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Nonequilibrium Brownian dynamics in periodic energy landscapes
Paidar, Jaroslav ; Ryabov, Artem (advisor) ; Žonda, Martin (referee)
The collective dynamics of Brownian particles in porous structures is an important topic for both theory and experiment. A good understanding of Brownian dynamics of interacting particles moving in one dimension has recently been achieved in several models. The theoretical description of these models focuses on infinitely large systems, although real systems are in usually small. This thesis studies the effect of the size of a system of interacting particles driven by a force on their transport behavior in a periodic potential. We have used simulations of a single-particle model with analytically solvable results as reference data. For this model, simulations were performed using the Euler- Maruyama method. Multi-particle simulations were performed for two different types of particle interactions. The rigid-ball type interaction served as the basis for the analysis of behavior of a smoothed-barrier type interaction potential case that allowed for the particles to pass through each other. The particle velocity and diffusion coefficient were studied as a function of various system parameters such as particle softness, size, and density or system size. 1
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Work and heat at the mesoscale
Pajger, Šimon ; Ryabov, Artem (advisor) ; Kolář, Michal (referee)
Title: Work and heat at the mesoscale Author: Bc. Šimon Pajger Department: Department of Macromolecular Physics Supervisor: RNDr. Artem Ryabov, Ph.D., KMF MFF UK Abstract: Understanding the conversion between heat and work by heat engines led to the discoveries of entropy and to the formulation of the Second law of clas- sical macroscopic thermodynamics. At the microscale and mesoscale, quantum coherences are a potential resource for various quantum processes. Quantum coherences can be used to enhance the performance of various devices beyond the limits demanded by classical physics. Recently many models have been es- tablished clarifying how coherences affect the speed and irreversibility of ther- modynamic processes and raising the question of what experimentally relevant consequences various generalizations of the formalism of classical thermodynam- ics to the microscopic level may have. Here we study a few of these models in great detail. Specifically, we discuss fluctuations of coherence-enhanced heat currents, propose a model of a heat engine that does work while being in a steady state, and derive a condition on the rate of decoherence that specifies, when coherence-enhanced currents provide a significant advantage over the case without any coherence. Then we discuss coherence-inducing heat bath...
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Entropy production in periodically driven systems
Jankola, Marek ; Ryabov, Artem (advisor) ; Novotný, Tomáš (referee)
Thermodynamic uncertainty relations (TURs) interrelate dynamical quantities, like the rate of current and its fluctuations, and the entropy production. They are well established for several thermodynamically consistent time-homogeneous Markov processes such as the overdamped Brownian motion in a tilted periodic potential (TP). However, for processes subjected to time-dependent external driving, the general framework for such relations is unknown. Here we focus on a class of periodically driven systems, whose dynamics can be mapped onto the ones of time-homogeneous Markov processes. We leverage this mapping to derive the entropy production for the overdamped Brownian motion in a travelling-wave potential (TW), which yields an inverse TUR, i.e., the upper bound on the entropy production. This bound is given by the rate of current and the dispersion coefficient, which are experimentally observable quantities. The inverse TUR delivers bounds on kinetic efficiency of a transport of particles by TW potential, such as the recently demonstrated experiments with an optical conveyor belt (OCB). The measured values of the resulting speed of submicrometer-sized colloidal particle, when subjected to transport by OCB moving at certain speeds, match our results. Additionally, using the inverse TUR, we analyse the bounds...
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Collective dynamics of Brownian particles in heterogeneous media
Voráč, David ; Ryabov, Artem (advisor) ; Allolio, Christoph (referee)
Non-equilibrium transport processes in confined geometries are of fundamental impor- tance in nature and engineering. In non-equilibrium statistical mechanics, models of such systems play a crucial role in our understanding of non-equilibrium steady states. Here we implement a recently introduced model, the Brownian asymmetric simple exclusion process, and discuss several of its unexplored properties. In jammed systems, particle currents are mediated via collective thermal excitation, rare events whose description can be quite involved. We approach them for crowded systems of hard spheres in peri- odic potential and derive generation rates together with their surprisingly high velocities. Eventually, we discuss an apparent jamming transition observable in the crowded system. Further, we investigate the transport properties of polydisperse hard-sphere mixtures in the periodic potential. We comment on and explain a link between a monodisperse re- current pattern of the current and patterns found in binary and ternary mixtures. We show a detrimental effect of size variance on the particle current. Lastly, we approximate currents for weak driving forces by applying density functional theory to the density func- tional of a polydisperse system and report the unsatisfactory results. The findings are also...
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Evaporation of simple and complex fluids at different surface wettability
Májek, Juraj ; Ryabov, Artem (advisor) ; Procházka, Marek (referee)
In this work, we investigate the evaporation dynamics of sessile droplets in two scenarios: (i) droplets evaporating on Teflon plasma polymer coated sur- faces, exhibiting anomalously long evaporation lifetime for their size, (ii) drying droplets with liposome suspensions that gradually spread while evaporating. (i) By observing water droplets evaporating on a silicon wafer coated with a Teflon thin film, we discover that the water disintegrates and penetrates the Teflon film. The droplets hide some of their volume underneath, which then does not evaporate. This leads to anomalously long evaporation times. We attribute this effect to structural instability of the Teflon layer, stemming from the contact of non-polar Teflon and polar SiO2. By using Teflon surfaces at most week old, this effect can be prevented. We further identify and describe typical features of the penetration, allowing for its early detection. (ii) We measure the spreading of liposome-laden droplets and find an increase of radius up to 30% of the initial value. During the increase, the droplet contact line spreads in bursts, or protrusions, not uniformly. Existing literature shows that liposomes adsorb on both the air/water and the water/surface interface and reduce the corresponding surface tensions γgl and γsl. We find that when the...
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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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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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Entropy production and irreversibility in transition state theory
Pajger, Šimon ; Ryabov, Artem (advisor) ; Novotný, Tomáš (referee)
Title: Entropy production and irreversibility in transition state theory Author: Šimon Pajger Department: Department of Macromolecular Physics Supervisor: RNDr. Artem Ryabov, Ph.D., Department of Macromolecular Physics Abstract: Modern experiments focusing on durations of nonequilibrium transi- tions provide valuable information on the underlying microscopic kinetics. Theo- retically, outcomes of such experiments are well understood for time-independent free energy landscapes only. Amongst the most fundamental results in this area belongs an identity of distributions of times of forward and backward transitions between arbitrary two points of a free energy landscape. However, recently it has been experimentally found, that this identity can be broken by an action of external time-dependent force. In the thesis, we explore this situation theo- retically and discuss under which conditions the identity of distributions can be restored. To this end, we introduce distributions of transition times weighted by the entropy production. In particular, we show that it is possible to find weight for each trajectory, such that weighted distributions of transition times resulting from such weights are identical. Assuming an external harmonic time-dependent force, we discuss two experimentally relevant situations. First,...
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