arXiv subjects

Chin-Kun Hu

Publications and source records attributed to Chin-Kun Hu.

At least 19 recordsLinked to original sources

arXiv2019

Nematic and smectic liquid crystals modeling with stiff and free-joint Lennard-Jones chain molecules

Liquid crystals (LCs) composed of mesogens play important roles in various scientific and engineering problems. How a system with many mesogens can enter a LC state is an interesting and important problem. Using stiff and free-joint Lennard-Jones chain molecules as mesogens, we study the conditions under which the mesogens can enter various LC phases. The guideline is to eliminate the unwanted translational orders under a controlled fine-tuning procedure across a sequence of systems. Instead of monitoring the growth of order out of the disorder, we prepare a configuration of high orientation ordering and find out where it relaxes to. Such a procedure begins with a reference system, consisting of short chains of homogeneous soft spheres, in a liquid-vapor coexistence situation, at which the thermodynamic instability triggers a fast spontaneous growing process. By applying a short pulse of auxiliary field to align the dispersedly oriented clusters, followed by reducing the volume and, finally, changing the homogeneous molecules into heterogeneous chains, we are able to obtain a range of systems, including nematic and smectic LCs, at their stable ordered states. The model can be extended to study the influence of nanoparticles or external field on the LC structure.

cond-mat.soft↗

arXiv2019

Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models

In some systems, the connecting probability (and thus the percolation process) between two sites depends on the geometric distance between them. To understand such process, we propose gravitationally correlated percolation models for link-adding networks on the two-dimensional lattice $G$ with two strategies $S_{\rm max}$ and $S_{\rm min}$, to add a link $l_{i,j}$ to connect site $i$ and site $j$ with mass $m_i$ and $m_j$, respectively; $m_i$ and $m_j$ are sizes of the clusters which contain site $i$ and site $j$, respectively. The probability to add the link $l_{i,j}$ is related to the generalized gravity $g_{ij} \equiv m_i m_j/r_{ij}^d$, where $r_{ij}$ is the geometric distance between $i$ and $j$, and $d$ is an adjustable decaying exponent. In the beginning of the simulation, all sites of $G$ are occupied and there is no link. In the simulation process, two inter-cluster links $l_{i,j}$ and $l_{k,n}$ are randomly chosen and the generalized gravities $g_{ij}$ and $g_{kn}$ are computed. In the strategy $S_{\rm max}$, the link with larger generalized gravity is added. In the strategy $S_{\rm min}$, the link with smaller generalized gravity is added, which include percolation on the Erd\H os-Rényi random graph and the Achlioptas process of explosive percolation as the limiting cases, $d \to \infty$ and $d \to 0$, respectively. Adjustable strategies facilitate or inhibit the network percolation in a generic view. We calculate percolation thresholds $T_c$ and critical exponents $β$ by numerical simulations. We also obtain various finite-size scaling functions for the node fractions in percolating clusters or arrival of saturation length with different intervening strategies.

physics.soc-ph↗

arXiv2019

Polymorphism in rapidly-changing cyclic environment

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic [fine-grained] environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a non-linear fitness that is induced by environmental changes. The non-linear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is examplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

q-bio.PE↗

arXiv2018

Universality and scaling in human and social systems

The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors appear. In this talk, I first introduce the concepts of universality and scaling in critical physical systems, I then briefly review some examples of universal and scaling behaviors in human and social systems, e.g. universal crossover behavior of stock returns, universality and scaling in the statistical data of literary works, universal trend in the evolution of states or countries etc. Finally, I mention some interesting problems for further studies.

physics.soc-ph↗

arXiv2017

Can morphological changes of erythrocytes be driven by hemoglobin?

At 49 C erythrocytes undergo morphological changes due to an internal force, but the origin of the force that drives changes is not clear. Here we point out that our recent experiments on thermally induced force-release in hemoglobin can provide an explanation for the morphological changes of erythrocytes.

q-bio.BM↗

arXiv2017

Exponential distance distribution of connected neurons in simulations of two-dimensional in vitro neural network development

The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brainś dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two-dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski's conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.

q-bio.NC↗

arXiv2016

Finite-size corrections and scaling for the dimer model on the checkerboard lattice

Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on an $2 M \times 2 N$ checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on finite checkerboard lattice we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent $λ$ is equal to $\infty$. We have also considered the limit $N \to \infty$ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges $c = 1$ for the height function description and $c = -2$ for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice.

cond-mat.stat-mech↗

arXiv2015

Mathematical model of influence of friction on the vortex motion

We study the influence of linear friction on the vortex motion in a non-viscous stratified compressible rotating media. Our method can be applied to describe the complex behavior of a tropical cyclone approaching land. In particular, we show that several features of the vortex in the atmosphere such as a significant track deflection, sudden decay and intensification, can be explained already by means of the simplest two dimensional barotropic model, which is a result of averaging over the height in the primitive equations of air motion in the atmosphere. Our theoretical considerations are in a good compliance with the experimental data. In contrast to other models, where first the additional physically reasonable simplifications are made, we deal with special solutions of the full system. Our method is able to explain the phenomenon of the cyclone attracting to the land and interaction of the cyclone with an island.

physics.flu-dyn↗

arXiv2015

Nonlinear stability of two-dimensional axisymmetric vortices in compressible inviscid medium in a rotating reference frame

We study the stability of the vortex in a 2D model of continuous compressible media in a uniformly rotating reference frame. As it is known, the axisymmetric vortex in a fixed reference frame is stable with respect to asymmetric perturbations for the solution of the 2D incompressible Euler equations and basically instable for compressible Euler equations. We show that the situation is quite different for a compressible axisymmetric vortex in a rotating reference frame. First, we consider special solutions with linear profile of velocity (or with spatially-uniform velocity gradients), which are important because many real vortices have similar structure near their centers. We analyze both cyclonic and anticyclonic cases and show that the stability of the solution depends only on the ratio of the vorticity to the Coriolis parameter. Using a very delicate analysis along with computer aided proof, we show that the stability of solutions can take place only for a narrow range of this ratio. Our results imply that the rotation of the coordinate frame can stabilize the compressible vortex. Further, we perform both analytical and numerical analysis of stability for real-shaped vortices.

math-ph↗

arXiv2015

Application of light pressure in the rheology of biopolymers

Precise measuring the deforming force and observation of the deformation dynamics along with difficulties of micro sample preparation are the main problems which make the micro-scale experiments difficult. Here we present a method for direct observation and measurements of mechanical parameters of elastic microfibrils in air using the pressure of optical light. For DNA microfibers, observation of the behavior dynamics of mechanical characteristics and the method sensitivity to changing the structure are demonstrated.

cond-mat.soft↗

arXiv2015

Thermal-induced proteinquake in oxyhemoglobin

Oxygen is released to living tissues via conformational changes of hemoglobin from R-state (oxyhemoglobin) to T-state (desoxyhemoglobin). The detailed mechanism of this process is not yet fully understood. We have carried out micromechanical experiments on oxyhemoglobin crystals to determine the behavior of the Young's modulus and the internal friction for temperatures between 20 C and 70 C. We have found that around 49 C oxyhemoglobin crystal samples undergo a sudden and strong increase of their Young's modulus, accompanied by a sudden decrease of the internal friction. This sudden mechanical change (proteinquake) takes place in a partially unfolded state and precedes the full denaturation transition at higher temperatures. The hemoglobin crystals after the proteinquake has the same mechanical properies as the initial state at room temperatures. We conjecture that it can be relevant for explaining the oxygen-releasing function of native oxyhemoglobin when the temperature is increased, e.g. due to active sport. The effect is specific for the quaternary structure of hemoglobin, and is absent for myoglobin with only one peptide sequence.

q-bio.BM↗

arXiv2014

Non-equilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson representation approach

We present a statistical physics framework for description of nonlinear non-equilibrium stochastic processes, modeled via chemical master equation, in the weak-noise limit. Using the Poisson representation approach and applying the large-deviation principle we first solve the master equation. Then we use the notion of the non-equilibrium free energy to derive an integral fluctuation relation for nonlinear non-equilibrium systems under feedback control. We point out that the free energy as well as some functionals can serve as non-equilibrium Lyapunov function which has an important property to decay to its minimal value monotonously at all times. The Poisson representation technique is illustrated via exact stochastic treatment of biophysical processes, such as bacterial chemosensing and molecular evolution.

physics.chem-ph↗

arXiv2013

On diffusive stability of Eigen's quasispecies model

Eigen's quasispecies system with explicit space and global regulation is considered. Limit behavior and stability of the system in a functional space under perturbations of a diffusion matrix with nonnegative spectrum are investigated. It is proven that if the diffusion matrix has only positive eigenvalues then the solutions of the distributed system converge to the equilibrium solution of the corresponding local dynamical system. These results imply that the error threshold does not change if the spatial interactions under the principle of global regulation are taken into account.

q-bio.PE↗

arXiv2013

A structure-based model fails to probe the mechanical unfolding pathways of the titin I27 domain

We discuss the use of a structure based C$α$-Go model and Langevin dynamics to study in detail the mechanical properties and unfolding pathway of the titin I27 domain. We show that a simple Go-model does detect correctly the origin of the mechanical stability of this domain. The unfolding free energy landscape parameters $x_u$ and $ΔG^{\ddagger}$, extracted from dependencies of unfolding forces on pulling speeds, are found to agree reasonably well with experiments. We predict that above $v=10^4$ nm/s the additional force-induced intermediate state is populated at an end-to-end extension of about $75 \mathring{A}$. The force-induced switch in the unfolding pathway occurs at the critical pulling speed $v_{crit} \approx 10^6-10^7$ nm/s. We argue that this critical pulling speed is an upper limit of the interval where Bell's theory works. However, our results suggest that the Go-model fails to reproduce the experimentally observed mechanical unfolding pathway properly, yielding an incomplete picture of the free energy landscape. Surprisingly, the experimentally observed intermediate state with the A strand detached is not populated in Go-model simulations over a wide range of pulling speeds. The discrepancy between simulation and experiment is clearly seen from the early stage of the unfolding process which shows the limitation of the Go model in reproducing unfolding pathways and deciphering the complete picture of the free energy landscape.

physics.bio-ph↗

arXiv2012

Biological Evolution in a Multidimensional Fitness Landscape

We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection and mutation, and calculated the mean fitness. For the case of recombination, we formulated a model with a multidimensional fitness landscape (the dimension of the space is equal to the number of blocks) and derived a theorem about the dynamics of initially narrow distribution. We also considered the case of lethal mutations. We also formulated the finite population version of the model in the case of lethal mutations. Our models, derived for the virus evolution, are interesting also for the statistical mechanics and the Hamilton-Jacobi equation as well.

q-bio.PE↗

arXiv2012

Finite-size corrections for logarithmic representations in critical dense polymers

We study (analytic) finite-size corrections in the dense polymer model on the strip by perturbing the critical Hamiltonian with irrelevant operators belonging to the tower of the identity. We generalize the perturbation expansion to include Jordan cells, and examine whether the finite-size corrections are sensitive to the properties of indecomposable representations appearing in the conformal spectrum, in particular their indecomposability parameters. We find, at first order, that the corrections do not depend on these parameters nor even on the presence of Jordan cells. Though the corrections themselves are not universal, the ratios are universal and correctly reproduced by the conformal perturbative approach, to first order.

hep-th↗

arXiv2012

Phase diagram and universality of the Lennard-Jones gas-liquid system

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexsisting density, the critical exponent of the order parameter is estimated to be $β= 0.3285(7)$. Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be $ν= 0.63 (4)$. The obtained values of $β$ and $ν$ are consistent with those of the Ising universality class.

cond-mat.stat-mech↗

arXiv2012

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A )) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.

physics.bio-ph↗