Loop exponent in DNA bubble dynamics

Dynamics of DNA bubbles are of interest for both statistical physics and biology. We present exact solutions to the Fokker-Planck equation governing bubble dynamics in the presence of a long-range entropic interaction. The complete meeting time and meeting position probability distributions are derived from the solutions. Probability distribution functions reflect the value of the loop exponent of the entropic interaction. Our results extend previous results which concentrated mainly on the tails of the probability distribution functions and open a way to determining the strength of the entropic interaction experimentally which has been a matter of recent discussions. Using numerical integration, we also discuss the influence of the finite size of a DNA chain on the bubble dynamics. Analogous results are obtained also for the case of subdiffusive dynamics of a DNA bubble in a heteropolymer, revealing highly universal asymptotics of meeting time and position probability functions.Comment: 24 pages, 11 figures, text identical to the published version; v3 - updated Ref. [47] and corrected Eqs. (3.6) and (3.10

Protein–DNA electrostatics

Gene expression and regulation rely on an apparently finely tuned set of reactions between some proteins and DNA. Such DNA-binding proteins have to find specific sequences on very long DNA molecules and they mostly do so in the absence of any active process. It has been rapidly recognized that, to achieve this task, these proteins should be efficient at both searching (i.e., sampling fast relevant parts of DNA) and finding (i.e., recognizing the specific site). A two-mode search and variants of it have been suggested since the 1970s to explain either a fast search or an efficient recognition. Combining these two properties at a phenomenological level is, however, more difficult as they appear to have antagonist roles. To overcome this difficulty, one may simply need to drop the dichotomic view inherent to the two-mode search and look more thoroughly at the set of interactions between DNA-binding proteins and a given DNA segment either specific or nonspecific. This chapter demonstrates that, in doing so in a very generic way, one may indeed find a potential reconciliation between a fast search and an efficient recognition. Although a lot remains to be done, this could be the time for a change of paradigm

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Non-ergodic phenomena in many-body quantum systems

The assumption of ergodicity is the cornerstone of conventional thermodynamics, connecting the equilibrium properties of macroscopic systems to the chaotic nature of the underlying microscopic dynamics, which eventuates in thermalization and the scrambling of information contained in any generic initial condition. The modern understanding of ergodicity in a quantum mechanical framework is encapsulated in the so-called eigenstate thermalization hypothesis, which asserts that thermalization of an isolated quantum system is a manifestation of the random-like character of individual eigenstates in the bulk of the spectrum of the system's Hamiltonian. In this work, we consider two major exceptions to the rule of generic thermalization in interacting many-body quantum systems: many-body localization, and quantum spin glasses. In the first part, we debate the possibility of localization in a system endowed with a non-Abelian symmetry. We show that, in line with proposed theoretical arguments, such a system is probably delocalized in the thermodynamic limit, but the ergodization length scale is anomalously large, explaining the non-ergodic behavior observed in previous experimental and numerical works. A crucial feature of this system is the quasi-tensor-network nature of its eigenstates, which is dictated by the presence of nontrivial symmetry multiplets. As a consequence, ergodicity may only be restored by extensively large cascades of resonating spins, explaining the system's resistance to delocalization. In the second part, we study the effects of non-ergodic behavior in glassy systems in relation to the possibility of speeding up classical algorithms via quantum resources, namely tunneling across tall free energy barriers. First, we define a pseudo-tunneling event in classical diffusion Monte Carlo (DMC) and characterize the corresponding tunneling rate. Our findings suggest that DMC is very efficient at tunneling in stoquastic problems even in the presence of frustrated couplings, asymptotically outperforming incoherent quantum tunneling. We also analyze in detail the impact of importance sampling, finding that it does not alter the scaling. Next, we study the so-called population transfer (PT) algorithm applied to the problem of energy matching in combinatorial problems. After summarizing some known results on a simpler model, we take the quantum random energy model as a testbed for a thorough, model-agnostic numerical characterization of the algorithm, including parameter setting and quality assessment. From the accessible system sizes, we observe no meaningful asymptotic speedup, but argue in favor of a better performance in more realistic energy landscapes

Kinetics of Brownian Transport

The rate of progress of Brownian processes is not easily quantifiable. An importantmeasure of the ”speed” of Brownian motion is themean first-passage time (FPT) to a given distance. FPTs exist in various flavours including exit- and transition-path times, which, for instance, can be used to quantify the length of reaction paths in folding transitions inmolecules such as DNA. Due to their inherently stochastic nature, measurements of any FPTs require repeated experiments under controlled conditions. In my thesis, I systematically explore FPTs in various contexts using a custom-built automated holographic optical tweezers (HOT) setup. More precisely, I investigate transition- and exit-path-time symmetries in equilibrium systems and demonstrate the breakdown of the symmetry in out-of-equilibriumsystems. Experimental data from folding DNA-hairpins show that the principles established on the mesoscale extend well into the molecular regime. In Kramers escape problem, the reciprocal of the escape rate corresponds to the time of first-passage to leave the initial state. A lower bound for the achievable FPT, e.g. of the reaction coordinate of a folding molecule, therefore corresponds to a speed-limit of the ensemble reaction rate. Using my setup, I show that certain barrier shapes can substantially lower the escape time across the barrier without changing the overall energy balance. This result has deep implications for reaction kinetics, e.g. in protein folding. Furthermore, I investigate the role of entropic forces in Brownian transport, show that hydrodynamic drag plays a crucial role in Brownian motion in confined systems, and give an experimental realisation of Fick-Jacobs theory. The thermodynamic applications of HOTs considered here necessitate the creation of fine-tuned optical landscapes, which requires precise phase-retrieval to compute the necessary holograms. In order to address this problem, I explore novel algorithms based on deep conditional generative models and test whether such models can assist in finding holograms for a given desired light distribution. I compare several differentmodels, including conditional generative-adversarial networks and conditional variational autoencoders, which are trained on data sets sampled on the HOT setup. Furthermore, I propose a novel forward-loss-minimising architecture and demonstrate its excellent performance on both validation and artificially-created test data sets.European Training Network (ETN) Grant No. 674979-NANOTRANS Winton Programme for the Physics of Sustainabilit

Three dimensional magnetohydrodynamics of fusion plasmas

The primary aim of the research on nuclear fusion is to obtain a new energy source to help satisfying a growing and sustainable consumption. This objective has to be reached through scientific research, both from the physics point of view and through the demonstration of the technological feasibility of a nuclear fusion reactor. The option on which the major efforts of the international community are focused is to obtain controlled nuclear fusion using a magnetic field to confine a plasma formed by deuterium and tritium, in a vacuum chamber of toroidal shape. The most promising magnetic configuration is the so called tokamak configuration. The scientific community aims at addressing the remaining problems connected with physics performing the experiment ITER (International Thermonuclear Experimental Reactor) and to verify the technological feasibility of a nuclear fusion reactor with the DEMO experiment. An important part of the scientific efforts is addressed to the study of configurations alternative to the tokamak, like the stellarator and the reversed-field pinch (RFP). These configurations achieve three dimensional helical states: in the RFP a global helical state is obtained spontaneously, due to the presence of a strong current flowing in the plasma, while currents flowing in external helically shaped coils generate a global helical state in the stellarator. Helical states can be obtained also in the tokamak configuration, for instance due to the presence of external magnetic field perturbations. The research activity of my PhD focuses on the study of the 3D nonlinear magnetohydrodynamics model applied to the numerical study of the RFP and tokamak helical configurations. The main aim of my research is the characterization, under three different aspects later described, of the three dimensional helical states. These states are presently believed to provide possible scenarios for reducing dangerous MHD activity for both RFP (magnetic chaos transport reduction) and tokamak (sawtooth mitigation, disruption avoidance). The research activity included the development and the exploitation of advanced numerical tools to deal with the numerical solution of the 3D nonlinear MHD model, while the interaction with the experimental environment provided the opportunity to develop tools for model-experiment comparison (validation) and benchmarking of numerical tools (verification). The results obtained during my PhD provide a further step towards a predictive capability of the employed modelling tools. In fact, the boundary conditions are proved to be a key ingredient in bringing the comparison of MHD simulations with the experiment at a quantitative level. Moreover it recently inspired a successful and promising experimental activity in RFX-mod, the biggest RFP experiment in the world, located in Padova. My PhD research activity and results can be divided into three main areas. The first is the dynamical simulation of a magnetically confined plasma through numerical solution of the 3D nonlinear visco-resistive MHD model. The second area of research consists in the topological study of the magnetic field configurations obtained from MHD simulations. The third area is the study of transport due to magnetic stochasticity in both tokamak and RFP states, with data coming from MHD simulations, gyrokinetics simulations and experimental results. The first area of research deals with the simulation of the dynamical properties of a magnetically confined plasma, performed using the 3D nonlinear MHD codes SPECYL and PIXIE3D. The most important achievement is represented by the level of agreement between MHD simulation and experimental dynamics of the RFP, a degree of agreement obtained in simulations where, for the first time, a helical boundary condition is applied. It is also demonstrated that by imposing a finite helical radial magnetic field at the edge it is possible to induce a global helical regime with the chosen helicity. As for the tokamak configuration the study of helical boundary conditions shows that they can favour a steady helical equilibrium, thus mitigating the sawtooth dynamics typically detrimental for the confinement. This area of research leads to a unifying vision for the RFP and the tokamak, as the use of helical boundary condition for the magnetic field seems to allow the easier establishment of a helical equilibrium in both configurations, with interesting properties for the configurations. The second area of research is centred on the topological study of the magnetic configurations obtained from the MHD simulations of the RFP. The separatrix expulsion of the dominant helical mode has been studied analyzing the magnetic field topology with the field line tracing code N EMATO. Two so called paradigmatic cases, characterized by a simplified MHD dynamics, have been analyzed. In the first one it was shown that the dominant mode separatrix expulsion can reduce the level of magnetic field lines stochasticity remarkably, in the second case an “exotic” (before these studies) dynamics was considered, i.e. the development of a helical equilibrium from a non-resonant mode. These results confirmed older studies that placed separatrix expulsion in direct connection with helical RFP states obtained in RFX-mod, which develop internal transport barriers observed as electronic temperature steep gradients. Furthermore it showed that the helical equilibrium based on a non-resonant mode can result in particularly strong magnetic order. The favourable properties found led to the proposal to experimentally drive QSH states built upon non-resonant MHD modes in the RFX-mod experiment: these states were successfully produced in the experiment, and the study of thermal properties is presently ongoing. Topological studies on more realistic cases coming from MHD simulations that show a quantitative agreements with the standard operation of the RFX-mod experiment are also tackled in this thesis. The results obtained underline the importance of the spectrum of secondary perturbations to the helical equilibrium. The third area of research focuses on the consequences of transport produced by the presence of magnetic stochasticity. Two specific cases relevant for the RFP and the tokamak are considered: the magnetic chaos produced by microtearing activity at the electron internal transport barrier in the RFP, and the case of edge magnetic stochasticity due to the action of edge helical magnetic perturbations in the tokamak. The tools to study transport were developed and used to calculate the energy diffusion coefficient and other meaningful quantities. Such tools are now available for further and more general applications. On a numerical ground two important activities were performed during the PhD. The parallelization of the field line tracing code NEMATO, during one month mobility at Oak Ridge National Laboratory, was fundamental for the speeding up of the research activity. The numerical verification of NEMATO and ORBIT was also performed. The verification gave a positive result, showing a satisfactory agreement, both qualitative and quantitative, on the features of the magnetic field topology in the RFP configuration

Speeding up the first-passage for subdiffusion by introducing a finite potential barrier

We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation