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Transcription of genetic information
Ryabov, Artem
Title: Transcription of genetic information Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: doc. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Supervisor's e-mail address: Petr.Chvosta@mff.cuni.cz Abstract: We investigate a one-dimensional diffusive motion of a system of interacting Brownian particles driven by an external time-dependent force. We assume the hard-core interaction between the particles. We construct the exact general solution of the N-particle problem. Specifically, we assume the spatially restricted two-particles dynamics, and the harmonically oscillating driving force. The inter-particle interaction induces effective entropic forces and hence also new effects comparing to the corresponding model without the inter- particle interaction. Especially, we have found an increase (decrease) of the work done on the right (left) particle. Similar effects are exhibited by the one-particle mean position, the one-particle entropy production, and heat released to the bath. These characteristics have been discussed depending on the model parameters. Resonance-like maxima have been detected if we plot the work accepted by the individual particles as the function of the driving frequency. Similarly, the entropy production exhibits a maximum as the...
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Symmetries of transition times in complex biophysical systems
Voráč, David ; Ryabov, Artem (advisor) ; Chvosta, Petr (referee)
Conformational changes of biomolecules can be described as Markov processes on net- works of discrete states representing minima of free energy landscapes. Network states for several types of membrane proteins and molecular motors are linked into cycles, and their reaction coordinates (represented by a "particle") jump between the cycle states predominantly in one direction with rare backward jumps occurring due to thermal fluc- tuations. Assuming that interactions of the particle with other degrees of freedom (other particles) cannot be neglected, we study times that it takes to complete one cycle. In par- ticular, we compare mean times of cycle completion in and against the bias direction and show that they satisfy the universal inequality: Cycle-completion times in bias direction are never shorter than the ones against the bias. We discuss how the times depend on the interaction strength, cycle topology, quenched disorder, number of interacting par- ticles, and check validity of our findings for two-dimensional models with canonical and grand-canonical particle reservoirs.
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Stochastic dynamics and thermodynamics in nonequilibrium steady states
Berestneva, Ekaterina ; Ryabov, Artem (advisor) ; Novotný, Tomáš (referee)
In this thesis we study two stochastic models related to operation of a molecular mo- tor. The first is a Brownian particle moving under the action of the highly unstable potential. It can describe fast processes related to individual steps of the motor. We study statistics of trajectories that by chance avoid the unstable region and do not diverge up to a long time. Conditioning on nondivergence gives rise to an effective force, which keeps the particles in the stable area of the potential. We present two stationary distributions which formally resemble the Gibbs canonical distribution with effective potentials and derive asymptotic behaviors of these potentials. The se- cond is the minimal discrete model of the Feynman-Smoluchowski ratchet coupled to two thermal reservoirs. We investigate stationary values of the average steady state currents, activities, and motor efficiency. For the ratchet we construct the driven processes representing mean quantities conditioned on fluctuations of entropy production and show how the entropy production affects mean probability currents and activity. 1
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Fractal growth of polyethylene nanoislands on polyethylene oxide thin films
Májek, Juraj ; Ryabov, Artem (advisor) ; Kylián, Ondřej (referee)
Plasma polymer fragments deposited from vapor on non-wetting polymer substrates are seen to aggregate into fractal nanoislands. Dependent on conditions of the experiment, the islands attain diverse shapes ranging from dendritic snowflakes, branching seaweed to twisting snakes. In our work, we identify dominant kinetic processes responsible for this diversity and relate them to physical characteristics of the experiment. We review and implement basic computer models of deposition and ag- gregation of diffusing particles: The Diffusion-Limited Aggregation (DLA), both on a lattice and without a lattice, and the Cluster-Cluster Aggregation (CCA). The off-lattice DLA yields isotropic random fractals. The lattice DLA fractals are influenced by the properties of the lattice itself, which can be chosen to represent the symmetry of the substrate layer on which the islands grow. Fractals generated in the CCA model are more linear. Com- petition between diffusion and deposition rates gives a transition between off-lattice DLA and CCA fractals. Each of these models comprises a mechanism that we conjecture to be dominant during growth of distinct observed polyethylene nanoislands. Thus the multiple observed fractal shapes allow us to draw conclusions on micro- scopic kinetics of the surface diffusion of deposited...
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Anomalous heat response in nonequilibrium stochastic models
Miřátský, Václav ; Netočný, Karel (advisor) ; Ryabov, Artem (referee)
The bachelor thesis deals with heat capacity generalization to systems in non-equilibrium steady states. The non-equilibrium state is kept by contact with many baths and by action of non-potential forces. Evolution of system is understood to be a Markovian process described in the first part of this thesis. After that the concept of reversible heat is presented and heat capacity matrix is introduced. Following chapter deals with the usage of heat capacity matrix for analysation of two-level model in contact with two baths. At the end the built formalism is used for describtion of transport of fermions through a quantum dot. 1
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Brownian motion in logarithmic potential
Berestneva, Ekaterina ; Ryabov, Artem (advisor) ; Chvosta, Petr (referee)
In this thesis we study first-passage properties of a Brownian particle diffusing under the action of logarithmic potential field U(x, t) = g(t) log(x). The main part of this thesis is de- voted to the case of time-dependent potential strength g(t). To obtain the corresponding survival probability, one may try to solve the Fokker-Planck equation. However, its exact solution for the time-dependent potential is yet unknown. In this work we propose a simple asymptotic theory which yields the long-time behaviour of the survival probability and the moments of the particle position. The survival probability exhibits a rather varied behaviour for different functions g(t). We identify three regimes of asymptotic decay: the regular regime, the marginal regime and the regime of enhanced absorption. We also address the question of how will the derived first-passage properties of Brownian motion change when the absorbing boundary is not exactly at the origin. 1
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Carnot efficiency revisited
Klimovič, Filip ; Holubec, Viktor (advisor) ; Ryabov, Artem (referee)
We introduce a simple discrete model of a molecular heat engine. The engine's dynamics is strongly influenced by thermal motion of ambient molecules. Thermodynamic quantities of heat and work observed at mesoscopic scale are thus fluctuating. We focus on the efficiency of the engine, which fluctuates as well. We use analytic methods as well as Monte Carlo simulations in order to examine probability distribution of quantities mentioned above. Exact analytic solution is found in case of short trajectories, while large deviation theory is exploited for long ones. Our interest in the efficiencies' definition is no less than in its values. Properties of the large deviation function stated in literature are demonstrated within the results. Meanwhile we show an example of an engine, where the properties regarded as general are not applied. Powered by TCPDF (www.tcpdf.org)
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Thermodynamics of interacting brownian particles
Herčík, Michal ; Chvosta, Petr (advisor) ; Ryabov, Artem (referee)
The thesis comprises single-file diffusion in an external time-dependent potential, the diffusion of particles in narrow channel where particles can not pass each other. We discuss the role of order statistics solving the dynamics of the particles. We focus on application of perturbation theory on Fokker- Planck equation for the combined stochastic process of position and work. The calculation of the first and second moment of work for a set of particles analytically. The comparison of these results with results based on computer simulations of trajectories. Computer simulation of marginal PDF of work for left and right particle and simultaneous PDF for a set of two external driven particles. Powered by TCPDF (www.tcpdf.org)
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Stochastic dynamics and energetics of biomolecular systems
Ryabov, Artem ; Chvosta, Petr (advisor) ; Novotný, Tomáš (referee) ; Papáček, Štěpán (referee)
Title: Stochastic dynamics and energetics of biomolecular systems Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis comprises exactly solvable models from non-equilibrium statistical physics. First, we focus on a single-file diffusion, the diffusion of particles in narrow channel where particles cannot pass each other. After a brief review, we discuss open single-file systems with absorbing boundaries. Emphasis is put on an interplay of absorption process at the boundaries and inter-particle entropic repulsion and how these two aspects affect the dynam- ics of a given tagged particle. A starting point of the discussions is the exact distribution for the particle displacement derived by order-statistics argu- ments. The second part of the thesis is devoted to stochastic thermodynam- ics. In particular, we present an exactly solvable model, which describes a Brownian particle diffusing in a time-dependent anharmonic potential. The potential has a harmonic component with a time-dependent force constant and a time-independent repulsive logarithmic barrier at the origin. For a particular choice of the driving protocol, the exact work characteristic func- tion is obtained. An asymptotic analysis of...
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Transcription of genetic information
Ryabov, Artem
Title: Transcription of genetic information Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: doc. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Supervisor's e-mail address: Petr.Chvosta@mff.cuni.cz Abstract: We investigate a one-dimensional diffusive motion of a system of interacting Brownian particles driven by an external time-dependent force. We assume the hard-core interaction between the particles. We construct the exact general solution of the N-particle problem. Specifically, we assume the spatially restricted two-particles dynamics, and the harmonically oscillating driving force. The inter-particle interaction induces effective entropic forces and hence also new effects comparing to the corresponding model without the inter- particle interaction. Especially, we have found an increase (decrease) of the work done on the right (left) particle. Similar effects are exhibited by the one-particle mean position, the one-particle entropy production, and heat released to the bath. These characteristics have been discussed depending on the model parameters. Resonance-like maxima have been detected if we plot the work accepted by the individual particles as the function of the driving frequency. Similarly, the entropy production exhibits a maximum as the...
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