State Equilibrium Research Articles

A Past Lunar Dynamo Thermally Driven by the Precession of Its Inner Core

AbstractThe Cassini state equilibrium associated with the precession of the Moon predicts that the mantle, fluid core, and solid inner core precess at different angles. We present estimates of the dissipation from viscous friction associated with the differential precession at the core‐mantle boundary (CMB), Qcmb, and at the inner core boundary (ICB), Qicb, as a function of the evolving lunar orbit. We focus on the latter and show that, provided the inner core was larger than 100 km, Qicb may have been as high as 1010–1011 W for most of the lunar history for a broad range of core density models. This is larger than the power required to maintain the fluid core in an adiabatic state; therefore, the heat released by the differential precession at the ICB can drive a past lunar dynamo by thermal convection. This dynamo can outlive the dynamo from precession at the CMB and may have shut off only relatively recently. Estimates of the magnetic field strength at the lunar surface are of the order of a few μT, compatible with the lunar paleomagnetic intensities recorded after 3 Ga. We further show that it is possible that a transition of the Cassini state associated with the inner core may have occurred as a result of the evolution of the lunar orbit. The heat flux associated with Qicb can be of the order of a few mW m−2, which should slow down inner core growth and be included in thermal evolution models of the lunar core.

Process-independent construction stage analysis of self-anchored suspension bridges

The construction process of self-anchored suspension (SAS) bridges undergoes frequent system transformations and loadings, accompanied by complex strong geometric and contact nonlinear behaviours. The accurate state assessment of such a process generally requires the nonlinear finite element analysis (FEA) to perform a stage-by-stage forward, cumulative calculation based on the principle of incremental superposition. This sort of calculation means that the structural equilibrium of any intermediate state of the process, referred to as a construction stage, must be accumulated from its previous construction loading history, which is susceptible to computational effort and divergence limitations. This paper overcomes these limitations by proposing a direct and fast method that is independent of the cumulative calculation in the analysis of any specified construction stage, in favour of the construction optimization design and uncertainty analysis. The unstrained assembly formats for the typical construction process of SAS bridges are established, and the elements with constant physical quantities as the characteristic parameters are used to describe the various structures, boundaries, loads and their changes during the construction. On this basis, an interactive analysis framework integrating the numerical iteration with the FEA is established to achieve an accurate equilibrium for the construction stages. An enhanced interval-genetic algorithm (IGA) is employed as the optimization engine to smoothly accelerate global convergence. The proposed framework is applied to an SAS bridge under construction, and the validity and performance of this approach are demonstrated by considering the in-field test data.

Effects of variable parameters on the behaviour of the single flexibly-mounted rod in a closely-packed array

Experiments of flow-induced vibrations using a closely-packed triangular rods array with a pitch-to-diameter ratio of 1.1 in water cross-flow were carried out to analyse the detected effects of system parameters in the frequency domain and vibration amplitudes. Single flexibly mounted rod with two degrees of freedom at each end of it was located in the second or the fourth row in the bundle with 21 row. Influence of increasing/decreasing flow, the test rod mass and support stiffness changes were analysed. Reynolds number based on the freestream velocity and a rod diameter was up to 1.64·104. Accelerometers and laser sensors were used to measure the time-varying response of the test rod. FFT approach was adopted to reconstruct the displacements from accelerometer measurements. Experimental results show that the behaviour of the flexibly-mounted rod is dependent on the flow time-history. Dominant flow-dependent and flow-independent frequencies were observed in the frequency domain. Changes in the frequency spectrum introduced by the test rod mass and support stiffness were identified. Oscillation regime of the test rod when the state equilibrium position becomes unstable with the limited oscillations was detected. Metamodeling approach was applied to develop mathematical approximation using three parameters: flow rate, stiffness coefficient and frequency ratio. Good accordance has been found between the inverse model and laboratory experiments.

Prethermalization in a classical phonon field: Slow relaxation of the number of phonons

We investigate the emergence of an astonishingly long pre-thermal plateau in a classical phonon field, here a harmonic chain with on-site pinning. Integrability is broken by a weak anharmonic on-site potential with strength $\lambda$. In the small $\lambda$ limit, the approach to equilibrium of a translation invariant initial state is described by kinetic theory. However, when the phonon band becomes narrow, we find that the (non-conserved) number of phonons relaxes on much longer time scales than kinetic. We establish rigorous bounds on the relaxation time, and develop a theory that yields exact predictions for the dissipation rate in the limit $\lambda \to 0$. We compare the theoretical predictions with data from molecular dynamics simulations and find good agreement. Our work shows how classical systems may exhibit phenomena which at the first glance appear to require quantization.

Effect of Ligand Field Strength on the Spin Crossover Behaviour in 5-X-SalEen (X=Me, Br and OMe) Based Fe(III) Complexes.

The reaction of Fe(NCS)3 prepared in situ in MeOH with 5-X-SalEen ligands (5-X-SalEen=condensation product of 5-substituted salicylaldehyde and N-ethylethylenediamine) provided three Fe(III) complexes, [Fe(5-X-SalEen)2 ]NCS; X=Me (1), X=Br (2), X=OMe (3). All the complexes reveal similar structural features but a very different magnetic profile. Complex 1 shows a gradual spin crossover while complexes 2 and 3 show a sharp spin transition. The T1/2 for complex 2 is 237 K while for complex 3 it is much higher with a value of 361 K. The spin transition temperature is shifted towards higher temperature with increasing electron-donation ability of the ligand substituents. This experimental observation has been rationalized with DFT calculations. UV-Vis and cyclic voltammetry studies support the fact that the electron density on the ligand increases from Me to Br to OMe substituents. To understand the change in spin states, temperature-dependent EPR spectra have been recorded. The spin state equilibrium in the liquid state has been probed with Evans NMR spectroscopic method, and thermodynamic parameters have been evaluated for all complexes.

Liquidity in High Resolution in Limit Order Markets

This paper investigates, in high resolution, the role of liquidity in a limit order market. Liquidity in these markets has two parts - a liquidity store and liquidity flow (time dimension). We model the liquidity residing in a limit order book and the liquidity flow from the latent order book, using a fully probabilistic model. Using a sample of stocks from NASDAQ 100 we find that liquidity residing in the order book, within five levels each on either side of the transaction price and the flow to this liquidity pool from the latent order book can explain the wealth traded through the trading system, when observed in business time. The explanatory power is satisfactory in high resolution and short periods of business time but weaker in aggregated longer time periods. We observe that the liquidity pool for large part of the trading day goes into a steady state equilibrium.

Non-competing persuaders

I study Bayesian persuasion games with multiple persuaders in which the persuaders are non-competing: all persuaders want the decision maker to take the same action, regardless of the state. In the case of a single persuader, it is known from previous research that the persuader-optimal information design leaves the decision maker with no surplus. In this paper, I show that with two or more non-competing persuaders and independent tests, there are always equilibria in which the decision maker receives surplus. If there is exogenous noise then the decision maker receives surplus in every symmetric equilibrium, provided the number of persuaders is sufficiently large; asymptotically, the decision maker learns the true state in every Pareto optimal symmetric equilibrium with infinitely many persuaders. Moreover, with sufficient exogenous noise, having more than one persuader not only improves the welfare of the decision maker but also improves the welfare of the persuaders.

Thermal Activation of Thin Filaments in Striated Muscle.

In skeletal and cardiac muscles, contraction is triggered by an increase in the intracellular Ca2+ concentration. During Ca2+ transients, Ca2+-binding to troponin C shifts the “on–off” equilibrium of the thin filament state toward the “on” sate, promoting actomyosin interaction. Likewise, recent studies have revealed that the thin filament state is under the influence of temperature; viz., an increase in temperature increases active force production. In this short review, we discuss the effects of temperature on the contractile performance of mammalian striated muscle at/around body temperature, focusing especially on the temperature-dependent shift of the “on–off” equilibrium of the thin filament state.

Observation of the magneto-optic Voigt effect in a paramagnetic diamond membrane

The magneto-optic Voigt effect is observed in a synthetic diamond membrane with a substitutional nitrogen defect concentration in the order of 200 ppm and a nitrogen-vacancy defect sub-ensemble generated through neutron irradiation and annealing. The measured polarisation rotation in the reflected light is observed to be quadratically proportional to the applied magnetic field and to the incident reflection angle. Additionally, it is observed to be modifiable by illuminating the diamond with a 532 nm laser. Spectral analysis of the reflected light under 532 nm illumination shows a slow narrowing of the spectral distribution, indicating a small increase in the overall magnetisation, as opposed to magnetisation degradation caused by heating. Further analysis of the optical power dependence suggest this may be related to a shift in the spin ensembles charge state equilibrium and, by extension, the resulting ensemble magnetisation.

An Option-Revenue Sharing Coordination Contract with Price and Sales Effort Dependent Demand

This study proposes a novel option-revenue sharing coordination contract framework. In the proposed model, the retailer determines the number of order sales effort. The manufacturer sets the price of products for the wholesale strategy. The investigated supply chain problem analyzes the results of different strategies. In the proposed coordination contract problem, two types of games including retailer-based game and manufacturer-based Stackelberg game are considered. In both cases the retailer adopts the value of order and the sales effort and the manufacturer determines the wholesale price. To assess the performance of the proposed contract, a wholesale and a basic selection contract are considered in the model. To obtain the Nash equilibrium in the retailer-based state of the proposed option-revenue sharing coordination contract problem, a hybrid algorithm consisting of a heuristic and a genetic algorithm is proposed by considering the computational complexities of the proposed model. A numerical comparison between the proposed contract and other cases demonstrates that the option-revenue sharing contract significantly dominates the basic option and the wholesale price contract. Finally, we implemented some numerical experiments on the critical parameters of the contract. Based on the results, increasing the price-dependency of demand results in less number of products ordered by the retailer.

Effective mass enhancement and ultrafast electron dynamics of Au(111) surface state coupled to a quantum well

The authors investigate the band dispersion and electron dynamics of the surface state of a gold quantum cavity grown on a tungsten substrate. They find a kink structure above the Fermi level that is consistent with a remarkable renormalization of the effective mass and electron relaxation times significantly slower than expected for a bulk metallic system. Their results demonstrate how the interplay between quantum confinement in the gold film and the electronic structure of the substrate determine the equilibrium and dynamical properties of the surface state

Are speculative bubbles welfare improving? A note on Wang and Wen (2012)

Wang and Wen (2012) show in a DSGE model that the existence of speculative bubbles are welfare improving. In their steady state analysis of the benchmark model the authors claim the existence of a unique steady state in the bubble equilibrium with a higher capital stock and hence higher output compared to the fundamental equilibrium. This is due to higher investment efficiency because firms can use bubble assets as a store of value when they are hit by an adverse investment shock. In this note we demonstrate that this claim is at odds with our finding of the existence of an additional, less favorable, steady state in the bubble equilibrium. In the new steady state, allocations are very similar to the steady state without bubbles, which implies a deterioration of investment efficiency, if the economy is in the new, less favorable bubble steady state.

By-passing fluctuation theorems

Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be by-passed if one allows for the use of catalysts---additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.

Distinct Regulation of σ 1 Receptor Multimerization by Its Agonists and Antagonists in Transfected Cells and Rat Liver Membranes.

Extensive studies have shown that the σ 1 receptor (σ 1R) interacts with and modulates the activity of multiple proteins with important biological functions. Recent crystal structures of σ 1R as a homotrimer differ from a dimer-tetramer model postulated earlier. It remains inconclusive whether ligand binding regulates σ 1R oligomerization. Here, novel nondenaturing gel methods and mutational analysis were used to examine σ 1R oligomerization. In transfected cells, σ 1R exhibited as multimers, dimers, and monomers. Overall, σ 1R agonists decreased, whereas σ 1R antagonists increased σ 1R multimers, suggesting that agonists and antagonists differentially affect the stability of σ 1R multimers. Endogenous σ 1R in rat liver membranes also showed similar regulation of oligomerization as in cells. Mutations at key residues lining the trimerization interface (Arg119, Asp195, Phe191, Trp136, and Gly91) abolished multimerization without disrupting dimerization. Intriguingly, truncation of the N terminus reduced σ 1R to apparent monomer. These results demonstrate that multiple domains play crucial roles in coordinating high-order quaternary organization of σ 1R. The E102Q σ 1R mutant implicated in juvenile amyotrophic lateral sclerosis formed dimers only, suggesting that dysregulation of σ 1R multimeric assembly may impair its function. Interestingly, oligomerization of σ 1R was pH-dependent and correlated with changes in [3H](+)-pentazocine binding affinity and Bmax Combined with mutational analysis, it is reasoned that σ 1R multimers possess high-affinity and high-capacity [3H](+)-pentazocine binding, whereas monomers likely lack binding. These results suggest that σ 1R may exist in interconvertible oligomeric states in a dynamic equilibrium. Further exploration of ligand-regulated σ 1R multimerization may provide novel approaches to modulate the function of σ 1R and its interacting proteins. SIGNIFICANCE STATEMENT: The σ 1 receptor (σ 1R) modulates the activities of various partner proteins. Recently, crystal structures of σ 1R were elucidated as homotrimers. This study used novel nondenaturing gel methods to examine σ1R oligomerization in transfected cells and rat liver membranes. Overall, agonist binding decreased, whereas antagonist binding increased σ 1R multimers, which comprised trimers and larger units. σ 1R multimers were shown to bind [3H](+)-pentazocine with high affinity and high capacity. Furthermore, mutational analysis revealed a crucial role of its N-terminal domain in σ 1R multimerization.

External Charges Influence Fluorescent Protein Proton Wires

Genetically encoded voltage indicators (GEVIs) based on the fluorescent protein Superecliptic pHluorin have been shown to alter fluorescent output in a voltage-dependent manner. The dimer affinity of the fluorescent proteins (FP) and specific charged residues in the dimer interface are involved in the mechanism of how the fluorescent output changes have been implicated in the optical signal. Here we show that the critical negative charge on the exterior of the β-can structure of the FP (A227D) can affect proton wires that ultimately affect the chromophore of the FP. When the negative charge is moved along the exterior of the β-barrel, the polarity of the voltage-dependent optical signal inverts. One hypothesis to explain this behavior is that the transient movement of the negative charge shifts the equilibrium of the protonation state of the chromophore. To test this hypothesis, alternating the excitation wavelength from 390 nm to 470 nm was performed revealing that the kinetics of the optical signal, voltage range of the optical signal, and the optimal linker length were wavelength dependent. These results suggest that the proton wires capable of responding to the external negative charge of a neighboring probe are different for the protonated chromophore and the anionic chromophore. To further investigate the effect on proton wires, several E222 mutations were tested which has been implicated as the proton release point for excited state proton transfer of GFP. The results imply that ArcLight-derived GEVIs can be used to alter and thereby study proton wires of fluorescent proteins. Combined with structural data, these GEVIs may enable the mapping of proton wires, which would enable the development of voltage sensors with large dynamic range.

Study of Tau N-Terminal Mutation, R5L, on Tau Interaction with the Microtubule Lattice

Understanding the physiological function of the intrinsically disordered microtubule associated protein (MAP) Tau has proven challenging. Tau, primarily expressed in neurons, is known to have a variety of axonal functions, including regulation of microtubule dynamics, modulation of kinesin motor motility, and participation in signaling cascades. Interestingly, research on the microtubule binding behavior of Tau reveals that Tau binds to the microtubule surface in a dynamic equilibrium between static and diffusive states. Although it is understood that the binding state equilibrium plays a role in physiological Tau function, such as modulation of kinesin motility, it is less understood how disease associated mutations affect Tau binding behavior and function. The canonical theory states that mutations in Tau reduce Tau affinity for the microtubule. Here, we investigate the role of an N-terminal disease associated mutation, R5L, in both the 3RS and 4RS Tau isoforms using an in vitro reconstituted system for single molecule Total Internal Reflection Fluorescence (smTIRF) Microscopy. Contrary to the canonical theory, we determined the R5L mutation does not reduce Tau affinity to the microtubule. This was seen across microtubule lattices and Tau isoforms. Currently, we are investigating the single molecule properties of microtubule bound R5L-Tau to better comprehend the consequence of the R5L mutation. Altogether, these results show the canonical theory of disease mechanism does not encompass all Tau mutations and the theory needs to be expanded. This work will inform the mechanisms by which N-terminal disease associated mutations alter Tau function.

Analysis of Cathode Reactions of Lithium Ion Cells Using Dynamic Electrochemical Impedance

We used dynamic electrochemical impedance spectroscopy (DEIS), a method that superimposes an alternating current on a direct current during battery charging and discharging, to analyze a cathode half-cell of lithium ion batteries. Based on the analysis using instantaneous impedances derived from time-interpolation of DEIS, a comparison between the instantaneous impedances and stationary impedances that are generally measured at the equilibrium of a specific state of charge (SOC), when no direct current is flowing (SEIS), have revealed that the charge transfer resistances (Rct) obtained by DEIS during charge (extraction of lithium in a cathode) always have lower values than Rct by DEIS during discharge (insertion of lithium), while the results obtained from SEIS are almost the same during charging and discharging. Moreover, the variations of Rct vs SOC during charge depend on C-rate, whereas those during discharge are independent of the C-rate. These variations of Rct observed in charging and discharging during DEIS are attributed to the differences of rate constants for charge transfer. The underlying cause of the series of variations of Rct on DEIS can be explained using the equation of Frumkin-Butler-Volmer with Rct, which was derived previously from cyclic voltammetry as a well-known dynamic electrochemical method.

Investigation on equation of state and ionization equilibrium for aluminum in warm dense matter regime

Warm dense matter is widely found in the high-energy-density-physics researches, such as inertial confinement fusion, X-ray source and wire-array Z-pinch. The equation of state and ionization equilibrium of material in warm dense matter regime play a significant role in explaining experimental results and simulations of physical process. In this paper, the Coulomb interaction between charged particles, and the excluded volume effect due to high density and polarization effect between neutral atoms and charged particles are considered in the equation of state for aluminum in warm dense matter regime. A non-ideal Saha equation is used to account for the ionization equilibrium. The data for pressure and concentration of particles of aluminum plasma are derived by iteration between equation of state and ionization equilibrium model. The pressure and average ionization degree of aluminum plasma are consistent with the calculation results from other models and relevant experimental data. The Coulomb interaction, which dominants the non-ideal effects, is insensitive to temperature and increases with density rising especially near the region of critical density. The excluded volume effect peaks at a density of ～0.5 g/cm<sup>3</sup>. The polarization effect first becomes stronger with density increasing and then decreases at a density of ～0.4 g/cm<sup>3</sup>. The ionization equilibrium results with density ranging from 1.0 × 10<sup>–4</sup> g/cm<sup>3</sup> to 3.0 g/cm<sup>3</sup> and temperature ranging from 1.0 × 10<sup>4</sup> K to 3.0 × 10<sup>4</sup> K reveal that the average ionization degree increases with density sharply increasing near the critical density. The non-ideal effects, which lead the ionization energy to decline and the effective ionization potential of specific ions in aluminum plasma to decrease substantially, are responsible for the sharp increase of average ionization degree near the region of critical density. When the temperature is lower than 12000 K, first and second stage of ionization occur in aluminum plasma, and the system is mainly composed of Al<sup>1+</sup>, Al<sup>2+</sup> and electrons. The average ionization degree can reach 2 at critical density. The third stage of ionization is dominant in the aluminum plasma when plasma temperature is higher than 12000 K. And then, the charged particles in the plasma are composed of Al<sup>3+</sup> and electrons, allowing the average ionization degree to reach 3 at critical density.

An Artificial Potential Field-Based Lithium-ion Battery SOC Equilibrium Method in Electric Vehicles

A novel cell equilibrium algorithm which is used for battery state of charge equilibrium of battery pack is proposed in this paper. Cell equilibrium algorithm is a key technology for lithium-ion battery pack in the energy storage systems. In order to eliminate the imbalance of battery state of charge, it’s generally controlled by adjusting the charging current. The artificial potential field can construct a virtual force function, which provides the mapping between state of charge deviation and charging current. Therefore, an artificial potential field-based equilibrium method to balance battery state of charge was proposed in this paper. By reasonably distributing the charging current of the battery, the equilibrium of the battery state of charge can be achieved. A laboratory testbed has been built to verify the effectiveness of the proposed method compared with conventional method. Experiment results analyzed the energy consumption and the convergence speed of state of charge deviation under artificial potential field control with different parameters.

To unravel the connection between the non-equilibrium and equilibrium solvation dynamics of tryptophan: success and failure of the linear response theory of fluorescence Stokes shift.

The connections between the non-equilibrium solvation dynamics upon optical transitions and the system's equilibrium fluctuations are explored in aqueous liquid. Linear response theory correlates time-dependent fluorescence with the equilibrium time correlation functions. In the previous work [T. Li, J. Chem. Theory Comput., 2017, 13, 1867], Stokes shift was explicitly decomposed into the contributions of various order time correlation functions on the excited state surface. Gaussian fluctuations of the solute–solvent interactions validate linear response theory. Correspondingly, the deviation of the Gaussian statistics causes the inefficiency of linear response evaluation. The above mechanism is thoroughly tested in this study. By employing molecular simulations, multiple non-equilibrium processes, not necessarily initiated from the ground state equilibrium minimum, were examined for tryptophan. Both the success and failure of linear response theory are found for this simple system and the mechanism is analyzed. These observations, assisted by the width dynamics, the initial state linear response approach, and the variation of the solvation structures, integrally verify the virtue of the excited state Gaussian statistics on the dynamics of Stokes shift.