Fluctuation Formula Research Articles

Fluctuations of thermal variables investigated by cross-correlation function.

Fluctuations in conjugate thermodynamic variables are studied using the cross-correlation function. A new procedure is given enabling the derivation of fluctuation formulas for a system in equilibrium. Specifically, the cross-correlation function between heat and temperature is employed for thermal variables. Additionally, fluctuation-dissipation relations involving the frequency-dependent specific heat are established. Moreover, a general relation concerning the average entropy production is also given, which is the microscopic analog of the dissipation formula of the linear response theory. In the case of thermal variables, this formula finds application in various scenarios describing fluctuating thermal systems in equilibrium.

Thermophysical properties of the SPC/E model of water between 250 and 400 K at pressures up to 1000 MPa

This work explores the thermophysical properties of the SPC/E model of water at temperatures between 250 and 400 K and at pressure from 0.1 to 1000 MPa. From a series of Molecular Dynamics simulations (in the NPT ensemble and also in the NVT ensemble), the constant pressure and constant volume heat capacity, the isobaric expansion coefficient, the isothermal compressibility, and the speed of sound are obtained from fluctuation formulas and thermodynamic numerical derivatives and compared with available experimental data.

Quantum corrections to molecular dynamics simulations of specific heat capacities of thin ices: Role of adsorption and quasi-liquid layers at interfaces

The thermodynamic properties of ice under confined conditions are significantly different from those of bulk, and their mechanisms are of great significance in many fields. In this work, we analyze thin ice under three different configurations, including freestanding, attached, and nanoconfined thin ice. The molecular dynamics method is employed to calculate the specific heat capacity of ice through the energy fluctuation formula, and quantum corrections are made to the simulations. The ice thickness is varied in the range of 28.57 Å–121.43 Å to explore its effect on the specific heat capacity at constant volume. The results show that the specific heat capacities of the thin ice are significantly higher than that of the bulk ice, with a tendency to increase and then decrease to a constant, and the maximum values of the specific heat capacities of the freestanding thin ice, the attached thin ice, and the nanoconfined thin ice decrease in order. The ice-copper plate interface and the ice-vacuum interface rearrange the surrounding ice molecules, which in turn form the adsorption layer and the quasi-liquid layer, respectively. Analysis of the vibrational density of states of the thin ice shows that the interface effect and the size effect play a competing role when it is smaller than a critical thickness and they play a synergistic role when it is larger than the critical thickness. This work reveals the important effects of interfacial and size effects on the specific heat capacities of thin ice and contributes to a better understanding of the thermophysical properties of ice in different configurations in fields such as atmospheric science and biology.

Surface water in C-S-H: Effect of the temperature on (de)sorption

Thermal desorption is a critical process in cement-based materials subjected to temperature increase. C-S-H surface is the most likely surface available for thermal desorption in these materials. Here, we investigate surface thermal desorption in C-S-H. Molecular simulations are used to get systems equilibrated under two drained poromechanical conditions: liquid water-saturated and constant partial fluid pressure conditions. Suited fluctuation formulas are deployed to acquire properties at the adsorbed layer level. We show that thermal desorption is driven by thermal expansion of water and liquid-to-vapor phase transition (leading to cavitation). The potential energy, isochoric specific heat capacity, molar incremental enthalpy, bulk modulus, coefficient of thermal expansion, surface tension, and pressure tensor components exhibit a marked dependence on the distance from the C-S-H adsorbing surface. Parameters usually adopted in sorption models (e.g., BET family) such as monolayer thickness and adsorption energy need to be revisited using molecular scale evidence.

Particle-number fluctuations near the critical point of nuclear matter

The equation of state with quantum statistics corrections is used for particle number fluctuations $\ensuremath{\omega}$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations, $\ensuremath{\omega}\ensuremath{\propto}1/\mathcal{K}$, are analytically derived through the isothermal incompressibility $\mathcal{K}$ at first order over a small quantum-statistics parameter. Our approximate analytical results appear to be in good agreement with the results of accurate numerical calculations. These results are also close to those obtained by using more accurate Tolman and Rowlinson expansions of the incompressibility $\mathcal{K}$ near the critical point. A more general formula for fluctuations $\ensuremath{\omega}$, improved at the critical point, was obtained for a finite particle number average $\ensuremath{\langle}N\ensuremath{\rangle}$ by neglecting, for simplicity, small quantum statistics effects. It is shown that for a large dimensionless parameter, $\ensuremath{\alpha}\ensuremath{\propto}{\mathcal{K}}^{2}\ensuremath{\langle}N\ensuremath{\rangle}/{\mathcal{K}}^{\ensuremath{'}\ensuremath{'}}$, where ${\mathcal{K}}^{\ensuremath{'}\ensuremath{'}}$ is the second derivative of the incompressibility $\mathcal{K}$ as function of the average particle density $n$, far from the critical point $(\ensuremath{\alpha}\ensuremath{\gg}1)$, one finds the traditional asymptote, $\ensuremath{\omega}\ensuremath{\propto}1/\mathcal{K}$, for the fluctuations $\ensuremath{\omega}$. For a small parameter, $\ensuremath{\alpha}\ensuremath{\ll}1$, near the critical point, where $\mathcal{K}=0$ and $\ensuremath{\alpha}=0$, one obtains another asymptote of $\ensuremath{\omega}$. These fluctuations, having a maximum near the critical point as function of the average density $n$, for finite values of $\ensuremath{\langle}N\ensuremath{\rangle}$ are finite and relatively small, in contrast to the results of the traditional calculations.

Research on voltage regulation ability of four‐level nested clamp converter based on virtual space vector modulation

AbstractThe four‐level nested neutral point clamped (4L‐NNPC) converter is a new multi‐level converter with a simple topology, which is suitable for the medium‐voltage application. But it has voltage balancing problems under the low output frequency condition. A space virtual vector modulation (SVVM) algorithm is introduced in this paper, and the dwell time formulas are given. It uses the synthesis between vectors to optimize the dwell time of each level in the virtual vector, in order to balance the flying capacitor voltage in the carrier period. In order to explore the boundary of the voltage regulation ability of the 4L‐NNPC converter, this paper analyses the mechanism of the voltage fluctuation of the flying capacitors and derives the voltage fluctuation formulas. The voltage regulation ability is calculated in different sectors, and the influence of the modulation ratio and power factor is explored. Finally, the voltage regulation ability under the sudden load and the flying capacitor voltage deviating from the rated value were investigated through simulation and experiments, which verified the correctness of the proposed theory.

A review of exact results for fluctuation formulas in random matrix theory

Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often large N universal forms for this correlation after smoothing, which results in particularly simple limiting formulas for the fluctuation of the linear statistics. We review these limiting formulas, derived in the simplest cases as corollaries of explicit knowledge of the truncated two-point correlation. One of the large N limits is to scale the eigenvalues so that limiting support is compact, and the linear statistics vary on the scale of the support. This is a global scaling. The other, where a thermodynamic limit is first taken so that the spacing between eigenvalues is of order unity, and then a scale imposed on the test functions so they are slowly varying, is the bulk scaling. The latter was already identified as a probe of random matrix characteristics for quantum spectra in the pioneering work of Dyson and Mehta.

Influence of conversion on dielectric constant of Dicyandiamide cured epoxy resin:a molecular dynamic simulation and experiment study

In this study, molecular dynamic simulation and experiment study are combined to explore the main control factors of dielectric constant of Dicyandiamide cured epoxy resin. The density and glass transition temperature obtained by experiment and simulation were compared to verify the rationality of simulation models. Then dielectric constant was calculated by dipole fluctuation formula, here motion mobility, polarity, and free volume were employed to interpret the influence mechanism of conversion on dielectric constant. Results indicate that before gelation the dielectric constant is controlled by the content of unreacted monomers especially dicyandiamide, and after gelation it is dominated by the segmental mobility, hydroxyl group density and free volume, where the influence of segmental mobility is more significant than that of free volume and hydroxyl group density.

Densities, Viscosities, Thermal Expansivities, and Isothermal Compressibilities of Carbonated Hydroalcoholic Solutions for Applications in Sparkling Beverages.

Densities, viscosities, isothermal compressibilities, and thermal expansivities of carbonated hydroalcoholic solutions relevant for sparkling beverages are evaluated by molecular dynamics simulations as a function of temperature and alcoholic degree. They are compared with available experimental data, among which new measurements of densities and viscosities are performed in that respect. The OPC water model seems to yield the most accurate results, and the choice of CO2 model has little influence on the results. Theoretical densities obtained with the OPC model typically deviate by ∼2 kg m-3 from experimental data. At low alcoholic degrees (<9% EtOH vol), experimental viscosities lie in between theoretical values derived from the Stokes-Einstein formula and the calculation of transverse current autocorrelation functions, but at higher alcoholic degrees (≥9% EtOH vol), the Stokes-Einstein relation leads to viscosities in quantitative agreement with experiments. Isothermal compressibilities estimated with a fluctuation formula roughly extend from 0.40 to 0.49 GPa-1 in close agreement with the experimental range of values. However, thermal expansivities are found to significantly overestimate experimental data, a behavior that is partly attributed to the low temperature of maximum density of the OPC model. Despite this discrepancy, our molecular model seems to be suitable for describing several transport and thermodynamic properties of carbonated hydroalcoholic solutions. It could therefore serve as a starting point to build more realistic models for carbonated beverages, from fizzy drinks to sparkling wines.

Calculation of Heat Capacity Changes in Enzyme Catalysis and Ligand Binding.

It has been suggested that heat capacity changes in enzyme catalysis may be the underlying reason for temperature optima that are not related to unfolding of the enzyme. If this were to be a common phenomenon, it would have major implications for our interpretation of enzyme kinetics. In most cases, the support for the possible existence of a nonzero (negative) activation heat capacity, however, only relies on fitting such a kinetic model to experimental data. It is therefore of fundamental interest to try to use computer simulations to address this issue. One way is simply to calculate the temperature dependence of the activation free energy and determine whether the relationship is linear or not. An alternative approach is to calculate the absolute heat capacities of the reactant and transition states from plain molecular dynamics simulations using either the temperature derivative or fluctuation formula for the enthalpy. Here, we examine these different approaches for a designer enzyme with a temperature optimum that is not caused by unfolding. Benchmark calculations for the heat capacity of liquid water are first carried out using different thermostats. It is shown that the derivative formula for the heat capacity is generally the most robust and insensitive to the thermostat used and its parameters. The enzyme calculations using this method give results in agreement with direct calculations of activation free energies and show no sign of a negative activation heat capacity. We also provide a simple scheme for the calculation of binding heat capacity changes, which is of clear interest in ligand design, and demonstrate it for substrate binding to the designer enzyme. Neither in that case do the simulations predict any negative heat capacity change.

AC Fault Ride-Through Strategy of a Transformerless Soft Normally Open Point

This paper focuses on the soft normally open point (SNOP) which has no transformers and connects to the 10 kV distribution network through the arc suppression coil grounding mode. A mathematical model containing positive-, negative-, and zero-sequence components under AC fault is established by the circuit analysis and the sequence component decomposition. Then the voltage fluctuation mechanism at the DC side and the non-fault AC side caused by the zero-sequence voltage on the fault side is analyzed under the case without transformers. Taking the single-phase grounding fault as an example, the fluctuation formula of the DC voltage and AC voltage is deduced in detail. Based on the theoretical analysis, the zero-sequence control strategy and the sub-module improvement strategy of the modular multilevel converter (MMC) are proposed. A back-to-back SNOP simulation model is established in PSCAD/EMTDC. The simulation results verify the accuracy of the theoretical analysis, as well as the validity of zero-sequence control and MMC topology improvement strategies.

A compact formula for the quantum fluctuations of energy

A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the canonical ensemble if the size is large enough. Not only one can use our expression to find the limit of the concepts of energy density or fluid element in connection to relativistic heavy-ion collisions, but also in other areas of physics where one studies matter with high temperature and velocity.

Jordan in The Church of The Higher Hilbert Space: Entanglement and Thermal Fluctuations

I revisit Jordan's derivation of Einstein's formula for energy fluctuations in the black body in thermal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctuations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan's treatment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein's result despite not using thermal states of radiation is that he focuses on fluctuations in a small (compared to the whole) volume of the black body. The state of radiation in a small volume is highly entangled to the rest of the black body which leads to the correct fluctuations even though the overall state might, in fact, be assumed to be pure (i.e. at zero temperature). I present a simple derivation of the fluctuations formula as an instance of mixed states being reductions of higher level pure states, a representation that is affectionately known as "Church of the Higher Hilbert Space". According to this view of mixed states, temperature is nothing but the amount of entanglement between the system and its environment.Quanta 2022; 11: 1–4.

Development of tools for local elasticity calculations in biomolecular simulations

Mechanical properties of subcellular components such as lipid membranes play an essential role in modulating numerous biological functions including membrane fission and fusion, organelle and cellular shaping, cardiovascular control and development, osmotic regulation, and touch and pain sensing. Here, I will present our recent advances on the implementation of general 3D local elasticity calculations into the open-source library MDStress and the GROMACS-LS post-processing analysis code. We make use of stress-stress fluctuation formulas to compute the complete elasticity tensor from equilibrium simulations.

Limitations and Hypothesis Underlying the Application of CIDA Price Fluctuation Formula in Sri Lanka

The CIDA price fluctuation formula has been recommended in construction projects of more than three months’ duration. The aim is to recover unforeseen costs due to open market escalation, at least to some extent. The industrial perception has not however been researched in detail for further improvements. This research is to gauge the industrial enthusiasm towards the CIDA price fluctuation formula as a means of recovery of loss. The objectives are to disclose the limitations and hypothesis underlying its application, reveal the context in which it operates, measure the perception and key concerns of the users with regard to its reliability. At the outset, a desk review was carried out to identify the logic behind the formula. Existing pre-published information was tracked down in this review. A literature survey was carried to understand the context in which it operates. A series of interview was conducted to gauge the individual perception of practitioners who have been dealing with the formula application. A Maximum Variation Sampling method was adopted to ensure collecting a wide range of participants with different viewpoints and, a narrative analysis method was used to identify shared comprehension among the practitioners. It was found that many of the criticisms entail a valid basis. Hence, it is recommended to publish the indices regularly and calculate the input proportions jointly. It is also recommended to calculate cost adjustment factors for individual contracts and publish the price indices in district basis or introduce price adjustment procedure specific to each administrative district.&#x0D; Keywords: CIDA formula; Compensation; Open market vacillations; Price escalation

Entropy of earthquakes: application to Vrancea earthquakes

The entropy of earthquakes is derived by using the Gutenberg–Richter statistical distributions. Both canonical and microcanonical earthquake distributions are given, and Einstein’s fluctuation formula is deduced for earthquakes. The seismic activity of Vrancea in the period 1980–2019 is analyzed, for earthquakes with magnitude greater than two, and the results are compared with the theoretical results. It is shown that the parameter of the magnitude distribution exhibits a tendency of increasing with time, due to the accumulation of small-magnitude earthquakes, interrupted from time to time by ruptures towards smaller values, caused by earthquakes with greater magnitudes. These variations do not obey the normal distribution of the fluctuations. The (small) time variations of the distribution parameter provide a measure of the departure of the seismic activity from an equilibrium process. For Vrancea, these deviations are very small (up to 1% per year).

Strain control of layer-resolved negative capacitance in superlattices

Negative capacitance in BaTiO3/SrTiO3 superlattices is investigated by Monte Carlo simulations in an atomistic effective Hamiltonian model, using fluctuation formulas for responses to the local macroscopic field that incorporates depolarizing fields. We show that epitaxial strain can tune the negative capacitance of the BaTiO3 ferroelectric layer and the overall capacitance of the system. In addition, we predict and explain an original switching of the negative capacitance from the BaTiO3 layer to the SrTiO3 layer at low temperatures for intermediate strains.

General trace formula for heat flux fluctuations

Within the framework of macroscopic quantum electrodynamics and scattering theory, we derive the general expressions for the variance of radiative heat transfer between two arbitrarily shaped objects placed in an arbitrary environment in terms of their T-operators. The such derived expression is valid in the far- and near-field regime of thermal radiation as well as for reciprocal and non-reciprocal objects of any size within a reciprocal or non-reciprocal environment as long as the distances between the objects and their sizes are covered by the macroscopic approach. As special cases we discuss the variance of the radiative heat flux between two nanoparticles and between a nanoparticle and a substrate in the near- and far-field regime.

The stochastic motion of self-thermophoretic Janus particles

Langevin equations for the self-thermophoretic dynamics of Janus motors partially coated with an absorbing layer that is heated by a radiation field are presented. The derivation of these equations is based on fluctuating hydrodynamics and radiative heat transfer theory involving stochastic equations for bulk phases and surface processes that are consistent with microscopic reversibility. Expressions for the self-thermophoretic force and torque for arbitrary slip boundary conditions are obtained using the separation of time scales in the phenomenon. The overdamped Langevin equations for the colloid displacement and radiative heat transfer provide expressions for the self-thermophoretic velocity and its reciprocal contribution where an external force can influence the radiative heat transfer. A nonequilibrium fluctuation formula is also derived and shows how the probability density of the Janus particle displacement and radiation energy transfer during the time interval are related to the mechanical and thermal affinities that characterize the nonequilibrium system state.

From single particle motion to collective dynamics in Janus motor systems.

The single-particle and collective dynamics of systems comprising Janus motors, solvent, and reactive solute species maintained in nonequilibrium states are investigated. Reversible catalytic reactions with the solute species take place on the catalytic faces of the motors, and the nonequilibrium states are established either by imposing constant-concentration reservoirs that feed and remove reactive species or through out-of-equilibrium fluid phase reactions. We consider general intermolecular interactions between the Janus motor hemispheres and the reactive species. For single motors, we show that the reaction rate depends nonlinearly on an applied external force when the system is displaced far from equilibrium. We also show that a finite-time fluctuation formula derived for fixed catalytic particles describes the nonequilibrium reactive fluctuations of moving Janus motors. Simulation of the collective dynamics of small ensembles of Janus motors with reversible kinetics under nonequilibrium conditions is carried out, and the spatial and orientational correlations of dynamic cluster states are discussed. The conditions leading to the instability of the homogeneous motor distribution and the onset of nonequilibrium dynamical clustering are described.