Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

Directed transport of two interacting particles in a washboard potential

We study the conservative and deterministic dynamics of two nonlinearly interacting particles evolving in a one-dimensional spatially periodic washboard potential. A weak tilt of the washboard potential is applied biasing one direction for particle transport. However, the tilt vanishes asymptotically in the direction of bias. Moreover, the total energy content is not enough for both particles to be able to escape simultaneously from an initial potential well; to achieve transport the coupled particles need to interact cooperatively. For low coupling strength the two particles remain trapped inside the starting potential well permanently. For increased coupling strength there exists a regime in which one of the particles transfers the majority of its energy to the other one, as a consequence of which the latter escapes from the potential well and the bond between them breaks. Finally, for suitably large couplings, coordinated energy exchange between the particles allows them to achieve escapes -- one particle followed by the other -- from consecutive potential wells resulting in directed collective motion. The key mechanism of transport rectification is based on the asymptotically vanishing tilt causing a symmetry breaking of the non-chaotic fraction of the dynamics in the mixed phase space. That is, after a chaotic transient, only at one of the boundaries of the chaotic layer do resonance islands appear. The settling of trajectories in the ballistic channels associated with transporting islands provides long-range directed transport dynamics of the escaping dimer

Universal properties of distorted Kerr-Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.Comment: 7 page

Nonlinear response of a linear chain to weak driving

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with suitably chosen frequency suffices to accomplish speedy escape. The latter requires the passage through a transition state the formation of which is triggered by permanent feeding of energy from a phonon background into humps of localised energy and elastic interaction of the arising breather solutions. In fact, cooperativity between the units of the chain entailing coordinated energy transfer is shown to be crucial for enhancing the rate of escape in an extremely effective and low-energy cost way where the effect of entropic localisation and breather coalescence conspire

Nonlinear charge transport mechanism in periodic and disordered DNA

We study a model for polaron-like charge transport mechanism along DNA molecules with emphasis on the impact of parametrical and structural disorder. Our model Hamiltonian takes into account the coupling of the charge carrier to two different kind of modes representing fluctuating twist motions of the base pairs and H-bond distortions within the double helix structure of $\lambda-$DNA. Localized stationary states are constructed with the help of a nonlinear map approach for a periodic double helix and in the presence of intrinsic static parametrical and/or structural disorder reflecting the impact of ambient solvent coordinates. It is demonstrated that charge transport is mediated by moving polarons respectively breather compounds carrying not only the charge but causing also local temporal deformations of the helix structure through the traveling torsion and bond breather components illustrating the interplay of structure and function in biomolecules.Comment: 23 pages, 13 figure

Charge transport in a nonlinear, three--dimensional DNA model with disorder

We study the transport of charge due to polarons in a model of DNA which takes in account its 3D structure and the coupling of the electron wave function with the H--bond distortions and the twist motions of the base pairs. Perturbations of the ground states lead to moving polarons which travel long distances. The influence of parametric and structural disorder, due to the impact of the ambient, is considered, showing that the moving polarons survive to a certain degree of disorder. Comparison of the linear and tail analysis and the numerical results makes possible to obtain further information on the moving polaron properties.Comment: 9 pages, 2 figures. Proceedings of the conference on "Localization and energy transfer in nonlinear systems", June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. To be publishe

Emergence of continual directed flow in Hamiltonian systems

We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven Hamiltonian systems with mixed phase space where transport is determined by intermittent behaviour exhibiting power-law decay statistics of the duration of regular ballistic periods

Batch Bayesian Optimization via Local Penalization

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These facilities could be computational or physical facets of the process being optimized. E.g. in biological experiments many experimental set ups allow several samples to be simultaneously processed. Batch methods, however, require modeling of the interaction between the evaluations in the batch, which can be expensive in complex scenarios. We investigate a simple heuristic based on an estimate of the Lipschitz constant that captures the most important aspect of this interaction (i.e. local repulsion) at negligible computational overhead. The resulting algorithm compares well, in running time, with much more elaborate alternatives. The approach assumes that the function of interest, $f$, is a Lipschitz continuous function. A wrap-loop around the acquisition function is used to collect batches of points of certain size minimizing the non-parallelizable computational effort. The speed-up of our method with respect to previous approaches is significant in a set of computationally expensive experiments.Comment: 11 pages, 10 figure

Modeling the thermal evolution of enzyme-created bubbles in DNA

The formation of bubbles in nucleic acids (NAs) are fundamental in many biological processes such as DNA replication, recombination, telomeres formation, nucleotide excision repair, as well as RNA transcription and splicing. These precesses are carried out by assembled complexes with enzymes that separate selected regions of NAs. Within the frame of a nonlinear dynamics approach we model the structure of the DNA duplex by a nonlinear network of coupled oscillators. We show that in fact from certain local structural distortions there originate oscillating localized patterns, that is radial and torsional breathers, which are associated with localized H-bond deformations, being reminiscent of the replication bubble. We further study the temperature dependence of these oscillating bubbles. To this aim the underlying nonlinear oscillator network of the DNA duplex is brought in contact with a heat bath using the Nos$\rm{\acute{e}}$-Hoover-method. Special attention is paid to the stability of the oscillating bubbles under the imposed thermal perturbations. It is demonstrated that the radial and torsional breathers, sustain the impact of thermal perturbations even at temperatures as high as room temperature. Generally, for nonzero temperature the H-bond breathers move coherently along the double chain whereas at T=0 standing radial and torsional breathers result.Comment: 19 pages, 7 figure