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SDE decomposition and A-type stochastic interpretation in nonequilibrium processes
Ruoshi Yuan, Ying Tang, Ping Ao
Front. Phys. . 2017, 12 (6 ): 120201-.
https://doi.org/10.1007/s11467-017-0718-2
An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.
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Order parameter analysis of synchronization transitions on star networks
Hong-Bin Chen, Yu-Ting Sun, Jian Gao, Can Xu, Zhi-Gang Zheng
Front. Phys. . 2017, 12 (6 ): 120504-.
https://doi.org/10.1007/s11467-017-0651-4
The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe–Strogatz transformation, Ott–Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
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Detectable states, cycle fluxes, and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis
Jie Ren
Front. Phys. . 2017, 12 (6 ): 120505-.
https://doi.org/10.1007/s11467-017-0658-x
The process by which a kinesin motor couples its ATPase activity with concerted mechanical handover-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.
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Synchronization of coupled metronomes on two layers
Jing Zhang,Yi-Zhen Yu,Xin-Gang Wang
Front. Phys. . 2017, 12 (6 ): 120508-.
https://doi.org/10.1007/s11467-017-0675-9
Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state, the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.
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Constructing backbone network by using tinker algorithm
Zhiwei He,Meng Zhan,Jianxiong Wang,Chenggui Yao
Front. Phys. . 2017, 12 (6 ): 120701-.
https://doi.org/10.1007/s11467-016-0645-7
Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in maintaining the main function of the biological network. We propose a new algorithm, the tinker algorithm, to determine this core structure and apply it in the cell-cycle system. With this algorithm, the backbone network of the cell-cycle network can be determined accurately and efficiently in various models such as the Boolean model, stochastic model, and ordinary differential equation model. Results show that our algorithm is more efficient than that used in the previous research. We hope this method can be put into practical use in relevant future studies.
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Renormalization group theory for temperature-driven first-order phase transitions in scalar models
Ning Liang, Fan Zhong
Front. Phys. . 2017, 12 (6 ): 126403-.
https://doi.org/10.1007/s11467-016-0633-y
We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ 3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found: a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ 3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and twoloop results for the static and dynamic exponents for the Yang–Lee edge singularity, respectively, which falls into the same universality class as φ 3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.
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Morphological transformations of diblock copolymers in binary solvents: A simulation study
Zheng Wang, Yuhua Yin, Run Jiang, Baohui Li
Front. Phys. . 2017, 12 (6 ): 128201-.
https://doi.org/10.1007/s11467-017-0678-6
Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent C S2 , the concentration of the polymer C p , and the polymer–solvent interactions ε ij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of C p , C S 2 , and/or ε AS2 . The copolymer morphological sequence from dissolved→sphere→rod→ring/cage→vesicle is obtained upon increasing C S 2 at a fixed C p . This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure significantly. In particular, when the interaction ε BS 2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar aggregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing C p or with decreasing C S 2 , but remains almost unchanged with variations in ε AS 2 .
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Recent progress in econophysics: Chaos, leverage, and business cycles as revealed by agent-based modeling and human experiments
Chen Xin, Ji-Ping Huang
Front. Phys. . 2017, 12 (6 ): 128910-.
https://doi.org/10.1007/s11467-017-0696-4
Agent-based modeling and controlled human experiments serve as two fundamental research methods in the field of econophysics. Agent-based modeling has been in development for over 20 years, but how to design virtual agents with high levels of human-like “intelligence” remains a challenge. On the other hand, experimental econophysics is an emerging field; however, there is a lack of experience and paradigms related to the field. Here, we review some of the most recent research results obtained through the use of these two methods concerning financial problems such as chaos, leverage, and business cycles. We also review the principles behind assessments of agents’ intelligence levels, and some relevant designs for human experiments. The main theme of this review is to show that by combining theory, agent-based modeling, and controlled human experiments, one can garner more reliable and credible results on account of a better verification of theory; accordingly, this way, a wider range of economic and financial problems and phenomena can be studied.
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13 articles