Presence Of Thermal Fluctuations Research Articles

Guiding of vortices and ratchet effect in superconducting films with asymmetric pinning potential

Two-dimensional vortex dynamics in a ratchet washboard planar pinning potential in the presence of thermal fluctuations is considered on the basis of a Fokker-Planck equation. Explicit expressions for two nonlinear anisotropic voltages (longitudinal and transverse with respect to the current direction) are derived and analyzed. The physical origin of these odd (with respect to magnetic field or transport current direction reversal) voltages is caused by the interplay between the even effect of vortex guiding and the ratchet asymmetry. Both voltages are going to zero in the linear regimes of the vortex motion [i.e., in the thermally activated flux flow (TAFF) and Ohmic flux flow (FF) regimes] and have a bumplike current or temperature dependence in the vicinity of the highly nonlinear resistive transition from the TAFF to the FF.

Dynamic pathways to mediate reactions buried in thermal fluctuations. I. Time-dependent normal form theory for multidimensional Langevin equation

We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.

Capacitance Effect on Microwave Power Spectra of Spin-Torque Oscillator With Thermal Noise

A macro-spin simulation has been carried out to study the thermal stability of a spin-torque oscillator (STO) connected in parallel with a capacitance. To study the impact of realistic thermal fluctuation on an STO, a stochastic magnetic field vector is added into the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. From the numerical solution, it is found that the addition of capacitance positively influences the thermal stability of the system, and can improve the quality factor of the microwave power spectrum even in the presence of thermal fluctuation. The results of I-V phase shift under different conditions suggest that there may exist an optimum capacitance for which the thermal stability of the system can be most enhanced.

Noise effects in two different biological systems

We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L.) (Heteroptera: Pentatomidae), and (ii) polymer translocation. In the first system we analyze, by directionality tests, the response of N. viridula individuals to subthreshold signals plus noise in their mating behaviour. The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum. Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise. In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source. At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed. At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia. We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport.

Amplitude-phase coupling in a spin-torque nano-oscillator

The spin-torque nano-oscillator in the presence of thermal fluctuation is described by the normal form of the Hopf bifurcation with an additive white noise. By the application of the reduction method, the amplitude-phase coupling factor, which has a significant effect on the power spectrum of the spin-torque nano-oscillator, is calculated from the Landau–Lifshitz–Gilbert–Slonczewski equation with the nonlinear Gilbert damping. The amplitude-phase coupling factor exhibits a large variation depending on an in-plane anisotropy under the practical external fields.

Side-by-side And End-to-end Attraction Of Double-stranded DNA

Genomic DNA is densely packed inside the cell nucleus and viral capsids. Such close packing suggests that electrostatic repulsion between negatively charged DNA in the condensed state is balanced by counterion-induced attraction. Indeed, effective attraction between DNA in high-valence electrolytes has been experimentally demonstrated. Several theoretical models have been proposed to explain DNA attraction, however, specific microscopic mechanisms could not be unequivocally determined. Here, we report sub-microsecond all-atom molecular dynamics (MD) simulations of the effective force between double-stranded DNA in the side-by-side and end-to-end orientations. In a typical simulation, two DNA molecules were placed in an electrolyte solution a certain distance away from one another. An external harmonic potential was applied to keep the distance between the molecules constant, which allowed the effective mean force to be computed directly by averaging over 160 ns-long trajectories. We found that, in a side-by-side conformation, two DNA molecules can form a bond state in the presence of magnesium ions. In the bond state, DNA molecules contact each other via negatively charged phosphate groups, bridged by magnesium ions. For DNA in a monovalent electrolyte, the effective attractive force is too weak to induce DNA condensation in the presence of thermal fluctuations. In the end-to-end orientation, the attraction was found to take place regardless of the electrolyte concentration. The presence of a phosphate group at the 5′-ends of the fragments was found to direct DNA end-to-end self-assembly and produce bound states resembling a continuosus DNA molecule. Our simulations suggest that the end-to-end attraction, rather than being mediated by counterions, is likely caused by hydrophobic and the van der Waals interactions between terminal nucleobases of the fragments.

DNA attraction in monovalent and divalent electrolytes.

The dependence of the effective force on the distance between two DNA molecules was directly computed from a set of extensive all-atom molecular dynamics simulations. The simulations revealed that in a monovalent electrolyte the effective force is repulsive at short and long distances but can be attractive in the intermediate range. This attractive force is, however, too weak (approximately 5 pN per turn of a DNA helix) to induce DNA condensation in the presence of thermal fluctuations. In divalent electrolytes, DNA molecules were observed to form a bound state, where Mg(2+) ions bridged minor groves of DNA. The effective force in divalent electrolytes was predominantly attractive, reaching a maximum of 42 pN per one turn of a DNA helix.

Magnetic flux noise in the three-Josephson-junction superconducting ring

We analyze the influence of noise on magnetic properties of a superconducting loop which contains three Josephson junctions. This circuit is a classical analog of a persistent current (flux) qubit. A loop supercurrent induced by external magnetic field in the presence of thermal fluctuations is calculated. To connect with experiment, we calculate the impedance of a low-frequency tank circuit which is inductively coupled with the loop of interest. We compare the results with the results obtained in the quantum mode — when the three junction loop exhibits quantum tunneling of the magnetic flux. We demonstrate that the tank–loop impedance in the classical and quantum modes have different temperature dependence and can be easily distinguished experimentally.

Numerical simulations of Fiske steps in intrinsic Jospehson junctions

We have numerically investigated the vortex dynamics in a stack of intrinsic Josephson junctions (IJJs) having length L=5λJ. We performed simulations by using the perturbed, coupled sine-Gordon model taking into account thermal fluctuations. In the absence of thermal fluctuations, the current–voltage characteristics show a series of smaller amplitude Fiske steps corresponding to different cavity modes, excited by the collective vortex-flow depending on an external magnetic field. However, in the presence of thermal fluctuations, we found that only Fiske steps corresponding to the lowest-velocity cavity mode appear clearly and others becomes indistinct. This suggests that the out-of-phase mode becomes more stable than other modes due to the fluctuations. In addition, the stable steps show a field dependence similar to the Fiske steps in single junction. The results are consistent with recent experimental observations in IJJs in the vortex-flow state.

Multiline Spectropolarimetry of the Quiet Sun at 5250 and 6302 A

The reliability of quiet-Sun magnetic field diagnostics based on the Fe I lines at 6302 A has been questioned by recent work. Here we present the results of a thorough study of high-resolution multiline observations taken with the new spectropolarimeter SPINOR, comprising the 5250 and 6302 A spectral domains. The observations were analyzed using several inversion algorithms, including Milne-Eddington, LTE with 1 and 2 components, and MISMA codes. We find that the line-ratio technique applied to the 5250 A lines is not sufficiently reliable to provide a direct magnetic diagnostic in the presence of thermal fluctuations and variable line broadening. In general, one needs to resort to inversion algorithms, ideally with realistic magnetohydrodynamic constrains. When this is done, the 5250 A lines do not seem to provide any significant advantage over those at 6302 A. In fact, our results point toward a better performance with the latter (in the presence of turbulent line broadening). In any case, for very weak flux concentrations, neither spectral region alone provides sufficient constraints to fully disentangle the intrinsic field strengths. Instead, we advocate for a combined analysis of both spectral ranges, which yields a better determination of the quiet-Sun magnetic properties. Finally, we propose the use of two other Fe I lines (at 4122 and 9000 A) with identical line opacities that seem to work much better than the others.

Stretching of buckled filaments by thermal fluctuations

We study the buckling instability of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical solution based on a renormalization-like procedure where we integrate out short wavelength fluctuations in order to obtain an effective theory governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and the average projected filament length parallel to the force direction as a function of the applied force and of the contour length of the filament. We find that, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our analytic results are confirmed by Monte Carlo simulations.

Stochastic immersed boundary method incorporating thermal fluctuations

AbstractWe give a brief introduction to the stochastic immersed boundary method which allows for simulation of small length‐scale physical systems in which elastic structures interact with a fluid flow in the presence of thermal fluctuations. The conventional immersed boundary method is extended to account for thermal fluctuations by introducing stochastic forcing terms in the fluid equations. This gives a system of stiff SPDE's for which standard numerical approaches perform poorly. We discuss a numerical method derived using stochastic calculus to overcome the stiff features of the equations. We then discuss results which indicate that the method captures physical features predicted by statistical mechanics for small length‐scale systems. The stochastic immersed boundary method holds promise as a numerical approach in simulating microscopic mechanical systems in which thermal fluctuations play a fundamental role. A more detailed discussion of this work is given in [1, 2, 3]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Radiative torque alignment: essential physical processes

We study the physical processes that affect the alignment of grains subject to radiative torques (RATs). To describe the action of RATs, we use the analytical model (AMO) of RATs introduced in our previous paper. We focus our discussion on the alignment by anisotropic radiation flux with respect to the magnetic field, which defines the axis of grain Larmor precession. Such an alignment does not invoke paramagnetic dissipation (i.e. the Davis–Greenstein mechanism), but, nevertheless, grains tend to be aligned with long axes perpendicular to the magnetic field. When we account for thermal fluctuations within grains, we show that for grains that are characterized by a triaxial ellipsoid of inertia, the zero-J attractor point obtained in our earlier study develops into a low-J attractor point. The value of angular momentum at the low-J attractor point is of the order of the thermal angular momentum corresponding to the grain temperature. We show that, for situations when the direction of radiative flux is nearly perpendicular to a magnetic field, the alignment of grains with long axes parallel to the magnetic field (i.e. ‘wrong alignment’) reported in our previous paper, disappears in the presence of thermal fluctuations. Thus, all grains are aligned with their long axes perpendicular to the magnetic field. We study the effects of stochastic gaseous bombardment and show that gaseous bombardment can drive grains from low-J to high-J attractor points in cases when high-J attractor points are present. As the alignment of grain axes with respect to angular momentum is higher for higher values of J, counter-intuitively, gaseous bombardment can increase the degree of grain alignment with respect to the magnetic field. We also study the effects of torques induced by H2 formation and show that they can change the value of angular momentum at high-J attractor points, but marginally affect the value of angular momentum at low-J attractor points. We compare the AMO results with those obtained using the direct numerical calculations of RATs acting upon irregular grains and we validate the use of the AMO for realistic situations of RAT alignment.

Dissipative particle dynamics simulations of liquid nanojet breakup

In this work, we use a dissipative-particle-dynamics (DPD)-based two-phase model to study the breakup of liquid nanojets. We show that the breakup of nanojets is accelerated by the presence of thermal fluctuations. Satellite drops, which are undesirable from an application viewpoint, are not observed in our simulations. We find that the presence of a repulsive wall enclosing the DPD liquid is necessary to prevent clogging of nanojets. We are able to recover the time evolution of minimum jet radius as given by prior theoretical analysis. This study shows that DPD is able to capture the thermal induced breakup phenomena at the sub-micron level. The coarse-grained nature of DPD along with its flexibility to allow for the modeling of complex fluids in combination with the results from this study show that DPD is a useful tool for sub-micron fluid flow simulations.

Exploration of the conformational space of myosin recovery stroke via molecular dynamics

Muscle contractions are driven by cyclic conformational changes of myosin, whose molecular mechanisms of operation are being elucidated by recent advances in crystallographic studies and single molecule experiments. To complement such structural studies and consider the energetics of the conformational changes of myosin head, umbrella sampling molecular dynamics (MD) simulations were performed with the all-atom model of the scallop myosin sub-fragment 1 (S1) with a bound ATP in solution in explicit water using the crystallographic near-rigor and transition state conformations as two references. The constraints on RMSD reaction coordinates used for the umbrella sampling were found to steer the conformational changes efficiently, and relatively close correlations have been observed between the set of characteristic structural changes including the lever arm rotation and the closing of the nucleotide binding pocket. The lever arm angle and key residue interaction distances in the nucleotide binding pocket and the relay helix show gradual changes along the recovery stroke reaction coordinate, consistent with previous crystallographic and computational minimum energy studies. Thermal fluctuations, however, appear to make the switch-2 coordination of ATP more flexible than suggested by crystal structures. The local solvation environment of the fluorescence probe, Trp 507 (scallop numbering), also appears highly mobile in the presence of thermal fluctuations.

Collective modes in a coupled ratchet model

We analyze a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be overdamped and driven by an external potential that is periodic both in space and time. The symmetries of the model allow to study the orbits with and without the presence of thermal fluctuations and for a changing intensity of the elastic coupling and the external driving force. We investigate the dependence of the transport current on the intensity of the elastic interaction. The direction of the current may be understood as resulting from the competition of collective transport modes in opposite directions and presents an inversion as the elastic coupling is increased.

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium

Crystal vs. glass formation in lattice models with many coexisting ordered phases

We present here new evidence that after a quench the planar Potts model on the square lattice relaxes towards a glassy state if the number of states q is larger than four. By extrapolating the finite size data we compute the average energy of these states for the infinite system with periodic boundary conditions, and find that it is comparable with that previously found using fixed boundary conditions. We also report preliminary results on the behaviour of these states in the presence of thermal fluctuations.

Statistical error in particle simulations of hydrodynamic phenomena

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress, and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.

New Hall voltages in a planar pinning potential

Two-dimensional vortex dynamics in a planar pinning potential (PPP) created by uniaxial or bianisotropic pinning planes in the presence of thermal fluctuations is considered on the basis of a Fokker–Planck equation. Explicit expressions for two new nonlinear anisotropic Hall voltages (longitudinal and transverse with respect to the current direction) are derived and analyzed. The physical origin of these odd (with respect to magnetic field reversal) voltages is caused by the subtle interplay between even effect of vortex guiding along the PPP and the odd Hall effect. Both new voltages are going to zero in the linear regimes of the vortex motion (i.e. in the thermoactivated flux flow (TAFF) and ohmic flux flow (FF) regimes) and have a bumplike current j or temperature θ dependence in the vicinity of highly nonlinear resistive transition from the TAFF to FF. As new odd voltages arise due to the Hall effect their characteristic scale is proportional to the Hall constant as for ordinary “steplike” odd Hall voltage, investigated earlier by Mawatari.