Nonequilibrium Scheme Research Articles

A novel framework of the lattice Boltzmann model for multilayer shallow water systems

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.

A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies.

A master-slave control strategy of the multi-modular SMR

Small modular reactor (SMR) is a type of advanced reactor depending on its inherent safety, good economic performance, and multipurpose. SMR always adopts the multi-modular layout, which uses several nuclear steam supply systems (NSSSs) to supply steam to a common steam header. A pressurized water reactor (PWR) type multi-modular SMR (MSMR) system is studied in this paper. Due to the operation demands of continuity and flexibility during load following, a proper control strategy and operation scheme of the MSMR must be investigated.A master-slave control strategy is proposed for steam flow sharing control of the MSMR systems. Under the proposed control strategy, one of the NSSS modules is selected as the master control channel, and its feed water flow rate is regulated using the steam header pressure error. The remaining NSSS modules are treated as the slave channels. The feed water flow rate of the master channel is utilized to slave the other channels, which are flow-controlled.Three operation schemes are set according to different operation demands. (1) Equilibrium Scheme (EquS), in which every module undertakes the same load during the load following operation. (2) Non-equilibrium Scheme (NEquS), in which every module undertakes the different loads during the load following operation. This operation scheme manages more modules operate at full power to ensure its economy and operation simplicity. (3) Constant Output Scheme (ConS), which is mainly used during refueling or maintenance process. When one module is disturbed, other modules undertake its load to ensure the total power output constant. Based on these schemes, four typical operation cases are defined and simulated.Through the analysis of the simulation results, the suitable operation conditions for these operation schemes are suggested, and the relevant control strategy is verified.

Lattice kinetic scheme for the Navier-Stokes equations coupled with convection-diffusion equations

In this paper, we target two basic issues residing in some modified lattice kinetic schemes for the Navier-Stokes (NS) equations coupled with convection-diffusion equations (CDEs). First, a lattice Boltzmann (LB) model motivated by the lattice kinetic scheme (LKS) is presented for the NS equations coupled with CDEs. Due to the nonequilibrium schemes for the gradient terms contained in the equilibria as well as the discrete source term, the collision process of the present model can be implemented locally in both time and space. The Chapman-Enskog analysis shows that the macroscopic equations can be correctly recovered from the present model without additional assumptions. Second, we prove that the present modified LKS model, though written in the Bhatnagar-Gross-Krook (BGK) form, has two relaxation rates essentially. Based on this theoretical result, the modified lattice kinetic schemes in the literature should not be grouped as the BGK model, and the better numerical stability is intrinsically attributed to the adjustment of their two relaxation rates. Several benchmark thermal flow problems are simulated to validate the present model and the local nonequilibrium schemes for the shear rate and temperature gradient. The accuracy of the present model as well as its better numerical stability compared with the BGK model are verified, which supports our theoretical results. In addition, we also demonstrate that the regularized LB (RLB) model has two relaxation times as the present LKS model.

Post-transcriptional bursting in genes regulated by small RNA molecules.

Gene expression programs in living cells are highly dynamic due to spatiotemporal molecular signaling and inherent biochemical stochasticity. Here we study a mechanism based on molecule-to-molecule variability at the RNA level for the generation of bursts of protein production, which can lead to heterogeneity in a cell population. We develop a mathematical framework to show numerically and analytically that genes regulated post transcriptionally by small RNA molecules can exhibit such bursts due to different states of translation activity (on or off), mostly revealed in a regime of few molecules. We exploit this framework to compare transcriptional and post-transcriptional bursting and also to illustrate how to tune the resulting protein distribution with additional post-transcriptional regulations. Moreover, because RNA-RNA interactions are predictable with an energy model, we define the kinetic constants of on-off switching as functions of the two characteristic free-energy differences of the system, activation and formation, with a nonequilibrium scheme. Overall, post-transcriptional bursting represents a distinctive principle linking gene regulation to gene expression noise, which highlights the importance of the RNA layer beyond the simple information transfer paradigm and significantly contributes to the understanding of the intracellular processes from a first-principles perspective.

Current noise of the interacting resonant level model

We study the zero-frequency current noise of the interacting resonant level model for arbitrary bias voltages using a functional renormalization group approach. For this we extend the existing nonequilibrium scheme by deriving and solving flow equations for the current-vertex functions. On-resonance artificial divergences of the latter found in lowest-order perturbation theory in the two-particle interaction are consistently removed. Away from resonance they are shifted to higher orders. This allows us to gain a comprehensive picture of the current noise in the scaling limit. At high bias voltages, the current noise exhibits a universal power-law decay, whose exponent is to leading order in the interaction identical to that of the current. The effective charge on resonance is analyzed in detail employing properties of the vertex correction. We find that it is only modified to second or higher order in the two-particle interaction.

Stochastic Proofreading Mechanism Alleviates Crosstalk in Transcriptional Regulation.

Gene expression is controlled primarily by interactions between transcription factor proteins (TFs) and the regulatory DNA sequence, a process that can be captured well by thermodynamic models of regulation. These models, however, neglect regulatory crosstalk: the possibility that noncognate TFs could initiate transcription, with potentially disastrous effects for the cell. Here, we estimate the importance of crosstalk, suggest that its avoidance strongly constrains equilibrium models of TF binding, and propose an alternative nonequilibrium scheme that implements kinetic proofreading to suppress erroneous initiation. This proposal is consistent with the observed covalent modifications of the transcriptional apparatus and predicts increased noise in gene expression as a trade-off for improved specificity. Using information theory, we quantify this trade-off to find when optimal proofreading architectures are favored over their equilibrium counterparts. Such architectures exhibit significant super-Poisson noise at low expression in steady state.

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

Conformational Transition Pathway of GlpT Transporter, Characterized by Nonequilibrium Molecular Dynamics Simulations

Glycerol-3-phosphate transporter (GlpT) is a member of major facilitator superfamily (MFS), the largest family of secondary transporters. Similar to other transporters, GlpT is believed to function using an “alternating-access” mechanism during which it undergoes large conformational changes. The only available structure of GlpT is in the apo inward-facing (IF) state. In our earlier work using equilibrium molecular dynamics (MD) simulations, the binding site of GlpT was characterized and the initial substrate-induced closing on the cytoplasmic side was observed. However, an atomic model of the outward-facing (OF) state of GlpT and the IF-to-OF transition pathway remain unknown. Here we have used a novel approach based on nonequilibrium MD simulations to drive the transition of GlpT from its available IF state to its unknown OF state in an explicit membrane environment. Based on the interhelical symmetries, a set of non-conventional collective variables were defined for the transmembrane helices to specifically reflect the conformational changes involved during the IF-to-OF transition. The system was then steered along these collective variables in a nonequilibrium scheme. The obtained IF-to-OF transition pathway was further optimized adaptively by minimizing the nonequilibrium work, which is a good way to produce more realistic transition pathways. Thus, the protocol of inducing the transition was optimized after each simulation based on the resulted trajectory. Nonequilibrium work relations were used to analyze the trajectories and extract information about the OF state structure, the IF-to-OF transition mechanism, the intermediate/occluded states, and the characteristics of the OF-state binding site, providing insight about the general mechanism of MFS transporters and more generally introducing a novel approach to study the IF-to-OF transitions in membrane transporters.

Multiconfigurational self-consistent field linear response for the polarizable continuum model: Theory and application to ground and excited-state polarizabilities of para-nitroaniline in solution

This paper presents the linear response (LR) function for a multiconfigurational self-consistent field (MCSCF) molecular wave function for the integral equation formalism version of the polarizable continuum model (PCM). Both equilibrium and nonequilibrium PCM solvation schemes are described: The nonequilibrium scheme is applied to the calculation of excited state wave functions (Franck–Condon states) and/or of dynamic response properties. An important characteristic of the LR-PCM-MCSCF theory is the explicit inclusion of the effects of solvent dynamics, and this allows us to treat a large variety of time-dependent phenomena. Here, in particular, the theory is applied to the study of the solvent effect on transition energies and on static and dynamic polarizabilities of para-nitroaniline (pNA). The study of the polarizability dispersion of pNA is performed for the ground state and for low-lying electronic excited states including the charge transfer state. We compare our results with available experimental and theoretical data.

Equilibrium theory of the symmetry energy of finite nuclei

The nuclear symmetry energy of finite nuclei is calculated first in a nonequilibrium scheme in which the binding energy is a function of the central density parameter as well as the mass number and neutron excess parameter, i.e. E(kc, A, ξ), and then in an equilibrium scheme with the central density parameter given as a function of A and ξ in the form kcE(A, ξ) = kc0(1 + q1ξ−q2ξ2 + q3ξ3−q4ξ4 + … ), where kc0 = k∞(1 + ρ0) f−1 and the qj(A) and ρ0(A) depend on Coulomb and surface effects. In the equilibrium scheme, the symmetry energy coefficients are functions of mass number. A connection is made between the symmetry energy coefficients as calculated in the nonequilibrium (NE) and equilibrium schemes, and we find these coefficients to be, β0(A) = β0NE(kc0), β2(A) = β2NE(kc0)−[Formula: see text], etc. We find that the fourth order coefficient β4(A) is large and negative for all A, and is about −47 MeV in the region A ≈ 125 which agrees reasonably well with the −37 MeV value predicted by the Cameron–Elkin exponential mass formula. No linear term is found in the symmetry energy, but third, fifth, and higher order odd symmetry energy coefficients are found to be present. The alternation of the signs of the symmetry energy coefficients as well as the density expansion coefficients are in accordance with Le Chatelier's principle. As in the case of infinite nuclear matter, we find that the binding energy of nuclei with neutron excess is larger than that calculated assuming constant density, and that a negative isospin compression energy must be added to the constant density calculation of the energy if the correct binding is to be predicted. Finally, the general expression for the symmetry energy coefficients of order j is[Formula: see text]