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X. -M. Zhu

Publications and source records attributed to X. -M. Zhu.

17 recordsLinked to original sources
arXiv2007

Cancer Genesis and Progression as Dynamics in Functional Landscape of Endogenous Molecular-Cellular Network

An endogenous molecular-cellular network for both normal and abnormal functions is assumed to exist. This endogenous network forms a nonlinear stochastic dynamical system, with many stable attractors in its functional landscape. Normal or abnormal robust states can be decided by this network in a manner similar to the neural network. In this context cancer is hypothesized as one of its robust intrinsic states. This hypothesis implies that a nonlinear stochastic mathematical cancer model is constructible based on available experimental data and its quantitative prediction is directly testable. Within such model the genesis and progression of cancer may be viewed as stochastic transitions between different attractors. Thus it further suggests that progressions are not arbitrary. Other important issues on cancer, such as genetic vs epigenetics, double-edge effect, dormancy, are discussed in the light of present hypothesis. A different set of strategies for cancer prevention, cure, and care, is therefore suggested.

q-bio.SC↗
arXiv2004

Limit Cycle and Conserved Dynamics

We demonstrate that a potential coexists with limit cycle. Here the potential determines the final distribution of population. Our demonstration consists of three steps: We first show the existence of limit from a typical physical sciences setting: the potential is a type of Mexican hat type, with the strength of a magnetic field scale with the strength the potential gradient near the limit cycle, and the friction goes to zero faster than the potential near the limit cycle. Hence the dynamics at the limit cycle is conserved. The diffusion matrix is nevertheless finite at the limit cycle. Secondly, we construct the potential in the dynamics with limit cycle in a typical dynamical systems setting. Thirdly, we argue that such a construction can be carried out in a more general situation based on a method discovered by one of us. This method of dealing with stochastic differential equation is in general different from both Ito and Stratonovich calculus. Our result may be useful in many related applications, such as in the discussion of metastability of limit cycle and in the construction of Hopfield potential in the neural network computation.

nlin.CD↗
arXiv2004

Robustness, Stability and Efficiency of Phage lambda Gene Regulatory Network: Dynamical Structure Analysis

Based on our physical and biological studies we have recently developed a mathematical framework for the analysis of nonlnear dynamics. We call this framework the dynamical structure analysis. It has four dynamical elements: potential landscape, transverse matrix, descendant matrix, and stochastic drive. In particular, the importance and the existence of the potential landscape is emphasized. The dynamical structure analysis is illustrated in detail by the study of stability, robustness, and efficiency of the simplest gene regulatory network of phage lambda.

q-bio.MN↗
arXiv2004

Calculating Biological Behaviors of Epigenetic States in Phage lambda Life Cycle

Gene regulatory network of lambda phage is one the best studied model systems in molecular biology. More 50 years of experimental study has provided a tremendous amount of data at all levels: physics, chemistry, DNA, protein, and function. However, its stability and robustness for both wild type and mutants has been a notorious theoretical/mathematical problem. In this paper we report our successful calculation on the properties of this gene regulatory network. We believe it is of its first kind. Our success is of course built upon numerous previous theoretical attempts, but following 3 features make our modeling uniqu: 1) A new modeling method particular suitable for stability and robustness study; 2) Paying a close attention to the well-known difference of in vivo and in vitro; 3) Allowing more important role for noise and stochastic effect to play. The last two points have been discussed by two of us (Ao and Yin, cond-mat/0307747), which we believe would be enough to make some of previous theoretical attempts successful, too. We hope the present work would stimulate a further interest in the emerging field of gene regulatory network.

q-bio.MN↗
arXiv2000

Microscopic theory of vortex dynamics in homogeneous superconductors

Vortex dynamics in fermionic superfluids is carefully considered from the microscopic point of view. Finite temperatures, as well as impurities, are explicitly incorporated. To enable readers understand the physical implications, macroscopic demonstrations based on thermodynamics and fluctuations- dissipation theorems are constructed. For the first time a clear summary and a critical review of previous results are given.

cond-mat↗
arXiv1999

Effective Mass of a Vortex in a Clean Superconductor

We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Using the effective action for a vortex, we arrive at the mass formula as the integral of the spectral function $J(ω)/ω^3$ over frequency. The spectral function is given in terms of the transition elements of the gradient of the Hamiltonian between Bogoliubov-deGennes eigenstates. We show that core-core, and core-extended transitions yield the vortex mass, near T=0, of order of electron mass displaced by the normal core. The extended-extended states contributions are linearly divergent with the low frequency cutoff $ω_c$, in accordance with the Ohmic character of the spectral function at low energies. We argue that the mass and friction are closely related in this system and arise from the same mechanism - interaction with the surrounding fermionic degrees of freedom.

cond-mat.supr-con↗
arXiv1998

Role of Impurities in Core Contribution to Vortex Friction

We present a microscopic calculation of core states contribution to vortex friction in a type II superconductor at zero temperature. In weak impurity limit, a perturbative calculation leads to a vortex friction proportional to the normal state resistivity. With the aid of random matrix theory, vortex friction due to core states is determined only by the Fermi energy and the energy gap in dirty limit, similar to the phenomenological results of Bardeen and Stephen, but disagrees with the results obtained under the relaxation time approximation. In addition, an explicit demonstration is given on the the insensitivity of transverse force to impurities.

cond-mat↗
arXiv1998

Vortex Dynamics, Resistivity Formula, and Fluctuation-dissipation Theorems

We investigate the problem of forces on moving vortex in a superfluid or superconductor. The main purpose is to locate the source which leads to the contradictory results in the literature. We establish the connection between this problem to the difficult but well studied subject of resistivity formula in transport theory. The relaxation time approximation used in the force calculation via force-force correlation function is shown to be invalid. The roles of Berry's phase and fluctuation-dissipation theorems are discussed.

cond-mat↗
arXiv1998

Friction on a Quantized Vortex in a Superfluid

We obtain the explicit expression of the friction on a moving quantized vortex, following the formulation of Thouless, Ao and Niu. It is shown that the friction on a moving vortex is sensitive to details but does not change the transverse force. We provide a general thermodynamic interpretation for the mutual independence of the transverse force and the friction. The friction is evaluated for the case of quasiparticle contributions in a clean fermionic superfluid, showing a new feature of logarithmic divergence.

cond-mat↗
arXiv1998

Friction Coefficient and Berry Phase for a Topological Singularity in a Superfluid

The coexistence of the universal transverse force and the non-universal friction force on a topological singularity in a superfluid is shown here. Based on the BCS type microscopic theory, we explicitly evaluate the quasiparticle contribution to the friction coefficient in a clean fermionic superfluid, showing a new feature of logarithmic divergence.

cond-mat↗
arXiv1998

Effects of Geometric Phases in Josephson Junction Arrays

We show that the en route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect in the classical limit. However, geometric phases due to the finite superfluid density at superconductor grains have a profound influence on the quantum dynamics of vortices. Subsequently we find rich and complex Hall behaviors analogous to the Thouless-Kohmoto-Nightingale-den Nijs effect in the quantum regime.

cond-mat↗
arXiv1997

Vortex Dynamics within the BCS Theory

We outline a conventional path integral derivation of the transverse force and the friction for a vortex in a superconductor based on the BCS theory. The derivation is valid in both clean and dirty limits at both zero and finite temperatures. The transverse force is found to be precisely as what has been obtained by Ao and Thouless using the Berry's phase method. The friction is essentially the same as the Bardeen and Stephen's result. Errors in some previous representive microscopic derivations are discussed.

cond-mat.supr-con↗
arXiv1997

From Lorentz Force on Electron to Magnus Force on Vortex, Role of Experiments

The vortex motion in a superfluid or a type II superconductor is similar to the electron motion in a magnetic field, because they both feel a transverse force. The vortex dynamics in a superconductor is a basic property of the superconductivity which remains controversial. It is also responsible for a large class of observed physical phenomena. We will examine this issue from the experimental point of view. In particular, we will compare the experiments which have set the stage to the Lorentz force and the experiments influencing our understanding of the Magnus force on vortices in superconductors.

cond-mat.supr-con↗
arXiv1996

Hall effect and geometric phases in Josephson junction arrays

Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect.

cond-mat↗
arXiv1994

Effective Lagrangians for BCS Superconductors at T=0

We show that the low frequency, long wavelength dynamics of the phase of the pair field for a BCS-type s-wave superconductor at T=0 is equivalent to that of a time-dependent non-linear Schrödinger Lagrangian (TDNLSL), when terms required by Galilean invariance are included. If the modulus of the pair field is also allowed to vary, the system is equivalent to two coupled TDNLSL's. We also refer the interested reader to our earlier paper, `Nonlinear Schrodinger equation for superconductors' [cond-mat/9312099], for a different line of derivation

cond-mat↗
arXiv1994

Nonlinear Schrödinger Equation for Superconductors

Using the Hartree-Fock-Bogoliubov factorization of the density matrix and the Born-Oppenheimer approximation we show that the motion of the condensate satisfies a nonlinear Schrödinger equation in the zero temperature limit. The Galilean invariance of the equation is explicitly manifested. {}From this equation some general properties of a superconductor, such as Josephson effects, the Magnus force, and the Bogoliubov-Anderson mode can be obtained readily.

cond-mat↗