Brownian Rotor Research Articles

An Inbuilt Electronic Pawl Gates Orbital Information Processing and Controls the Rotation of a Double Ratchet Rotary Motor.

A direct external input energy source (e.g., light, chemical reaction, redox potential, etc.) is compulsory to supply energy to rotary motors for accomplishing rotation around the axis. The stator leads the direction of rotation, and a sustainable rotation requires two mutual input energy supplies (e.g., light and heat, light and pH or metal ion, etc.); however, there are some exceptions (e.g., covalent single bond rotors and/or motors). On the contrary, our experiment suggested that double ratchet rotary motors (DRMs) can harvest power from available thermal noise, kT, for sustainable rotation around the axis. Under a scanning tunneling microscope, we have imaged live thermal noise movement as a dynamic orbital density and resolved the density diagram up to the second derivative. A second input energy can synchronize multiple rotors to afford a measurable output. Therefore, we hypothesized that rotation control in a DRM must be evolved from an orbital-level information transport channel between the two coupled rotors but was not limited to the second input energy. A DRM comprises a Brownian rotor and a power stroke rotor coupled to a -C≡C- stator, where the transport of information through coupled orbitals between the two rotors is termed the vibrational information flow chain (VIFC). We test this hypothesis by studying the DRM's density functional theory calculation and variable-temperature 1H nuclear magnetic resonance. Additionally, we introduced inbuilt pawl-like functional moieties into a DRM to create different electronic environments by changing proton intercalation interactions, which gated information processing through the VIFC. The results show the VIFC can critically impact the motor's noise harvesting, resulting in variable rotational motions in DRMs.

Quantum spin-liquid states in an organic magnetic layer and molecular rotor hybrid

The exotic properties of quantum spin liquids (QSLs) have continually been of interest since Anderson's 1973 ground-breaking idea. Geometrical frustration, quantum fluctuations, and low dimensionality are the most often evoked material's characteristics that favor the long-range fluctuating spin state without freezing into an ordered magnet or a spin glass at low temperatures. Among the few known QSL candidates, organic crystals have the advantage of having rich chemistry capable of finely tuning their microscopic parameters. Here, we demonstrate the emergence of a QSL state in [EDT-TTF-CONH2]2 +[[Formula: see text]] (EDT-BCO), where the EDT molecules with spin-1/2 on a triangular lattice form layers which are separated by a sublattice of BCO molecular rotors. By several magnetic measurements, we show that the subtle random potential of frozen BCO Brownian rotors suppresses magnetic order down to the lowest temperatures. Our study identifies the relevance of disorder in the stabilization of QSLs.

Radio Waveguide-Double Ratchet Rotors Work in Unison on a Surface to Convert Heat into Power.

Synchronizing thousands of 100% efficient rotors in a macrodevice for harvesting noise is unapprehended. Thermodynamically, realizing a thermal gradient at the atomic scale is critical. Harvesting free thermal energy or noise by resonance has a hidden clause; either externally activating a directed self-powered motion or constructing a nanoscale power supply. To accomplish this, we combined two rotor concepts, Brownian rotor, BR, and power stroke, PS, rotors available in living systems in two planes of a single molecule. Quantum tunneling images reveal how a radio-wave guided synchronization of PS-BR combination tweaks rotational dynamics of a rotor to bypass the necessity of temperature gradient (ΔT). Live imaging of thermal noise movement as electron density between a pair of molecular planes helped in optimizing the rotor design. The rotor's monolayer harvests heat from the liquid's Brownian noise and electromagnetic noise, together delivering a finite, usable power. The chip supplies the power if we wet the surface or shine electric noise.

Stochastic stability of a piezoelectric vibration energy harvester under a parametric excitation and noise-induced stabilization

Vibration energy harvesters seek to convert the energy of ambient, random vibrations into electrical power, often using piezoelectric transduction. The stochastic dynamics of a piezoelectric harvester subjected to a parametric (state-dependent) excitation has not been comprehensively investigated in the nonequilibrium regime. Motivated by mathematical results that establish the stabilization of dynamic response using noise, we investigate the stochastic stability of a generic harvester in the linear and the monostable nonlinear regimes excited by a multiplicative noise process characterized by both Brownian and Lévy distributions. Stability is characterized in each case by studying the approach of the harvester response towards equilibrium in the time domain, longer term proximity (or divergence) of two solutions starting with nearby initial conditions in the phase plane as well as the Lyapunov exponent. In the linear case, we analytically obtain a lower bound on the magnitude of the noise intensity that guarantees stability. The bound is derived as an inequality in terms of the system parameters. This analytic result is validated numerically using the Euler-Maruyama scheme by: (1) computing the harvester response and its approach to equilibrium in terms of its displacement, velocity and voltage, (2) computing the trajectories of two solutions with nearby initial conditions in the phase plane and (3) the sign of the maximal Lyapunov exponent in terms of energy. We find that noise-induced stabilization occurs consistently for the noise intensities greater than the lower bound in linear and weakly nonlinear harvesters, for both Brownian and Lévy excitation. Instabilities emerge for the noise intensities lower than the bound. The results lead to the interesting conclusion that noise of appropriate strength can induce stabilization and are expected to be useful in the design of energy harvesters. In addition, the results are expected to be significant in the study of phenomena such as noise-induced transport in Brownian rotors where stability is an important aspect of the stochastic dynamics.

Dynamics and efficiency of Brownian rotors

Brownian rotors play an important role in biological systems and in future nanotechnological applications. However the mechanisms determining their dynamics, efficiency, and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of the Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depend on the magnitude of its stochastic motion driven by the free energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and--by this--the efficiency.

Compartmental Modeling of the Fluorescence Anisotropy Decay of a Cylindrically Symmetric Brownian Rotor: Identifiability Analysis

We present the results of the deterministic identifiability analysis based on similarity transformation for models of one-state excited-state events of cylindrically symmetric rotors in isotropic environments undergoing rotational diffusion described by Brownian reorientation. Such an analysis on error-free time-resolved fluorescence (anisotropy) data can reveal whether the parameters of the considered model can be determined. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to construct, in convenient matrix form, expressions of the sum S(t) = I(parallel)(t) + 2I(perpendicular)(t), the difference D(t) = I(parallel)(t) - I(perpendicular)(t), and the time-resolved fluorescence anisotropy r(t) = D(t)/S(t). The identifiability analysis of r(t) demonstrates that the rotational diffusion coefficients D(parallel) and D(perpendicular) for rotation respectively about and perpendicular to the symmetry axis can be uniquely resolved. However, the polar and azimuthal angles defining the absorption and emission transition moments in the molecular reference frame are not individually identifiable. Nevertheless, the difference between the polar angles of these transition moments is uniquely determined.

Kinetic Accessibility of Buried DNA Sites in Nucleosomes

Using a theoretical model for spontaneous partial DNA unwrapping from histones, we study the transient exposure of protein-binding DNA sites within nucleosomes. We focus on the functional dependence of the rates for site exposure and reburial on the site position, which is measurable experimentally and pertinent to gene regulation. We find the dependence to be roughly described by a random walker model. Close inspection reveals a surprising physical effect of flexibility-assisted barrier crossing, which we characterize within a toy model, the "semiflexible Brownian rotor."

Basis set study of classical rotor lattice dynamics.

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems.

Orientational relaxation in Brownian rotors with frustrated interactions on a square lattice.

We present simulation results on the equilibrium relaxation of Brownian planar rotors based on a uniformly frustrated XY model on a square lattice. The rotational relaxation exhibits typical dynamic features of fragile supercooled liquids including the two-step relaxation. We observe a dynamic crossover from the high-temperature regime with Arrhenius behavior to the low-temperature regime with temperature-dependent activation energy. A consistent picture for the observed slow dynamics can be given in terms of the caging effect and thermal activation across potential barriers in the energy landscapes.

Spectral properties of a time-periodic Fokker-Planck equation.

The Floquet spectrum of the time-periodic Fokker-Planck equation for a driven Brownian rotor is studied. We show that the Fokker-Planck equation can be transformed to a Schr\odinger-like equation, with the same set of eigenvalues, whose dynamics is governed by a time-periodic Hamiltonian in which the diffusion coefficient plays a role analogous to Planck's constant. For a small diffusion coefficient, numerical calculations of the spectrum starting from the Schr\odinger-like equation are more convergent than those starting from the Fokker-Planck equation. When the Hamiltonian exhibits a transition to chaos, those decay rates affected by the chaotic regime exhibit level repulsion. This level repulsion of decay rates, in turn, changes the behavior of a typical mean first passage time in the problem. The size of the diffusion coefficient determines the extent to which the stochastic dynamics is affected by the transition to chaos in the underlying Hamiltonian.

A delta-kicked Brownian rotor

We study the evolution of a delta-kicked Fokker-Planck equation which is a certain limiting case of a driven Brownian rotor with large friction. The time evolution of the rotor is given by a Floquet map in which the effects of diffusion and of the kick are decoupled. For the case where absorbing boundaries are introduced, we show the mechanism causing an abrupt drop in the average survival time as the kick strength is increased.

Comments on the Coupling between Linear and Angular Momentum of Structured Molecules

We consider systems of structured molecules which are capable of translational as well as rotational motion. Using symmetry arguments we show that the linear and the angular momentum of each molecule are statistically independent for systems which possess a center of symmetry. This result applies, in particular, to the case of Brownian rotors, and it implies that the Langevin equations for translational and rotational motion are uncoupled.