exactly the canonical measure restricted on a submanifold, using a Metropolis-Hastings correction in the spirit of the Generalized Hybrid Monte Carlo (GHMC) algorithm. Moreover, we obtain, in some ...limiting regime, a consistent discretization of the overdamped Langevin (Brownian) dynamics on a submanifold, also sampling exactly the correct canonical measure with constraints. (ii) For free energy computation using thermodynamic integration, we rigorously prove that the longtime average of the Lagrange multipliers of the constrained Langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints. A second order time discretization using the Lagrange multipliers is proposed. (iii) The Jarzynski-Crooks fluctuation relation is proved for Langevin processes with mechanical constraints evolving in time. An original numerical discretization without time discretization error is proposed, and its overdamped limit is studied. Numerical illustrations are provided for (ii) and (iii).>
In this paper, we study Jarzynski’s equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, ...we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski’s equality.
Analyzing the behavior of semiflexible polymers experiencing hydrodynamic forces is an important step toward a better understanding of polymer dynamics in microfluidic applications as well as in ...living cells. In particular, studying conformational changes of fluorescently labeled, semiflexible actin filaments in flow fields of spatially varying flow strength will significantly contribute to this goal. The experimental situation is realized in flows through structured microchannels with alternating high‐ and low‐velocity segments. While entering the wider channel segments, the semiflexible filaments undergo a buckling transition under compression whereas they are stretched with a suppression of thermal fluctuations in the extensional regime when reentering the narrow segments. The nature of these nonequilibrium and nonstationary conformational transitions is characterized by analyzing the evolution of the end‐to‐end distances, center‐of‐mass velocities, and bending energies along the passage of the filaments through the channels.
The presented studies elucidate the non‐Newtonian flow behavior of semiflexible filaments in specific microflows and therefore may have an impact on the analysis as well as sorting of polymers, which may consequently lead to a better understanding of intercellular flows.
Resilience-based frameworks, founded upon the existence of multiple attractors and regime shifts, have long been applied to complex dynamics of semiarid systems. Utilizing seed addition tests in ...experimental plantings along grazing gradients, we applied an increase-when-rare criterion to identify bidirectional (states can invade each other) and directional (only one state can invade) transitions among vegetation states characteristic of California grasslands over five years. Annual forage and medusahead grasslands were able to invade each other at all grazing intensities, indicating coexistence. Directional transitions involving invasion of native bunchgrass by other species occurred as grazing intensity increased; recovery (transitions to natives) did not occur at low grazing. While directional transitions at some grazing intensities were accompanied by state persistence at others, we found little evidence for persistence of alternative states at any grazing intensity. Our results suggest that grazing can affect resilience by causing hard-to-reverse transitions, but rarely produces alternative states. However, variation in precipitation seems to dominate grazing responses, supporting the applicability of the nonequilibrium concept in our study system.
We suggest a microscopic model describing the nonlocal ac response of a pair of Majorana states in fermionic superfluids beyond the tunneling approximation. The time-dependent perturbations of ...quasiparticle transport are shown to excite finite period beating of the wavefunction between the distant Majorana states. We propose an experimental test to measure the characteristic time scales of quasiparticle transport through the pair of Majorana states defining, thus, quantitative characteristics of nonlocality known to be a generic feature of Majorana particles.
Probing Nonexponential Decay in Floquet–Bloch Bands Cao, Alec; Fujiwara, Cora J.; Sajjad, Roshan ...
Zeitschrift für Naturforschung. A, A journal of physical sciences,
05/2020, Volume:
75, Issue:
5
Journal Article
Peer reviewed
Open access
Exponential decay laws describe systems ranging from unstable nuclei to fluorescent molecules, in which the probability of jumping to a lower-energy state in any given time interval is static and ...history-independent. These decays, involving only a metastable state and fluctuations of the quantum vacuum, are the most fundamental nonequilibrium process and provide a microscopic model for the origins of irreversibility. Despite the fact that the apparently universal exponential decay law has been precisely tested in a variety of physical systems, it is a surprising truth that quantum mechanics requires that spontaneous decay processes have nonexponential time dependence at both very short and very long times. Cold-atom experiments have proven to be powerful probes of fundamental decay processes; in this article, we propose the use of Bose condensates in Floquet–Bloch bands as a probe of long-time nonexponential decay in single isolated emitters. We identify a range of parameters that should enable observation of long-time deviations and experimentally demonstrate a key element of the scheme: tunable decay between quasi-energy bands in a driven optical lattice.
Aim
To identify the effect of multiple, temporally close, forcing events (i.e. climate‐driven habitat fragmentations/homogenizations) in shaping current patterns of biodiversity in alpine areas. ...Given their spatial configuration, alpine areas have been traditionally seen as islands surrounded by an “ocean” of unsuitable lands. A quantitative assessment of the effects of Holocene climate fluctuations on islands area and inter‐island connectivity is crucial to finely reconstruct past biodiversity dynamics and forecast species responses to future changes.
Location
Italy.
Taxa
Carabidae (Ground beetles), Chrysomelidae (Leaf beetles), Elateridae (Click beetles), Orthoptera (Grasshoppers and Crickets) and Papilionoidea (Butterflies and Skippers).
Methods
A total of 1,077 species for 128,093 records were analysed and a classification based on their functional traits allowed identifying groups of good and poor dispersers within each taxon. A dynamic discrete model of ecosystem evolution provided the spatio‐temporal context to test two competing (transient equilibria vs. nonequilibrium) dynamics based on different colonization capabilities. In the transient equilibria dynamic the species are able to respond to island evolution through successful dispersal and colonization events, whereas in the nonequilibrium dynamic ineffective immigration constrains the current species richness to that generated by the strongest island contraction.
Results
With the exception of Elateridae, good dispersers (Chrysomelidae and Papilionoidea) responded to environmental changes by establishing a series of transient equilibria. In contrast, the nonequilibrium dynamic better described patterns of species richness in poor dispersers (Carabidae and Orthoptera).
Main conclusions
Our approach could be used as the basis for the development of spatially and temporally explicit models of island evolution and could be a valuable tool for quantifying the sensitivity of single taxa to climate‐driven habitat changes. It also represents a further step towards the forecasting of future responses to climate change and the accompanying development of conservation strategies that more effectively respond to the detrimental impacts of climate change on biodiversity.
The atomic scale details of single-walled carbon nanotube (SWNT) nucleation on metal catalyst particles are elusive to experimental observations. Computer simulation of metal-catalyzed SWNT ...nucleation is a challenging topic but potentially of great importance to understand the factors affecting SWNT diameters, chirality, and growth efficiency. In this work, we use nonequilibrium density functional tight-binding molecular dynamics simulations and report nucleation of sp2-carbon cap structures on an iron particle consisting of 38 atoms. One C2 molecule was placed every 1.0 ps around an Fe38 cluster for 30 ps, after which a further 410 ps of annealing simulation without carbon supply was performed. We find that sp2-carbon network nucleation and annealing processes occur in three sequential and repetitive stages: (A) polyyne chains on the metal surface react with each other to evolve into a Y-shaped polyyne junction, which preferentially form a five-membered ring as a nucleus; (B) polyyne chains on the first five-membered ring form an additional fused five- or six-membered ring; and (C) pentagon-to-hexagon self-healing rearrangement takes place with the help of short-lived polyyne chains, stabilized by the mobile metal atoms. The observed nucleation process resembles the formation of a fullerene cage. However, the metal particle plays a key role in differentiating the nucleation process from fullerene cage formation, most importantly by keeping the growing cap structure from closing into a fullerene cage and by keeping the carbon edge “alive” for the addition of new carbon material.
We present nonequilibrium physics in spin ice as a unique setting that combines kinematic constraints, emergent topological defects, and magnetic long-range Coulomb interactions. In spin ice, ...magnetic frustration leads to highly degenerate yet locally constrained ground states. Together, they form a highly unusual magnetic state—a “Coulomb phase”—whose excitations are point-like defects—magnetic monopoles—in the absence of which effectively no dynamics is possible. Hence, when they are sparse at low temperature, dynamics becomes very sluggish. When quenching the system from a monopole-rich to a monopole-poor state, a wealth of dynamical phenomena occur, the exposition of which is the subject of this article. Most notably, we find reaction diffusion behavior, slow dynamics owing to kinematic constraints, as well as a regime corresponding to the deposition of interacting dimers on a honeycomb lattice. We also identify potential avenues for detecting the magnetic monopoles in a regime of slow-moving monopoles. The interest in this model system is further enhanced by its large degree of tunability and the ease of probing it in experiment: With varying magnetic fields at different temperatures, geometric properties—including even the effective dimensionality of the system—can be varied. By monitoring magnetization, spin correlations or zero-field NMR, the dynamical properties of the system can be extracted in considerable detail. This establishes spin ice as a laboratory of choice for the study of tunable, slow dynamics.
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