-energy relation. The generalized heat conduction model containing non-Fourier effects was established by thermomass gas model. The thermomass theory reshapes the concept of the generalized force and flux, temperature, and entropy production in nonequilibrium thermodynamics and revisits the assumption for the linear regression of the fluctuations in Onsager reciprocal relation. The generalized heat conduction model based on thermomass theory has been used to study thermal conductivity, thermoelectric effect, and thermal rectification effect in nanosystems.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"28 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139522568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Energetic laser-accelerated ions can heat a small solid-density sample homogeneously to temperatures over 10,000 K in less than a nanosecond. During this brief heating time, the electron temperature of the sample rises first, and then the ion temperature increases owing to the heat transfer between the hot electrons and cold ions. Since energy deposition from the incident heavy ion beam continues concurrently with the electron-ion relaxation process within the heated sample, the electron and ion temperatures do not reach equilibrium until the end of the heating. Here we calculate the temperature evolutions of electrons and ions within a dense aluminum sample heated by a laser-accelerated gold ions using the two-temperature model. For these calculations, we use the published stopping power data, known electron-ion coupling factors, and the SESAME equation-of-state (EOS) table for aluminum. For the first time, we investigate the electron and ion temperature distributions within the warm dense aluminum sample and the heating uniformity throughout the entire heating period. We anticipate that knowledge of the temperature evolution during heating will allow for the study of the stopping power, thermal conductivity, EOS, and opacity of warm dense matter heated by an energetic heavy ion beam.
高能激光加速离子可在不到一纳秒的时间内将固体密度较小的样品均匀加热到 10,000 K 以上的温度。在这一短暂的加热时间内，样品的电子温度首先升高，然后由于热电子和冷离子之间的热传递，离子温度也随之升高。由于入射重离子束的能量沉积与加热样品内的电子-离子弛豫过程同时进行，电子和离子温度直到加热结束时才达到平衡。在这里，我们使用双温模型计算了在激光加速金离子加热的致密铝样品中电子和离子的温度变化。在计算过程中，我们使用了已公布的停止功率数据、已知的电子-离子耦合因子以及铝的 SESAME 状态方程（EOS）表。我们首次研究了暖致密铝样品内的电子和离子温度分布以及整个加热期间的加热均匀性。我们预计，了解加热过程中的温度演变将有助于研究被高能重离子束加热的暖致密物质的停止功率、热导率、EOS 和不透明度。
{"title":"Heat transfer within nonequilibrium dense aluminum heated by a heavy ion beam","authors":"Chiwan Song, Seongmin Lee, Woosuk Bang","doi":"10.1515/jnet-2023-0061","DOIUrl":"https://doi.org/10.1515/jnet-2023-0061","url":null,"abstract":"Energetic laser-accelerated ions can heat a small solid-density sample homogeneously to temperatures over 10,000 K in less than a nanosecond. During this brief heating time, the electron temperature of the sample rises first, and then the ion temperature increases owing to the heat transfer between the hot electrons and cold ions. Since energy deposition from the incident heavy ion beam continues concurrently with the electron-ion relaxation process within the heated sample, the electron and ion temperatures do not reach equilibrium until the end of the heating. Here we calculate the temperature evolutions of electrons and ions within a dense aluminum sample heated by a laser-accelerated gold ions using the two-temperature model. For these calculations, we use the published stopping power data, known electron-ion coupling factors, and the SESAME equation-of-state (EOS) table for aluminum. For the first time, we investigate the electron and ion temperature distributions within the warm dense aluminum sample and the heating uniformity throughout the entire heating period. We anticipate that knowledge of the temperature evolution during heating will allow for the study of the stopping power, thermal conductivity, EOS, and opacity of warm dense matter heated by an energetic heavy ion beam.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"105 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139522654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The thermal and electrical properties of photovoltaic cell (PVC) under linear phenomenological heat transfer law between it and the environment is studied through finite time thermodynamics and the volt-ampere characteristic equation. The properties of PVC are affected by heat transfer between PVC and environment. There are optimal solar radiation intensity and PVC output voltage (OV), which make the photoelectric conversion efficiency (PECE) of PVC reach the highest value. When OV and solar radiation intensity are 28.50 V and 700 W/m2, the maximum PECE is 0.156. There is also the best solar radiation intensity, which makes the open-circuit voltage (OCV) reach the maximum. When solar radiant intensity is 669 W/m2, the maximum OCV is 33.14 V. The values of power output and short-circuit current (SCC) are monotonically increasing with solar radiation intensity. Given solar radiation intensity, the power output and OV exhibit a parabolic shape. The operating temperature falls first and then grows with the OV. However, the change of operating temperature with OV is not much. Band gap is a decreasing function of operating temperature. This article can give theoretical support for the design and use of PVCs.
通过有限时间热力学和伏安特性方程，研究了光伏电池（PVC）与环境之间线性现象传热规律下的热特性和电特性。聚氯乙烯的特性受聚氯乙烯与环境之间热传递的影响。存在最佳太阳辐射强度和聚氯乙烯输出电压（OV），使聚氯乙烯的光电转换效率（PECE）达到最高值。当 OV 和太阳辐射强度分别为 28.50 V 和 700 W/m2 时，PECE 最大，为 0.156。还有一个最佳的太阳辐射强度，它使开路电压（OCV）达到最大值。当太阳辐射强度为 669 W/m2 时，最大开路电压为 33.14 V。功率输出和短路电流（SCC）值随太阳辐射强度单调递增。在太阳辐射强度一定的情况下，功率输出和 OCV 呈现抛物线形状。工作温度先下降，然后随 OV 增长。不过，工作温度随 OV 的变化不大。带隙是工作温度的递减函数。本文可为聚氯乙烯的设计和使用提供理论支持。
{"title":"Thermal and electrical properties of photovoltaic cell with linear phenomenological heat transfer law","authors":"Jun Li, Lingen Chen","doi":"10.1515/jnet-2023-0056","DOIUrl":"https://doi.org/10.1515/jnet-2023-0056","url":null,"abstract":"The thermal and electrical properties of photovoltaic cell (PVC) under linear phenomenological heat transfer law between it and the environment is studied through finite time thermodynamics and the volt-ampere characteristic equation. The properties of PVC are affected by heat transfer between PVC and environment. There are optimal solar radiation intensity and PVC output voltage (OV), which make the photoelectric conversion efficiency (PECE) of PVC reach the highest value. When OV and solar radiation intensity are 28.50 V and 700 W/m<jats:sup>2</jats:sup>, the maximum PECE is 0.156. There is also the best solar radiation intensity, which makes the open-circuit voltage (OCV) reach the maximum. When solar radiant intensity is 669 W/m<jats:sup>2</jats:sup>, the maximum OCV is 33.14 V. The values of power output and short-circuit current (SCC) are monotonically increasing with solar radiation intensity. Given solar radiation intensity, the power output and OV exhibit a parabolic shape. The operating temperature falls first and then grows with the OV. However, the change of operating temperature with OV is not much. Band gap is a decreasing function of operating temperature. This article can give theoretical support for the design and use of PVCs.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"3 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139110209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper evaluates a passive method for heat transfer improvement in heat exchangers, which implies the use of nanofluids. All calculations were carried out with a constant volumetric flow rate. The study examines three fluids with 0–4 % volume concentrations of CuO, MgO, and Al2O3 particles. The results indicate an increase in the heat transfer coefficient with increasing temperature. An Al2O3 nanofluid (4 % concentration) contributed to the best thermal performance. The incorporation of a 4 % content of MgO yielded an augmentation in heat transfer ranging from 15 % to 22 %, whereas an analogous concentration of CuO led to a more substantial enhancement of 25 %. Notably, the introduction of nanoparticles of Al2O3 produces a remarkable augmentation in heat transfer performance, with potential improvements of up to 36 %. The Nusselt number increases with increasing particle volume fraction and Reynolds number, according to results obtained for several nanoparticles (Al2O3, CuO, SiO2, and ZnO) with volume percentages in the range of 1–4 % and nanoparticle diameters of 25–70 nm. For all nanofluids, the time-averaged Nusselt number rises with a solid phase volume fraction increase of less than 5 %.
{"title":"Strategies to improve the thermal performance of solar collectors","authors":"Bader Alshuraiaan","doi":"10.1515/jnet-2023-0040","DOIUrl":"https://doi.org/10.1515/jnet-2023-0040","url":null,"abstract":"The paper evaluates a passive method for heat transfer improvement in heat exchangers, which implies the use of nanofluids. All calculations were carried out with a constant volumetric flow rate. The study examines three fluids with 0–4 % volume concentrations of CuO, MgO, and Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub> particles. The results indicate an increase in the heat transfer coefficient with increasing temperature. An Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub> nanofluid (4 % concentration) contributed to the best thermal performance. The incorporation of a 4 % content of MgO yielded an augmentation in heat transfer ranging from 15 % to 22 %, whereas an analogous concentration of CuO led to a more substantial enhancement of 25 %. Notably, the introduction of nanoparticles of Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub> produces a remarkable augmentation in heat transfer performance, with potential improvements of up to 36 %. The Nusselt number increases with increasing particle volume fraction and Reynolds number, according to results obtained for several nanoparticles (Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub>, CuO, SiO<jats:sub>2</jats:sub>, and ZnO) with volume percentages in the range of 1–4 % and nanoparticle diameters of 25–70 nm. For all nanofluids, the time-averaged Nusselt number rises with a solid phase volume fraction increase of less than 5 %.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"1 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139110268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The consequences of introducing the fourth order orientation tensor as an independent variable in addition to the second order one are investigated. In the first part consequences of the Second Law of Thermodynamics are exploited. The cases with the second order alignment tensor in the state space on one hand and with the second and fourth order alignment tensors on the other hand are analogous. In the latter case differential equations for the second and fourth order tensors result from linear force-flux relations with a coupling arising due to coupling terms in the free energy. In the second part the differential equations for the second order orientation tensor or the second and fourth order orientation tensors, respectively are given explicitly in the special case of a rotation symmetric orientation distribution. The Folgar-Tucker equation with a quadratic closure relation leads to a Riccati equation for the second order parameter. In comparison the Folgar-Tucker equation and the differential equation for the fourth order parameter are considered. The fourth order parameter is eliminated later. The resulting equation for the second order parameter is a Duffing equation with a behavior of solutions completely different from the solutions of the Riccati equation.
{"title":"On the influence of the fourth order orientation tensor on the dynamics of the second order one","authors":"Christina Papenfuss","doi":"10.1515/jnet-2023-0066","DOIUrl":"https://doi.org/10.1515/jnet-2023-0066","url":null,"abstract":"The consequences of introducing the fourth order orientation tensor as an independent variable in addition to the second order one are investigated. In the first part consequences of the Second Law of Thermodynamics are exploited. The cases with the second order alignment tensor in the state space on one hand and with the second and fourth order alignment tensors on the other hand are analogous. In the latter case differential equations for the second and fourth order tensors result from linear force-flux relations with a coupling arising due to coupling terms in the free energy. In the second part the differential equations for the second order orientation tensor or the second and fourth order orientation tensors, respectively are given explicitly in the special case of a rotation symmetric orientation distribution. The Folgar-Tucker equation with a quadratic closure relation leads to a Riccati equation for the second order parameter. In comparison the Folgar-Tucker equation and the differential equation for the fourth order parameter are considered. The fourth order parameter is eliminated later. The resulting equation for the second order parameter is a Duffing equation with a behavior of solutions completely different from the solutions of the Riccati equation.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"13 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138679097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Brian Straughan, Vincenzo Tibullo, Francesca Passarella
We review models for convective motion which have a flux law of Cattaneo type. This includes thermal convection where the heat flux law is a Cattaneo one. We additionally analyse models where the convective motion is due to a density gradient caused by a concentration of solute. The usual Fick’s law in this case is replaced by a Cattaneo one involving the flux of solute and the concentration gradient. Other effects such as rotation, the presence of a magnetic field, Guyer–Krumhansl terms, or Kelvin–Voigt theories are briefly introduced.
{"title":"Buoyancy driven convection with a Cattaneo flux model","authors":"Brian Straughan, Vincenzo Tibullo, Francesca Passarella","doi":"10.1515/jnet-2023-0078","DOIUrl":"https://doi.org/10.1515/jnet-2023-0078","url":null,"abstract":"We review models for convective motion which have a flux law of Cattaneo type. This includes thermal convection where the heat flux law is a Cattaneo one. We additionally analyse models where the convective motion is due to a density gradient caused by a concentration of solute. The usual Fick’s law in this case is replaced by a Cattaneo one involving the flux of solute and the concentration gradient. Other effects such as rotation, the presence of a magnetic field, Guyer–Krumhansl terms, or Kelvin–Voigt theories are briefly introduced.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"39 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138582570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The equivalence between irreversibility and dissipation entails that the Onsager reciprocal relations hold unconditionally, requiring the part of the phenomenological matrix describing dissipative phenomena to be symmetric. The antisymmetric part of the phenomenological matrix corresponds to the Casimir’s variant of the reciprocal relations and describes reversible phenomena. Further, we discuss the relationship of the reversibility and entropy production, including the role of the level of description, and we use the chemotaxis as an illustrative example.
{"title":"Onsager-Casimir reciprocal relations as a consequence of the equivalence between irreversibility and dissipation","authors":"Václav Klika, Sylvain D. Bréchet","doi":"10.1515/jnet-2023-0069","DOIUrl":"https://doi.org/10.1515/jnet-2023-0069","url":null,"abstract":"The equivalence between irreversibility and dissipation entails that the Onsager reciprocal relations hold unconditionally, requiring the part of the phenomenological matrix describing dissipative phenomena to be symmetric. The antisymmetric part of the phenomenological matrix corresponds to the Casimir’s variant of the reciprocal relations and describes reversible phenomena. Further, we discuss the relationship of the reversibility and entropy production, including the role of the level of description, and we use the chemotaxis as an illustrative example.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":"56 1","pages":""},"PeriodicalIF":6.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138635103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We employ the generalized bracket formalism of nonequilibrium thermodynamics by Beris and Edwards to derive Lorentz-covariant time-evolution equations for an imperfect fluid with viscosity, dilatational viscosity, and thermal conductivity. Following closely the analysis presented by Öttinger (Physica A, 259, 1998, 24–42; Physica A, 254, 1998, 433–450) to the same problem but for the GENERIC formalism, we include in the set of hydrodynamic variables a covariant vector playing the role of a generalized thermal force and a covariant tensor closely related to the velocity gradient tensor. In our work here, we derive first the nonrelativistic equations and then we proceed to obtain the relativistic ones by elevating the thermal variable to a four-vector, the mechanical force variable to a four-by-four tensor, and by representing the Hamiltonian of the system with the time component of the energy-momentum tensor. For the Poisson and dissipation brackets we assume the same general structure as in the nonrelativistic case, but with the phenomenological coefficients in the dissipation bracket describing friction to heat and viscous effects being properly constrained for the resulting dynamic equations to be manifest Lorentz-covariant. The final relativistic equations are identical to those derived by Öttinger but the present approach seems to be more general in the sense that one could think of alternative forms of the phenomenological coefficients describing friction that could ensure Lorentz-covariance.
{"title":"Relativistic hydrodynamics from the single-generator bracket formalism of nonequilibrium thermodynamics","authors":"Vlasis G. Mavrantzas","doi":"10.1515/jnet-2023-0068","DOIUrl":"https://doi.org/10.1515/jnet-2023-0068","url":null,"abstract":"We employ the generalized bracket formalism of nonequilibrium thermodynamics by Beris and Edwards to derive Lorentz-covariant time-evolution equations for an imperfect fluid with viscosity, dilatational viscosity, and thermal conductivity. Following closely the analysis presented by Öttinger (Physica A, 259, 1998, 24–42; Physica A, 254, 1998, 433–450) to the same problem but for the GENERIC formalism, we include in the set of hydrodynamic variables a covariant vector playing the role of a generalized thermal force and a covariant tensor closely related to the velocity gradient tensor. In our work here, we derive first the nonrelativistic equations and then we proceed to obtain the relativistic ones by elevating the thermal variable to a four-vector, the mechanical force variable to a four-by-four tensor, and by representing the Hamiltonian of the system with the time component of the energy-momentum tensor. For the Poisson and dissipation brackets we assume the same general structure as in the nonrelativistic case, but with the phenomenological coefficients in the dissipation bracket describing friction to heat and viscous effects being properly constrained for the resulting dynamic equations to be manifest Lorentz-covariant. The final relativistic equations are identical to those derived by Öttinger but the present approach seems to be more general in the sense that one could think of alternative forms of the phenomenological coefficients describing friction that could ensure Lorentz-covariance.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":" 21","pages":""},"PeriodicalIF":6.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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