We study force generation and motion of molecular motors using a simple two-state model in the paper.Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that a...We study force generation and motion of molecular motors using a simple two-state model in the paper.Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.展开更多
We study the random motion of a charged test particle with a normal classical constant velocity in a spacetime with a perfectly reflecting plane boundary and calculate both the velocity and position dispersions of the...We study the random motion of a charged test particle with a normal classical constant velocity in a spacetime with a perfectly reflecting plane boundary and calculate both the velocity and position dispersions of the test particle. Our results show that the dispersions in the normal direction are weakened while those in the parallel directions are strengthened as compared to the classical static case when the test particle classically moves away from the boundary. However, if the classical motion reverses its direction, then the dispersions in the normal direction are reinforced while those in the parallel directions get weakened.展开更多
We believe that well-known principles and relationships between physical entities are the key for a deep knowledge of reality. However, they must be applied using innovative points of view, points of view that can be ...We believe that well-known principles and relationships between physical entities are the key for a deep knowledge of reality. However, they must be applied using innovative points of view, points of view that can be provided by, for example, experts on information theory （as we are）. Our previous efforts in this direction led to a fascinating result： the theoretical total mass ofa spacetime in which Planck＇s length is an observer-independent scale of length is equal （both in expression and value） to the mass of our portion of Universe measured by national aeronautics and space administration wilkinson microwave anisotropy probe （NASA WMAP） spacecraft. In the following paragraphs we＇ll show how granularity （i.e., discontinuity） of physical entities of our portion of observable spacetime descends directly from the principles of information theory, and how a physical theory about the discontinuity of reality built on these basis can lead to an elegant descriptions of both microcosm and macrocosm.展开更多
In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the ...In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.展开更多
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The ...The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.展开更多
We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kahler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian sub...We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kahler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly KahlerS3 × S3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function A, such that g（（△↓h）（v, v, v）, Jr） = λ holds for all unit tangent vector v.展开更多
文摘We study force generation and motion of molecular motors using a simple two-state model in the paper.Asymmetric and periodic potential is adopted to describe the interaction between motor proteins and filaments that are periodic and polar. The current and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the current is also calculated. It is shown that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states.
基金The project supported by the National Natural Science Foundation of China under Grant No. 10575035
文摘We study the random motion of a charged test particle with a normal classical constant velocity in a spacetime with a perfectly reflecting plane boundary and calculate both the velocity and position dispersions of the test particle. Our results show that the dispersions in the normal direction are weakened while those in the parallel directions are strengthened as compared to the classical static case when the test particle classically moves away from the boundary. However, if the classical motion reverses its direction, then the dispersions in the normal direction are reinforced while those in the parallel directions get weakened.
文摘We believe that well-known principles and relationships between physical entities are the key for a deep knowledge of reality. However, they must be applied using innovative points of view, points of view that can be provided by, for example, experts on information theory （as we are）. Our previous efforts in this direction led to a fascinating result： the theoretical total mass ofa spacetime in which Planck＇s length is an observer-independent scale of length is equal （both in expression and value） to the mass of our portion of Universe measured by national aeronautics and space administration wilkinson microwave anisotropy probe （NASA WMAP） spacecraft. In the following paragraphs we＇ll show how granularity （i.e., discontinuity） of physical entities of our portion of observable spacetime descends directly from the principles of information theory, and how a physical theory about the discontinuity of reality built on these basis can lead to an elegant descriptions of both microcosm and macrocosm.
文摘In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.
文摘The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.
基金supported by National Natural Science Foundation of China (Grant No. 11371330)
文摘We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kahler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly KahlerS3 × S3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function A, such that g（（△↓h）（v, v, v）, Jr） = λ holds for all unit tangent vector v.
