Thermally Fluctuating Research Articles

Imaging Thermally Fluctuating Néel Vectors in van der Waals Antiferromagnet NiPS3.

Studying antiferromagnetic domains is essential for fundamental physics and potential spintronics applications. Despite their importance, few systematic studies have been performed on antiferromagnet (AFM) domains with high spatial resolution in van der Waals (vdW) materials, and direct probing of the Néel vectors remains challenging. In this work, we found multidomain states in the vdW AFM NiPS3, a material extensively investigated for its unique magnetic exciton. We employed photoemission electron microscopy combined with the X-ray magnetic linear dichroism (XMLD-PEEM) to image the NiPS3's magnetic structure. The nanometer-spatial resolution of XMLD-PEEM allows us to determine local Néel vector orientations and discover thermally fluctuating Néel vectors that are independent of the crystal symmetry even at 65 K, well below the TN of 155 K. We demonstrate that an in-plane orbital moment of the Ni ion is responsible for the weak magnetocrystalline anisotropy. The observed thermal fluctuations of the antiferromagnetic domains may explain the broadening of magnetic exciton peaks at higher temperatures.

Simulating Brownian motion in thermally fluctuating viscoelastic fluids by using the smoothed profile method

To investigate the Brownian motion of individual particles suspended in viscoelastic fluids, the stochastic smoothed profile method (SPm) for direct numerical simulation is developed by extending deterministic SPm for suspensions in viscoelastic media. To simulate viscoelastic flow driven by thermal fluctuations in the suspending medium, the random stress in the fluid momentum equation as well as the random driving force for the conformation tensor in the Oldroyd-B model are incorporated according to the fluctuating hydrodynamics and fluctuating viscoelasticity formalisms. The thermal equilibrium and dynamical properties calculated by using numerical simulations successfully reproduce the analytic predictions, validating the direct simulation for the coupled fluctuating Navier–Stokes and Oldroyd-B equations and for the coupling between the stochastic viscoelastic medium and individual particles. As an application of the stochastic SPm, we investigate finite system-size effects under periodic boundary conditions (PBCs) on the passive microrheological relationship between the mean-square displacement (MSD) of a Brownian particle and the medium's dynamic modulus. Comparing the modulus that was microrheologically calculated from the MSD with the input modulus reveals that the effect of periodic image cell interaction appears not only in the long-time diffusive regime but also in the short-time region. A frequency-dependent finite system-size correction is implemented by phenomenologically extending the long-time diffusive regime correction, allowing passive microrheology analysis under PBCs. This result can be directly applied to other mesoscale numerical simulations including coarse-grained molecular dynamics and dissipative particle dynamics simulations.

Steric Communication between Dynamic Components on DNA Nanodevices.

Biomolecular nanotechnology has helped emulate basic robotic capabilities such as defined motion, sensing, and actuation in synthetic nanoscale systems. DNA origami is an attractive approach for nanorobotics, as it enables creation of devices with complex geometry, programmed motion, rapid actuation, force application, and various kinds of sensing modalities. Advanced robotic functions like feedback control, autonomy, or programmed routines also require the ability to transmit signals among subcomponents. Prior work in DNA nanotechnology has established approaches for signal transmission, for example through diffusing strands or structurally coupled motions. However, soluble communication is often slow and structural coupling of motions can limit the function of individual components, for example to respond to the environment. Here, we introduce an approach inspired by protein allostery to transmit signals between two distal dynamic components through steric interactions. These components undergo separate thermal fluctuations where certain conformations of one arm will sterically occlude conformations of the distal arm. We implement this approach in a DNA origami device consisting of two stiff arms each connected to a base platform via a flexible hinge joint. We demonstrate the ability for one arm to sterically regulate both the range of motion and the conformational state (latched or freely fluctuating) of the distal arm, results that are quantitatively captured by mesoscopic simulations using experimentally informed energy landscapes for hinge-angle fluctuations. We further demonstrate the ability to modulate signal transmission by mechanically tuning the range of thermal fluctuations and controlling the conformational states of the arms. Our results establish a communication mechanism well-suited to transmit signals between thermally fluctuating dynamic components and provide a path to transmitting signals where the input is a dynamic response to parameters like force or solution conditions.

Spontaneous Tilt of Single-Clamped Thermal Elastic Sheets.

Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here, we use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic sheet with one end clamped at its zero-temperature length. We uncover a tilted phase in which the sheet fluctuates about a mean configuration inclined with respect to the horizontal, thus breaking reflection symmetry. We determine the phase behavior as a function of the aspect ratio of the sheet and the temperature. We show that tilt may be viewed as a type of transverse buckling instability induced by clamping coupled to thermal fluctuations and develop an analytic model that predicts the tilted and untilted regions of the phase diagram. Qualitative agreement is found with the molecular dynamics simulations. Unusual response driven by control of purely geometric quantities like the aspect ratio, as opposed to external fields, offers a very rich playground for two-dimensional mechanical metamaterials.

Thermally fluctuating, semiflexible sheets in simple shear flow.

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

A Hybrid Immersed Boundary/Coarse-Graining Method for Modeling Inextensible Semi-Flexible Filaments in Thermally Fluctuating Fluids

A new and computationally efficient version of the immersed boundary method, which is combined with the coarse-graining method, is introduced for modeling inextensible filaments immersed in low-Reynolds number flows. This is used to represent actin biopolymers, which are constituent elements of the cytoskeleton, a complex network-like structure that plays a fundamental role in shape morphology. An extension of the traditional immersed boundary method to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the fluid at smaller scales. By way of validation, the response of a single, massless, inextensible semiflexible filament immersed in a thermally fluctuating fluid is obtained using the suggested numerical scheme and the resulting time-averaged contraction of the filament is compared to the theoretical value obtained from the worm-like chain model.

Nonmonotonic Temperature-Dependent Dissipation at Nonequilibrium in Atomically Thin Clean-Limit Superconductors.

Resistance in superconductors arises from the motion of vortices driven by flowing supercurrents or external electromagnetic fields and may be strongly affected by thermal or quantum fluctuations. The common expectation is that as the temperature is lowered, vortex motion is suppressed, leading to a decreased resistance. We show experimentally that in clean-limit atomically thin 2H-NbSe2 the resistance below the superconducting transition temperature may be nonmonotonic, passing through a minimum before increasing again as the temperature is decreased further. The effect is most pronounced in monolayer devices and cannot be understood in terms of known mechanisms. We propose a qualitative two-fluid vortex model in which thermal fluctuations of pinned vortices control the mobility of the free vortices. The findings provide a new perspective on fundamental questions of vortex mobility and dissipation in superconductors.

Binding of a Brownian nanoparticle to a thermally fluctuating membrane surface.

We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.

Measuring Stepwise Binding of Thermally Fluctuating Particles to Cell Membranes without Fluorescence

Thermal motions enable a particle to probe the optimal interaction state when binding to a cell membrane. However, especially on the scale of microseconds and nanometers, position and orientation fluctuations are difficult to observe with common measurement technologies. Here, we show that it is possible to detect single binding events of immunoglobulin-G-coated polystyrene beads, which are held in an optical trap near the cell membrane of a macrophage. Changes in the spatial and temporal thermal fluctuations of the particle were measured interferometrically, and no fluorophore labeling was required. We demonstrate both by Brownian dynamic simulations and by experiments that sequential stepwise increases in the force constant of the bond between a bead and a cell of typically 20 pN/μm are clearly detectable. In addition, this technique provides estimates about binding rates and diffusion constants of membrane receptors. The simple approach of thermal noise tracking points out new strategies in understanding interactions between cells and particles, which are relevant for a large variety of processes, including phagocytosis, drug delivery, and the effects of small microplastics and particulates on cells.

How Thermal Fluctuations Affect Hard-Wall Repulsion and Thereby Hertzian Contact Mechanics

Contact problems as they occur in tribology and colloid science are often solved with the assumption of hard-wall and hard-disk repulsion between locally smooth surfaces. This approximation is certainly meaningful at sufficiently coarse scales. However, at small scales, thermal fluctuations can become relevant. In this study, we address the question how they render non-overlap constraints into finite-range repulsion. To this end, we derive a closed-form analytical expression for the potential of mean force between a hard wall and a thermally fluctuating, linearly elastic counterface. Theoretical results are validated with numerical simulations based on the Green's function molecular dynamics technique, which is generalized to include thermal noise while allowing for hard-wall interactions. Applications consist of the validation of our method for flat surfaces and the generalization of the Hertzian contact to finite temperature. In both cases, similar force-distance relationships are produced with effective potentials as with fully thermostatted simulations. Analytical expressions are identified that allow the thermal corrections to the Hertzian load-displacement relation to be accurately estimated. While these corrections are not necessarily small, they turn out surprisingly insensitive to the applied load.

Topological Protection Can Arise from Thermal Fluctuations and Interactions.

Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example, for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of interline interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales

The combination of fluid-structure interactions with stochasticity, due to thermal fluctuations, remains a challenging problem in computational fluid dynamics. We develop an efficient scheme based on the stochastic immersed boundary method, Stokeslets, and multiple timestepping. We test our method for spherical particles and filaments under purely thermal and deterministic forces and find good agreement with theoretical predictions for Brownian Motion of a particle and equilibrium thermal undulations of a semi-flexible filament. As an initial application, we simulate bio-filaments with the properties of F-actin. We specifically study the average time for two nearby parallel filaments to bundle together. Interestingly, we find a two-fold acceleration in this time between simulations that account for long-range hydrodynamics compared to those that do not, suggesting that our method will reveal significant hydrodynamic effects in biological phenomena.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing.

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)2160-330810.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

Monte Carlo methods used in inverted hexagonal lipid phase and in simulations of thermally fluctuating lipid vesicles

Two different uses of Monte Carlo methods in soft matter physics are presented in the following work. Firstly, the Monte Carlo simulated annealing is used to minimize the elastistic energy of the inverted hexagonal phase (HII) optimal geometry. We will do a brief overview on the mechanics of the HII lipid phase. In our model the expression for the lipid monolayer free energy consists of two energy contributions: the bending energy which involves also a deviatoric term, and the interstitial energy which describes the deformation energy due to stretching of the phospholipid molecule chains. On the basis of the derived expression for the lipid monolayer free energy, we will theoretically predict optimal geometry and physical conditions for the stability of the inverted hexagonal phase. Using the Monte Carlo simulated annealing method, we will theoretically describe first steps in the LαHII phase transition. Another interesting subject investigated by means of Monte Carlo simulations are the thermal fluctuations of nearly spherical vesicles. The theoretical basis of this analysis was done by Milner and Safran (Phys Rev A 36(9):4371–4379, 1987. doi:10.1103/PhysRevA.36.4371) that uses the mean field approximation. In this work we will show the application of the Monte Carlo simulations and show the correlation between the time mean simulated thermal fluctuations decomposed into spherical harmonics and the bending stiffness in 2-dimensional and 3-dimensional space.

Pseudo-Casimir stresses and elasticity of a confined elastomer film.

Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links. Herein, we consider an incompressible and flat elastomer film of an axisymmetric shape confined between two large hard co-planar substrates, with the axis of the film perpendicular to the substrates. We address the impact that thermal fluctuations of the cross-links have on the free energy of elastic deformation of the system, subject to the requirement that the fluctuating elastomer cannot detach from the substrates. We examine the behavior of the deformation free energy for one case where a rigid pinning boundary condition is applied to a class of elastic fluctuations at the confining surfaces, and another case where the same elastic fluctuations are subjected to soft "gluing" potentials. We find that there can be significant departures (both quantitative and qualitative) from the prediction of classical rubber elasticity theory when elastic fluctuations are included. Finally, we compare the character of the attractive part of the elastic fluctuation-induced, or pseudo-Casimir, stress with the standard thermal Casimir stress in confined but non-elastomeric systems, finding the same power law decay behavior when a rigid pinning boundary condition is applied; for the case of the gluing potential, we find that the leading order correction to the attractive part of the fluctuation stress decays inversely with the inter-substrate separation.

Energy exchange network of inter-residue interactions within a thermally fluctuating protein molecule: A computational study.

Protein function is regulated not only by the structure but also by physical dynamics and thermal fluctuations. We have developed the computer program, CURrent calculation for proteins (CURP), for the flow analysis of physical quantities within thermally fluctuating protein media. The CURP program was used to calculate the energy flow within the third PDZ domain of the neuronal protein PSD-95, and the results were used to illustrate the energy exchange network of inter-residue interactions based on atomistic molecular dynamics simulations. The removal of the α3 helix is known to decrease ligand affinity by 21-fold without changing the overall protein structure; nevertheless, we demonstrated that the helix constitutes an essential part of the network graph.

Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method

We develop computational methods for the simulation of osmotic swelling phenomena relevant to microscopic vesicles containing transformable solute molecules. We introduce stochastic immersed boundary methods (SIBMs) that can capture osmotically driven fluid transport through semipermeable elastic membranes subject to thermal fluctuations. We also develop numerical methods to handle within SIBMs an elastic shell model for a neo-Hookean material. Our extended SIBM allows for capturing osmotic swelling phenomena driven by concentration changes and interactions between a discrete collection of confined particles while accounting for the thermal fluctuations of the semipermeable membrane and the hydrodynamic transport of solvent. We use our computational methods to investigate osmotic phenomena in regimes that go beyond the classical Van't Hoff theory. We develop statistical mechanics theories for osmotic swelling of vesicles when there are significant interactions between particles that can transform over time. We validate our theoretical results against detailed computational simulations. Our methods are expected to be useful for a wide class of applications allowing for the simulation of osmotically driven flows, thermally fluctuating semipermeable elastic structures, and solute interactions.

Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations

We explore the derivation of interatomic exchange interactions in ferromagnets within density-functional theory (DFT) and the mapping of DFT results onto a spin Hamiltonian. We delve into the problem of systems comprising atoms with strong spontaneous moments together with atoms with weak induced moments. All moments are considered as degrees of freedom, with the strong moments thermally fluctuating only in angle and the weak moments thermally fluctuating in angle and magnitude. We argue that a quadratic dependence of the energy on the weak local moments magnitude, which is a good approximation in many cases, allows for an elimination of the weak-moment degrees of freedom from the thermodynamic expressions in favor of a renormalization of the Heisenberg interactions among the strong moments. We show that the renormalization is valid at all temperatures accounting for the thermal fluctuations and resulting in temperature-independent renormalized interactions. These are shown to be the ones directly derived from total-energy DFT calculations by constraining the strong-moment directions, as is done e.g. in spin-spiral methods. We furthermore prove that within this framework the thermodynamics of the weak-moment subsystem, and in particular all correlation functions, can be derived as polynomials of the correlation functions of the strong-moment subsystem with coefficients that depend on the spin susceptibility and that can be calculated within DFT. These conclusions are rigorous under certain physical assumptions on the measure in the magnetic phase space. We implement the scheme in the full-potential linearized augmented plane wave method using the concept of spin-spiral states, considering applicable symmetry relations and the use of the magnetic force theorem. Our analytical results are corroborated by numerical calculations employing DFT and a Monte Carlo method.

Manipulation of graphene’s dynamic ripples by local harmonic out-of-plane excitation**Contribution of the National Institute of Standards and Technology, an agency of the US government. Not subject to copyright in the USA.

With use of carefully designed molecular dynamics simulations, we demonstrate tuning of dynamic ripples in free standing, thermally fluctuating graphene by applying a local out-of-plane sinusoidal excitation. The local dynamic morphology can be controlled via varying external modulation and the boundary conditions. We fully account for the discrete atomistic structure of graphene, as well as natural energy dissipation due in part to its remarkably high thermal conductivity. In addition to stable dynamic rippling patterns, we observed an unexpected flattening of graphene well below the thermal limit. Our results provide insight into the dynamic response of atomically thin layers to an external time-varying excitation in the presence of realistic thermal fluctuations and energy loss. This suggests intriguing possibilities for modulating the electrical and optical properties of atomically thin membranes via local dynamic morphology control.

Flies developed small bodies and small cells in warm and in thermally fluctuating environments.

Although plasma membranes benefit cells by regulating the flux of materials to and from the environment, these membranes cost energy to maintain. Because smaller cells provide relatively more membrane area for transport, ectotherms that develop in warm environments should consist of small cells despite the energetic cost. Effects of constant temperatures on cell size qualitatively match this prediction, but effects of thermal fluctuations on cell size are unknown. Thermal fluctuations could favour either small or large cells; small cells facilitate transport during peaks in metabolic demand whereas large cells minimize the resources needed for homeoviscous adaptation. To explore this problem, we examined effects of thermal fluctuations during development on the size of epidermal cells in the wings of Drosophila melanogaster. Flies derived from a temperate population were raised at two mean temperatures (18 and 25°C), with either no variation or a daily variation of ±4°C. Flies developed faster at a mean temperature of 25°C. Thermal fluctuations sped development, but only at 18°C. An increase in the mean and variance of temperature caused flies to develop smaller cells and wings. Thermal fluctuations reduced the size of males at 18°C and the size of females at 25°C. The thorax, the wings and the cells decreased with an increase in the mean and in the variance of temperature, but the response of cells was the strongest. Based on this pattern, we hypothesize that development of the greater area of membranes under thermal fluctuations provides a metabolic advantage that outweighs the greater energetic cost of remodelling membranes.