Equilibrium distribution of mutators in the single fitness peak model

This Letter develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak model, which has been used in Eigen's quasispecies equations in order to understand various aspects of evolutionary dynamics. As with the quasispecies model, our model for mutator-nonmutator equilibrium undergoes a phase transition in the limit of infinite sequence length. This "repair catas-trophe" occurs at a critical repair error probability of epsilon(r)=L(via)/L, where L(via) denotes the length of the genome controlling viability, while L denotes the overall length of the genome. The repair catastrophe therefore occurs when the repair error probability exceeds the fraction of deleterious mutations. Our model also gives a quantitative estimate for the equilibrium fraction of mutators in Escherichia coli.     

Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.     

Monte Carlo study of low/high spin transitions

We study the finite temperature property of a model on two dimensional square lattices with two Ising spins at each lattice site by Monte Carlo simulations. When those Ising spins at a lattice site are parallel the site is said to be in the high-spin state (HS), while when they are antiparallel the site is said to be in the low-spin state (LS). Throughout the study, the energy of HS is presumed to be higher than that of LS. Two Ising spins at each site are added to form a total spin, which interacts with its nearest neighbour total spins via spin-spin couplings. The spin-phonon coupling also is introduced via harmonic springs between nearest neighbour sites with spring constants and equilibrium distances depending on the spin states of the sites involved. In this system, we investigate the feature of transitions between LS and HS (to be called low/high spin transition (LHST)) by varying the temperature. As for the ferromagnetic interaction between total spins, the second order phase transition: pure HSmixed state of HS and LS is possible to occur in a pure spin system, as is expected from mean field calculations. The role of lattice distortions by the change of lattice spacings is shown to be essential for LHST: pure LS(pure)HS. In the model investigated, there appears an indication of the strong first order phase transition which reveals a conspicuous hysteresis.     

Chemical memory erasure; a photochemical model

In this paper we propose an exactly solvable model of a topological insulator defined on a spin- \(\tfrac{1}{2}\) square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin- \(\tfrac{1}{2}\) Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model’s ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem’s spectrum from band to flat-band states.     

Boson pairing and unusual criticality in a generalized XY model

We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm Monte?Carlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)condensate via an Ising transition, a situation reminiscent of the "deconfined criticality" scenario.     

Information geometry,phase transitions,and the Widom line: Magnetic and liquid systems

We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via a conjectured equality of the correlation lengths ξ$\xi$ in co-existing phases, where ξ$\xi$ is related to the scalar curvature of the equilibrium thermodynamic state space. The 1-D Ising model, and the mean-field Curie–Weiss model are discussed, and we show that information geometry correctly describes the phase behavior for the latter. The Widom lines for these systems are also established. We further study a toy model for the thermodynamics of liquid–liquid phase co-existence, and show that our method provides a simple and direct way to obtain its phase behavior and the location of the Widom line. Our analysis points towards the possibility of multiple Widom lines in liquid systems.     

Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement

Zernike phase contrast microscopy is extended and combined with a phase-shifting mechanism to perform quantitative phase measurements of microscopic objects. Dozens of discrete point light sources on a ring are constructed for illumination. For each point light source, three different levels of point-like phase steps are designed, which are alternatively located along a ring on a silica plate to perform phase retardation on the undiffracted (dc) component of the object waves. These three levels of the phase steps are respectively selected by rotating the silica plate. Thus, quantitative evaluation of phase specimens can be performed via phase-shifting mechanism. The proposed method has low "halo" and "shade-off" effects, low coherent noise level, and high lateral resolution due to the improved illumination scheme.     

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

Phase Transitions and Topology Changes in Configuration Space

The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant (the Euler characteristic) of certain submanifolds in the configuration space of two physical models. The models are the mean-field XY model and the one-dimensional XY model with nearest-neighbor interactions. The former model undergoes a second-order phase transition at a finite critical temperature while the latter has no phase transitions. The computation of this topologic invariant is performed within the framework of Morse theory. In both models topology changes in configuration space are present as the potential energy is varied; however, in the mean-field model there is a particularly strong topology change, corresponding to a big jump in the Euler characteristic, connected with the phase transition, which is absent in the one-dimensional model with no phase transition. The comparison between the two models has two major consequences: (i) it lends new and strong support to a recently proposed topological approach to the study of phase transitions; (ii) it allows us to conjecture which particular topology changes could entail a phase transition in general. We also discuss a simplified illustrative model of the topology changes connected to phase transitions using of two-dimensional surfaces, and a possible direct connection between topological invariants and thermodynamic quantities.     

Nucleation and bulk crystallization in binary phase field theory

We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters evaluated from the free energy and thickness of the interface. The critical undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft impingement" of particles via diffusion fields are consistent with experiment.     

Pinning Model in Random Correlated Environment: Appearance of an Infinite Disorder Regime

We study the influence of a correlated disorder on the localization phase transition in the pinning model (Random polymer models, 2007). When correlations are strong enough, an infinite disorder regime arises: large and frequent attractive regions appear in the environment. We present here a pinning model in random binary ( $\{-1,1\}$ -valued) environment. Defining infinite disorder via the requirement that the probability of the occurrence of a large attractive region is sub-exponential in its size, we prove that it coincides with the fact that the critical point is equal to its minimal possible value, namely $h_c(\beta )=-\beta $ . We also stress that in the infinite disorder regime, the phase transition is smoother than in the homogeneous case, whatever the critical exponent of the homogeneous model is: disorder is therefore always relevant. We illustrate these results with the example of an environment based on the sign of a Gaussian correlated sequence, in which we show that the phase transition is of infinite order in presence of infinite disorder. Our results contrast with results known in the literature, in particular in the case of an IID disorder, where the question of the influence of disorder on the critical properties is answered via the so-called Harris criterion, and where a conventional relevance/irrelevance picture holds.     

Renormalization group approach to three-state spin models in two dimensions

The real space renormalization group approach is used to study spin one anisotropic models with dipolar and quadrupolar interactions on the triangular lattice. The method is tested for the three state Potts model and the Blume-Emery-Griffiths model leading to results which are basically in agreement with other treatments of these models. The phase diagram for a quadrupolar model (anisotropic Potts model) is obtained and the influence of an external magnetic field on the transition temperature to the quadrupolar phase is determined. The fixed point which controls a transition to the phase with Ising dipolar order andXY-type quadrupolar order is found.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

A perturbative RS I cosmological phase transition

We identify a class of Randall–Sundrum type models with a successful first order cosmological phase transition during which a 5D dual of approximate conformal symmetry is spontaneously broken. Our focus is on soft-wall models that naturally realize a light radion/dilaton and suppressed dynamical contribution to the cosmological constant. We discuss phenomenology of the phase transition after developing a theoretical and numerical analysis of these models both at zero and finite temperature. We demonstrate a model with a TeV-Planck hierarchy and with a successful cosmological phase transition where the UV value of the curvature corresponds, via AdS/CFT, to an N of 20, where 5D gravity is expected to be firmly in the perturbative regime.     

Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

The two-dimensional extended Holstein-Hubbard model is investigated in the strong correlation regime to study the nature of self-trapping transition and the polaron phase diagram in the absence of superconductivity. Using a series of canonical transformations followed by zero-phonon averaging the extended Holstein-Hubbard model is converted into an effective extended Hubbard model which is subsequently transformed into an effective t-J model in the strong correlation limit. This effective t-J model is finally solved using the mean-field Hartree-Fock approximation to show that the self-trapping transition is continuous in the anti-adiabatic limit while it is discontinuous in the adiabatic limit. The phase diagrams for the localization-delocalization transition, namely the phase line and the phase surface separating the small polaron and large polaron states are also shown.     

Stochastic resonance at phase noise in signal transmission

A model is developed for a periodic signal corrupted by an arbitrarily distributed phase noise and transmitted by an arbitrary memoryless system. The model establishes a new form of the phenomenon of stochastic resonance, whereby signal transmission can be enhanced by addition of noise. This is revealed by the standard signal-to-noise ratio of stochastic resonance, which here receives an explicit theoretical expression, and which is shown improvable via noise addition. This model is the first to propose a theory of stochastic resonance with phase noise. It represents a unique framework for further investigations on stochastic resonance and its applications.     

Phase transitions in a holographic s $$$$ p model with back-reaction

In a previous paper (Nie et al. in JHEP 1311:087, arXiv:1309.2204 [hep-th], 2013), we presented a holographic s \(+\) p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction. The model shows a rich phase structure and various condensate behaviors such as the “n-type” and “u-type” ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s \(+\) p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s \(+\) p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back-reaction parameter, which show that the region for the s \(+\) p coexisting phase is enlarged with a small or medium back-reaction parameter but is reduced in the strong back-reaction cases.     

低阻抗强流箍缩电子束二极管的3阶段电子束流模型

 在顺位流模型与“4阶段”粒子流动模型的基础上，提出了一种用于分析100ns／MA级电子束流的低阻抗强箍缩二极管物理过程的理论模式。在这种理论分析模式中，将电子和离子的流动情况随时间的演变过程分成非箍缩电子流、弱箍缩电子流、强箍缩电子流3个不同的阶段，分别结合聚焦流和顺位流模型对各个阶段特性进行估算。利用KARAT PIC数值模拟软件并结合“强光一号”加速器的工作状态，对该类型二极管中电子束的流动过程作了数值模拟，并在“强光一号”加速器上开展了实验研究。数值模拟和实验结果的对比表明，所提出的新的理论分析模式是合理可行的 。     

Glass models on Bethe lattices

We consider lattice glass models in which each site can be occupied by at most one particle, and any particle may have at most occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and discuss different equilibrium glassy phases. Finally, we show that a kinetic freezing, depending on the particular dynamical rules chosen for the model, can prevent the equilibrium glass transitions.Received: 23 July 2003, Published online: 19 February 2004PACS: 64.70.Pf Glass transitions - 64.60.Cn Order-disorder and statistical mechanics of model systems - 75.10.Nr Spin-glass and other random models