Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034103
Evan Wonisch, Jonas Mensing, Andreas Heuer
Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this mean-field approach avoids any random elements. A comparison of results between the mean-field approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using Eulerian time-integration schemes.
{"title":"Second-order mean-field approximation for calculating dynamics in Au-nanoparticle networks","authors":"Evan Wonisch, Jonas Mensing, Andreas Heuer","doi":"10.1103/physreve.110.034103","DOIUrl":"https://doi.org/10.1103/physreve.110.034103","url":null,"abstract":"Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this mean-field approach avoids any random elements. A comparison of results between the mean-field approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using Eulerian time-integration schemes.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"15 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034401
Lily Watkins, Saikat Mukherjee, Jeffrey Tithof
Over the past few decades, research has indicated that the buildup of waste proteins, like amyloid- (), in the brain's interstitial spaces is linked to neurodegenerative diseases like Alzheimer's, but the details of how such proteins are removed from the brain are not well understood. We have developed a numerical model to investigate the aggregation and clearance mechanisms of in the interstitial spaces of the brain. The model describes the volume-averaged transport of in a segment of the brain interstitium modeled as a porous medium, oriented between the perivascular space (fluid-filled channel surrounding a blood vessel) of a penetrating arteriole and that of a venule. Our numerical approach solves coupled advection-diffusion-aggregation equations that model the production, aggregation, fragmentation, and clearance of species of . We simulate species to investigate the oligomer-size dependence of clearance and aggregation. We introduce a timescale plot that helps predict buildup for different neurological conditions. We show that a sudden increase in monomer concentration, as occurs in conditions like traumatic brain injury, leads to significant plaque formation, which can qualitatively be predicted using the timescale plot. Our results also indicate that impaired protein clearance (as occurs with aging) and fragmentation are both mechanisms that sustain large intermediate oligomer concentrations. Our results provide novel insight into several known risk factors for Alzheimer's disease and cognitive decline, and we introduce a unique framing of dynamics as a competition between different timescales associated with production rates, aggregation rates, and clearance conditions.
过去几十年的研究表明，大脑间隙中淀粉样蛋白-β（Aβ）等废弃蛋白质的堆积与阿尔茨海默氏症等神经退行性疾病有关，但人们对如何从大脑中清除这些蛋白质的细节还不甚了解。我们建立了一个数值模型来研究 Aβ 在大脑间隙中的聚集和清除机制。该模型描述了 Aβ 在一段被模拟为多孔介质的脑间质中的体积平均传输，该段脑间质位于穿支动脉的血管周围空间（血管周围充满液体的通道）和静脉的血管周围空间之间。我们的数值方法求解了 N 个耦合平流-扩散-聚集方程，模拟了 N 种 Aβ 的生成、聚集、破碎和清除。我们模拟了 N=50 个物种，以研究清除和聚集的低聚物大小依赖性。我们引入了一个时间刻度图，有助于预测不同神经状况下的 Aβ 积累情况。我们发现，单体浓度的突然增加（如在脑外伤等情况下）会导致大量斑块的形成，而这可以通过时标图进行定性预测。我们的研究结果还表明，蛋白质清除能力受损（如衰老）和碎裂都是维持大量中间寡聚体浓度的机制。我们的研究结果为阿尔茨海默病和认知能力衰退的几个已知风险因素提供了新的见解，并将 Aβ 动态的独特框架描述为与生成率、聚集率和清除条件相关的不同时标之间的竞争。
{"title":"Dynamics of waste proteins in brain tissue: Numerical insights into Alzheimer's risk factors","authors":"Lily Watkins, Saikat Mukherjee, Jeffrey Tithof","doi":"10.1103/physreve.110.034401","DOIUrl":"https://doi.org/10.1103/physreve.110.034401","url":null,"abstract":"Over the past few decades, research has indicated that the buildup of waste proteins, like amyloid-<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math> (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math>), in the brain's interstitial spaces is linked to neurodegenerative diseases like Alzheimer's, but the details of how such proteins are removed from the brain are not well understood. We have developed a numerical model to investigate the aggregation and clearance mechanisms of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math> in the interstitial spaces of the brain. The model describes the volume-averaged transport of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math> in a segment of the brain interstitium modeled as a porous medium, oriented between the perivascular space (fluid-filled channel surrounding a blood vessel) of a penetrating arteriole and that of a venule. Our numerical approach solves <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math> coupled advection-diffusion-aggregation equations that model the production, aggregation, fragmentation, and clearance of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math> species of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math>. We simulate <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>N</mi><mo>=</mo><mn>50</mn></mrow></math> species to investigate the oligomer-size dependence of clearance and aggregation. We introduce a timescale plot that helps predict <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math> buildup for different neurological conditions. We show that a sudden increase in monomer concentration, as occurs in conditions like traumatic brain injury, leads to significant plaque formation, which can qualitatively be predicted using the timescale plot. Our results also indicate that impaired protein clearance (as occurs with aging) and fragmentation are both mechanisms that sustain large intermediate oligomer concentrations. Our results provide novel insight into several known risk factors for Alzheimer's disease and cognitive decline, and we introduce a unique framing of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">A</mi><mi>β</mi></mrow></math> dynamics as a competition between different timescales associated with production rates, aggregation rates, and clearance conditions.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"17 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034403
Dmitriy V. Melnikov, Nelson R. Barker, Maria E. Gracheva
Nanopores in solid-state membranes have been used to detect, identify, filter, and characterize nanoparticles and biological molecules. In this work, we simulate an ionic flow through a nanopore while an ellipsoidal nanoparticle translocates through a pore. We numerically solve the Poisson-Nernst-Planck equations to obtain the ionic current values for different aspect ratios, sizes, and orientations of a translocating particle. By extending the existing theoretical model for the ionic current in the nanopore to the particles of ellipsoidal shape, we propose semiempirical fitting formulas which describe our computed data within 5% accuracy. We also demonstrate how the derived formulas can be used to identify the dimensions of nanoparticles from the available experimental data which may have useful applications in bionanotechnology.
{"title":"Ionic current blockade in a nanopore due to an ellipsoidal particle","authors":"Dmitriy V. Melnikov, Nelson R. Barker, Maria E. Gracheva","doi":"10.1103/physreve.110.034403","DOIUrl":"https://doi.org/10.1103/physreve.110.034403","url":null,"abstract":"Nanopores in solid-state membranes have been used to detect, identify, filter, and characterize nanoparticles and biological molecules. In this work, we simulate an ionic flow through a nanopore while an ellipsoidal nanoparticle translocates through a pore. We numerically solve the Poisson-Nernst-Planck equations to obtain the ionic current values for different aspect ratios, sizes, and orientations of a translocating particle. By extending the existing theoretical model for the ionic current in the nanopore to the particles of ellipsoidal shape, we propose semiempirical fitting formulas which describe our computed data within 5% accuracy. We also demonstrate how the derived formulas can be used to identify the dimensions of nanoparticles from the available experimental data which may have useful applications in bionanotechnology.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"17 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce an approach to derive a lower bound for the entropy production rate of a subsystem by utilizing the Cauchy-Schwarz inequality. It extends to establishing comprehensive upper and lower bounds for the efficiency of two subsystems. These bounds are applicable to a wide range of Markovian stochastic processes, which enhances the accuracy in depicting the range of energy conversion efficiency between subsystems. Empirical validation is conducted using a two-quantum-dot system model, which serves to confirm the effectiveness of our inequality in refining the boundaries of efficiency.
{"title":"Efficiency bounds for bipartite information-thermodynamic systems","authors":"Shihao Xia, Shuanglong Han, Ousi Pan, Yuzhuo Pan, Jincan Chen, Shanhe Su","doi":"10.1103/physreve.110.034102","DOIUrl":"https://doi.org/10.1103/physreve.110.034102","url":null,"abstract":"In this paper, we introduce an approach to derive a lower bound for the entropy production rate of a subsystem by utilizing the Cauchy-Schwarz inequality. It extends to establishing comprehensive upper and lower bounds for the efficiency of two subsystems. These bounds are applicable to a wide range of Markovian stochastic processes, which enhances the accuracy in depicting the range of energy conversion efficiency between subsystems. Empirical validation is conducted using a two-quantum-dot system model, which serves to confirm the effectiveness of our inequality in refining the boundaries of efficiency.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034108
Hyogeon Park, Yong Woon Kim, Juyeon Yi
We study the fluctuations of work caused by applying cyclic perturbations and obtain an exact sum rule satisfied by the moments of work for a broad class of quantum stationary ensembles. In the case of the canonical ensemble, the sum rule reproduces the Jarzynski equality. The sum rule can also be simplified into a linear relationship between the work average and the second moment of work, which we numerically confirm via an exact diagonalization of a spin model system.
{"title":"Sum rule for fluctuations of work","authors":"Hyogeon Park, Yong Woon Kim, Juyeon Yi","doi":"10.1103/physreve.110.034108","DOIUrl":"https://doi.org/10.1103/physreve.110.034108","url":null,"abstract":"We study the fluctuations of work caused by applying cyclic perturbations and obtain an exact sum rule satisfied by the moments of work for a broad class of quantum stationary ensembles. In the case of the canonical ensemble, the sum rule reproduces the Jarzynski equality. The sum rule can also be simplified into a linear relationship between the work average and the second moment of work, which we numerically confirm via an exact diagonalization of a spin model system.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"17 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034109
Michael Gaida, Stefan Nimmrichter
We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regard to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. We prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle.
{"title":"Otto cycles with a quantum planar rotor","authors":"Michael Gaida, Stefan Nimmrichter","doi":"10.1103/physreve.110.034109","DOIUrl":"https://doi.org/10.1103/physreve.110.034109","url":null,"abstract":"We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regard to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. We prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"47 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034402
Michael F. Staddon
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.
{"title":"How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces","authors":"Michael F. Staddon","doi":"10.1103/physreve.110.034402","DOIUrl":"https://doi.org/10.1103/physreve.110.034402","url":null,"abstract":"Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"44 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034105
Xiu-Hua Zhao, Z. C. Tu, Yu-Han Ma
Microscopic particle separation plays a vital role in various scientific and industrial domains. Conventional separation methods relying on external forces or physical barriers inherently exhibit limitations in terms of efficiency, selectivity, and adaptability across diverse particle types. To overcome these limitations, researchers are constantly exploring new separation approaches, among which ratchet-based separation is a noteworthy method. However, in contrast to the extensive numerical studies and experimental investigations on ratchet separation, its theoretical exploration appears weak, particularly lacking in the analysis of energy consumption involved in the separation processes. The latter is of significant importance for achieving energetically efficient separation. In this paper, we propose a nonequilibrium thermodynamic approach, extending the concept of shortcuts to isothermality, to realize controllable separation of overdamped Brownian particles with low energy cost. By utilizing a designed ratchet potential with temporal period <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi></math>, we find in the slow-driving regime that the average particle velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mover accent="true"><mi>v</mi><mo>¯</mo></mover><mi>s</mi></msub><mo>∝</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>D</mi><mo>/</mo><msup><mi>D</mi><mo>*</mo></msup><mo>)</mo></mrow><msup><mi>τ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, indicating that particles with different diffusion coefficients <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> can be guided to move in distinct directions with a preset <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mo>*</mo></msup></math>. It is revealed that an inevitable portion of the energy cost in separation depends on the driving dynamics of the ratchet, with an achievable lower bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>W</mi><mrow><mi>ex</mi></mrow><mrow><mo>(</mo><mi>min</mi><mo>)</mo></mrow></msubsup><mo>∝</mo><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>|</mo><msub><mover accent="true"><mi>v</mi><mo>¯</mo></mover><mi>s</mi></msub><mo>|</mo></mrow></mrow></math>. Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">L</mi></math> is the thermodynamic length of the driving loop in the parametric space. With a sawtooth potential, we numerically test the theoretical findings and illustrate the optimal separation protocol associated with <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>W</mi><mrow><mi>ex</mi></mrow><mrow><mo>(</mo><mi>min</mi><mo>)</mo></mrow></msubsup></math>. Finally, for practical considerations, we compare our approach with the conventional ratchets in terms of separation velocity and energy consumption. The scalability of the current framework for separating various particles in two-dimensional space is al
{"title":"Engineering ratchet-based particle separation via extended shortcuts to isothermality","authors":"Xiu-Hua Zhao, Z. C. Tu, Yu-Han Ma","doi":"10.1103/physreve.110.034105","DOIUrl":"https://doi.org/10.1103/physreve.110.034105","url":null,"abstract":"Microscopic particle separation plays a vital role in various scientific and industrial domains. Conventional separation methods relying on external forces or physical barriers inherently exhibit limitations in terms of efficiency, selectivity, and adaptability across diverse particle types. To overcome these limitations, researchers are constantly exploring new separation approaches, among which ratchet-based separation is a noteworthy method. However, in contrast to the extensive numerical studies and experimental investigations on ratchet separation, its theoretical exploration appears weak, particularly lacking in the analysis of energy consumption involved in the separation processes. The latter is of significant importance for achieving energetically efficient separation. In this paper, we propose a nonequilibrium thermodynamic approach, extending the concept of shortcuts to isothermality, to realize controllable separation of overdamped Brownian particles with low energy cost. By utilizing a designed ratchet potential with temporal period <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>τ</mi></math>, we find in the slow-driving regime that the average particle velocity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mover accent=\"true\"><mi>v</mi><mo>¯</mo></mover><mi>s</mi></msub><mo>∝</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>D</mi><mo>/</mo><msup><mi>D</mi><mo>*</mo></msup><mo>)</mo></mrow><msup><mi>τ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, indicating that particles with different diffusion coefficients <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>D</mi></math> can be guided to move in distinct directions with a preset <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>D</mi><mo>*</mo></msup></math>. It is revealed that an inevitable portion of the energy cost in separation depends on the driving dynamics of the ratchet, with an achievable lower bound <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msubsup><mi>W</mi><mrow><mi>ex</mi></mrow><mrow><mo>(</mo><mi>min</mi><mo>)</mo></mrow></msubsup><mo>∝</mo><msup><mi mathvariant=\"script\">L</mi><mn>2</mn></msup><mrow><mo>|</mo><msub><mover accent=\"true\"><mi>v</mi><mo>¯</mo></mover><mi>s</mi></msub><mo>|</mo></mrow></mrow></math>. Here, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"script\">L</mi></math> is the thermodynamic length of the driving loop in the parametric space. With a sawtooth potential, we numerically test the theoretical findings and illustrate the optimal separation protocol associated with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>W</mi><mrow><mi>ex</mi></mrow><mrow><mo>(</mo><mi>min</mi><mo>)</mo></mrow></msubsup></math>. Finally, for practical considerations, we compare our approach with the conventional ratchets in terms of separation velocity and energy consumption. The scalability of the current framework for separating various particles in two-dimensional space is al","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"728 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034106
Keiji Sakakibara, Daniel M. Packwood
Little is known about how commodity price fluctuations transmit to the prices of products. In this paper we present a price dynamics model for a product which is in competition with a commodity. The price of the commodity is treated as a stochastic process. Commodity price fluctuations are transmitted to the product price through a demand function which is obtained by aggregating the choices of a consumer population. Importantly, these consumers make their choices on the basis of a utility function which includes a term relating to product characteristics. Numerical simulations show that improved product characteristics tend to suppress the transmission of commodity price fluctuations. We apply our model to a realistic case of monolayer platinum (a product) in competition with platinum metal (a commodity) for adoption by consumers as a catalyst material. While monolayer platinum shows only a minor improvement in catalytic turnover rates for oxygen reduction, the resulting product characteristic improvement is sufficient to effectively eliminate product price fluctuations, at least for the consumer population regime considered here.
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Pub Date : 2024-09-03DOI: 10.1103/physreve.110.034107
Anxo Biasi
While it is known that Hamiltonian systems may undergo a phenomenon of condensation akin to Bose-Einstein condensation, not all the manifestations of this phenomenon have been uncovered yet. In this work, we present a novel form of condensation in conservative Hamiltonian systems that stands out due to its evolution through highly coherent states. The result is based on a deterministic approach to obtain exact explicit solutions representing the dynamical formation of condensates in finite time. We reveal a dual-cascade behavior during the process, featuring inverse and direct transfer of conserved quantities across the spectrum. The direct cascade yields the excitation of arbitrarily high modes in finite time, being associated with the formation of a small-scale coherent structure. We provide a fully analytic description of the processes involved.
{"title":"Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems","authors":"Anxo Biasi","doi":"10.1103/physreve.110.034107","DOIUrl":"https://doi.org/10.1103/physreve.110.034107","url":null,"abstract":"While it is known that Hamiltonian systems may undergo a phenomenon of condensation akin to Bose-Einstein condensation, not all the manifestations of this phenomenon have been uncovered yet. In this work, we present a novel form of condensation in conservative Hamiltonian systems that stands out due to its evolution through highly coherent states. The result is based on a deterministic approach to obtain exact explicit solutions representing the dynamical formation of condensates in finite time. We reveal a dual-cascade behavior during the process, featuring inverse and direct transfer of conserved quantities across the spectrum. The direct cascade yields the excitation of arbitrarily high modes in finite time, being associated with the formation of a small-scale coherent structure. We provide a fully analytic description of the processes involved.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"4 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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