Search Results (41)

We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of $\mathrm{PGL}(2,\mathbb{Q}\left(\sqrt{5}\right))$. Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a $62\%:38\%$ split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length ${\mathcal{D}}_{\alpha }={\xi }^z/\tau$, and a $\vartheta ={45}^{\circ }$ eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium. Full article

We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our calculations are presented in a pedagogical way with the explicit goal of serving as a tutorial from a physicists’ perspective into applying kinetic theory ideas beyond mean-field to active matter systems with essentially no prerequisites and yield predictions without free parameters that are in quantitative agreement with direct agent-based simulations Full article

Variable flow emitters are used in subsurface drip irrigation to address challenges in soil moisture transport. This study investigates the impact of flow channel structural parameters on the hydraulic performance and anticlogging ability of emitters using computational fluid dynamics (CFD) simulations and experimental tests. The results show that the realizable k–ε turbulence model can be used to simulate the flow field inside the variable flow emitter flow channel. The nRMSE between the measured (q_m) and simulated (q) values of the flow rate is 11.23%, and the relative error between the measured (x_m) and simulated (x) values of the flow index is 4.66%, which gives a high simulation accuracy. A polar analysis shows that the tooth angle (A) has the smallest effect on the effluent flow rate at 0.1 MPa (q_0.1), x, and particle passage rate (η) of the variable flow emitter. Flow channel depth (D), tooth spacing (B), and tooth height (E) have a different order of precedence in the influence of the three indices, which are D > B > E > A, B > E > D > A and E > B > D > A, respectively. The value of η is positively correlated with the mean flow velocity (v) and the mean turbulent kinetic energy (k) in the flow channel, and η tends to increase and then decrease with the increase of x. The retention time of the particles in the flow channel is closely related to the magnitude of v and k. Three multivariate lin ear regression equations (R² = 0.883–0.995) were constructed for q_0.1, x, and η versus the flow channel structural parameters. The optimal design combination of channel structure parameters for different scenarios was determined using the scipy.optimize.minimize function in Python 3.8.0. The research results provide a reference for the optimal design of variable flow emitters. Full article

Tropical cyclones (TCs) can be characterized as a 3D annular structure of elevated potential vorticity (PV). However, strong mature TCs often develop a secondary eyewall, leading to a 3D annular vortex with a double-eyewall structure. Using 2D linear stability analysis, it is shown that three types of barotropic instability (BI) are present for annular vortices with a double-eyewall structure: Type-1 BI across the secondary eyewall, Type-2 BI across the moat of the vortex, and Type-3 BI across the primary eyewall. The overall stability of these vortices (and the type of BI that develops) depends principally upon five vortex parameters: the thickness of the primary eyewall, the thickness of the secondary eyewall, the moat width, the vorticity ratio between the eye and the primary eyewall, and the vorticity ratio between the primary and secondary eyewall. The adiabatic evolution of 3D annular vortices with a double-eyewall structure is examined using a primitive equation model in normalized isobaric coordinates. It is shown that Type-2 BI is the most common type of BI for 3D annular vortices whose vortex parameters mimic TCs with a double-eyewall structure. During the onset of Type-2 BI, eddy kinetic energy budget analysis indicates that barotropic energy conversion from the mean azimuthal flow is the dominant energy source of the eddies, which produces a radial velocity field with a quadrupole structure. Absolute angular momentum budget analysis indicates that Type-2 BI generates azimuthally averaged radial outflow across the moat, and the eddies transport absolute angular momentum radially outward towards the secondary eyewall. The combination of these processes leads to the dissipation of the primary eyewall and the maintenance of the secondary eyewall for the vortex. Full article

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási–Albert (BA), Erdös–Rényi (ER), and Watts–Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers $R_M,R_0$ with and without mortality, respectively, and prove that $R_M<R_0$. For $R_M,R_0>1$, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others. Full article

At energy lower than 2 eV, the dispersion law of the electrons in a graphene sheet presents a linear dependence of the energy on the kinetic momentum, which is typical of photons and permits the description of the electrons as massless particles by means of the Dirac equation and the study of massless particles acted upon by forces. We analytically solve the Dirac equation of an electron in a graphene disk with radius of 10,000 atomic units pierced by a magnetic field and find the eigenenergies and eigenstates of the particles for spin up and down. The magnetic field ranges within three orders of magnitude and is found to confine the electron in the disk. States with a relatively large total angular momentum exist and can be considered in a vorticose condition; these states are seen to peak at different distances from the disk centre and can be used to store few bit of information. Full article

As is well known, magnetic fields in space are distributed very inhomogeneously. Sometimes, field distributions have forms of filaments with high magnetic field values. As many observations show, such a filamentation takes place in convective cells in the Sun and other astrophysical objects. This effect is associated with the frozenness of the magnetic field into a medium with high conductivity that leads to the compression of magnetic field lines and formation of magnetic filaments. We analytically show, based on the general analysis, that the magnetic field intensifies in the regions of downward flows in both two-dimensional and three-dimensional convective cells. These regions of the hyperbolic type in magnetic fields play the role of a specific attractor. This analysis was confirmed by numerical simulations of 2D roll-type convective cells. Without dissipation, the magnetic field grows exponentially in time and does not depend on the aspect ratio between the horizontal and vertical scales of the cell. An increase due to compression in the magnetic field of highly conductive plasma is saturated due to the natural limitation associated with dissipative effects when the maximum magnitude of a magnetic field is of the order of the root of the magnetic Reynolds number Re_m. For the solar convective zone, the mean kinetic energy density exceeds the mean magnetic energy density for at least two orders of magnitude, which allows one to use the kinematic approximation of the MHD induction equation. In this paper, based on the stability analysis, we explain why downward flows influence magnetic filaments, making them flatter with orientation along the interfaces between convective cells. Full article

The aim of this study is to better understand cross-reef wave-driven current characteristics, which are crucial to biological, ecological, and geomorphological processes within coral reefs. This study reports a set of new wave flume measurements to assess flow along the water depth and across a fringing reef profile under the action of a plunging breaker. Laboratory results are presented in view of cross-reef variations in both the wave height and the mean water level (MWL); the vertical profiles of wave-averaged mean currents below the wave trough and along the reef are also presented. To resolve the two-dimensional vertical (2DV) flow characteristics across the reef, Reynolds-Averaged Navier–Stokes (RANS) equations were solved using k-ω SST closure, modified to improve stability, and a Volume of Fluid (VOF) approach was used to capture the water surface. This numerical model was first validated via experimental measurements in view of waves and flows. It was then used to analyze the cross-reef distributions of the mean flow field, turbulent kinetic energy (TKE), and Reynolds shear stress across the reef. Full article

Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers. Full article

This paper presents a numerical model for simulating melting and solidification driven by natural convection, and validates it against a previous experiment. The experiment involved filling a rectangular aluminum enclosure with RT28HC Phase Change Material (PCM) to 95% of its capacity. To investigate the thermal behavior of the PCM during phase change, the enclosure underwent independent heating and cooling procedures. The simulation was conducted using ANSYS CFX^®, and the additional heat source (AHS) method was implemented in conjunction with the Boussinesq approximation to account for the latent heat during melting and solidification driven by natural convection. This allowed the calculation of temperature fields, the melted fraction, and fluid dynamics during phase change. The momentum equations were modified to include a source term that accounted for a gradual decrease in fluid velocity as the PCM transitions from solid to liquid. To account for density variation, an artificial specific heat curve was implemented based on the assumption that the product of density and specific heat remains constant during phase change. The proposed numerical model achieved good agreement with the experimental data, with an average root mean square error of 2.6% and 3.7% for temperature profiles during charging and discharging simulations, respectively. This model can be easily implemented in ANSYS CFX^® and accurately predicts charging and discharging kinetics, as well as stored/released energy, without any numerical convergence issues. Full article

In this paper, the numerical models are selected to simulate the hydrothermal plume based on the water temperature observation data of the Longqi hydrothermal field in the Southwest Indian Ridge (SWIR). Then, the unsteady Reynolds-averaged Navier–Stokes equations are solved to evaluate the performance of the Realizable k-ε (rke) model and the SST k-ω (sst) model in hydrothermal plume simulation. By comparing the calculated results with the Conductivity Temperature Depth (CTD) observation data and the literature results, the difference in prediction performance between the two models is evaluated. Before the numerical simulation, the optimal mesh parameters are determined by considering the grid independence test. The results show that the relative difference of the maximum plume height calculated by the two models is within 5%. Compared with the CTD 05-2, the rke model calculates the root mean square error of the velocity is 0.5081, which is smaller than that of the sst model. In terms of turbulent viscosity, the rke model is in good agreement with reference value in predicting turbulent viscosity. Therefore, the turbulent viscosity distribution calculated by the rke model is more consistent with the plume development process than that calculated by the sst model. In addition, the two models have the same effect on the prediction of turbulent kinetic energy and plume temperature. Full article

This research employs computational methods to analyze the velocity and mixture fraction distributions of a non-reacting Propane jet flow that is discharged into parallel co-flowing air under iso-thermal conditions. This study includes a comparison between the numerical results and experimental results obtained from the Sandia Laboratory (USA). The objective is to improve the understanding of flow structure and mixing mechanisms in situations where there is no involvement of chemical reactions or heat transfer. In this experiment, the Realizable k-ε eddy viscosity turbulence model with two equations was utilized to simulate turbulent flow on a nearly 2D plane (specifically, a 5-degree partition of the experimental cylinder domain). This was achieved using OpenFOAM open-source software and swak4Foam utility, with the reactingFoam solver being manipulated carefully. The selection of this turbulence model was based on its superior predictive capability for the spreading rate of both planar and round jets, as compared to other variants of the k-ε models. Numerical axial and radial profiles of different parameters were obtained for a mesh that is independent of the grid (mesh B). These profiles were then compared with experimental data to assess the accuracy of the numerical model. The parameters that are being referred to are mean velocities, turbulence kinetic energy, mean mixture fraction, mixture fraction half radius (L_f), and the mass flux diagram. The validity of the assumption that w߰ = v߰ for the determination of turbulence kinetic energy, k, seems to hold true in situations where experimental data is deficient in w߰. The simulations have successfully obtained the mean mixture fraction and its half radius, L_f, which is a measure of the jet’s width. These values were determined from radial profiles taken at specific locations along the X-axis, including x/D = 0, 4, 15, 30, and 50. The accuracy of the mean vertical velocity fields in the X-direction (U_mean) is noticeable, despite being less well-captured. The resolution of mean vertical velocity fields in the Y-direction (V_mean) is comparatively lower. The accuracy of turbulence kinetic energy (k) is moderate when it is within the range of U_mean and V_mean. The absence of empirical data for absolute pressure (p) is compensated by the provision of numerical pressure contours. Full article

Recrystallization kinetics and two critical temperatures—the non-recrystallization temperature T_NR and the static recrystallization critical temperature T_SRCT—of five Nb, Ti, and V microalloyed steel grades are evaluated. The experimental examination is realized by employing isothermal double-hit compression tests and continuous hot torsion tests, both performed on a Gleeble^® 3800 thermo-mechanical simulator. The experimental results are used for the critical assessment of predicted T_NR using four empirical equations from the literature, and for the validation of simulated T_NR and T_SRCT. The thermokinetic computer simulations are realized using the mean-field microstructure modeling software MatCalc. Analysis shows that higher microalloying contents increase both critical temperatures, T_NR and T_SRCT, whereby the effect of recrystallization retardation of Nb is more pronounced than that of Ti or V. The most accurate reproduction of the experimental recrystallization behavior of the five examined steel grades is realized by the employed physics-based simulation approach. Full article

Swirling flames are widely used in engineering to intensify mixing and stabilize combustion in gas turbine power plants and industrial burners. Swirling induces new instability modes, leading to intensification of coherent structures, asymmetric geometry, vortex core precession, and flame oscillations. Large-Eddy Simulation (LES) has the capability to furnish more accurate and reliable results than the simulations based on Reynolds-averaged Navier–Stokes equations (RANS). Subgrid-scale models in LES need to describe the backscatter (local transfer of kinetic energy from small scales to larger scales) that is intensified in swirling flames. In this paper, the Differential Subgrid Stress Model (DSM), previously developed by the authors, is assessed using an experimental database from Sydney University on swirl-stabilized turbulent unconfined non-premixed methane-air flame. Regime without vortex precession is simulated numerically using the DSM and Smagorinsky subgrid-scale model. Experimental measurements of mean velocity, profiles of mass fractions, and temperature are used for comparison with the simulation data. The standard Smagorinsky model is considered the basic approach. Differences in the flow field statistics obtained in both subgrid-scale LES models are analyzed and discussed. The importance of taking the backscatter into account is highlighted. Full article

Boundary layer pumps, although attractive due to their compactness, robustness and multi-fluid and phase-handling capability, have been reported to have low experimental efficiencies despite optimistic predictions from analytical models. A lower-order flow-physics-based analytical model that can be used as a 1D design code for sizing and predicting pump performance is described. The rotor component is modelled by means of the Navier–Stokes equations as simplified using velocity profiles in the inter-disk gap, while the volute is modelled using kinetic-energy-based coefficients inspired by centrifugal pumps. The code can predict the rotor outlet and overall pump pressure ratio with an around 3% and 10% average error, respectively, compared to the reference experimental data for a water pump. Moreover, 3D RANS flow-field explorations of the rotor are carried out for different inter-disk gaps to provide insights concerning the improvement of the 1D design code for the better prediction of the overall pump performance. Improvements in volute loss modelling through the inclusion of realistic flow properties at the rotor outlet rather than the detailed resolution of the velocity profiles within the rotor are suggested as guidelines for improved predictions. Such improved design codes could close the gap between predictions and experimental values, thereby paving the way for the appropriate sizing of boundary layer pumps for several applications, including aircraft thermal management. Full article