Uniform Gradient Research Articles

Robustness of Stark many-body localization in the J1−J2 Heisenberg model

Stark many-body localization (SMBL) is a phenomenon observed in interacting systems with a nearly uniform spatial gradient applied field. Contrasting to the traditional many-body localization phenomenon, SMBL does not require disorder. Here we investigate SMBL in a spin-$1/2$ described by a Heisenberg model including a next-nearest-neighbor exchange coupling. By employing an exact diagonalization approach and time evolution calculation we analyze both level spacing ratio (LSR) statistics of the Hamiltonian model as well as the dynamics of the system from a given initial state. Our results reveals that for zero field in our finite system, LSR statistics suggest localization while the dynamics shows thermalization, which has been attributed to a finite-size effect. Slightly nonuniform field gradient, LSR statistic predictions agree very well with the dynamics of the physical quantities indicating delocalization and localization for small and large field gradient, respectively. More interestingly, we find that localization is robust in the presence of next-nearest-neighbor coupling in the Hamiltonian. Moreover, this coupling can be tuned to enhance SMBL in the system, meaning that localized regimes can be obtained for smaller field gradient as compared to the traditional nearest-neighbor isotropic Heisenberg model.

Thermocapillary droplet migration in a vertical temperature gradient controlled by thermal radiations

Thermocapillary migration of a droplet in a vertical temperature gradient controlled by uniform and non-uniform thermal radiations is theoretically analyzed and numerically investigated. A non-dimensionlized thermal radiation number is proposed to quantitatively depict the intensity ratio of the thermal radiation flux to the uniform temperature gradient. From the momentum and energy equations at zero limits of Reynolds and Marangoni numbers, analytical results for the uniform and non-uniform thermal radiations are determined. The steady migration velocity raises with the increasing of the thermal radiation number. By using the front-tracking method, it is observed that thermocapillary droplet migration under the uniform thermal radiation at moderate Marangoni and moderate thermal radiation numbers reaches a steady process. The steady migration velocity decreases with the increasing of Marangoni number and increases with the increasing of thermal radiation number. Moreover, the intensity of thermal energy transferred from the interface to both fluids depends on the volume heat capacity ratio. For the larger/smaller volume heat capacity ratio, more heat is transferred into the continuous phase fluid/the droplet. Furthermore, when the uniform thermal radiation is replaced by the non-uniform ones, the time evolutions, the structures of temperature fields, and parameter dependencies of thermocapillary droplet migration at moderate Marangoni and moderate thermal radiation numbers remain qualitatively unchanged. This study provides a profound understanding of thermocapillary droplet migration in a vertical temperature gradient controlled by thermal radiations, which is of great significance for practical applications in microgravity and microfluidic fields.

Nanofluidic chips for cryo-EM structure determination from picoliter sample volumes.

Cryogenic electron microscopy has become an essential tool for structure determination of biological macromolecules. In practice, the difficulty to reliably prepare samples with uniform ice thickness still represents a barrier for routine high-resolution imaging and limits the current throughput of the technique. We show that a nanofluidic sample support with well-defined geometry can be used to prepare cryo-EM specimens with reproducible ice thickness from picoliter sample volumes. The sample solution is contained in electron-transparent nanochannels that provide uniform thickness gradients without further optimisation and eliminate the potentially destructive air-water interface. We demonstrate the possibility to perform high-resolution structure determination with three standard protein specimens. Nanofabricated sample supports bear potential to automate the cryo-EM workflow, and to explore new frontiers for cryo-EM applications such as time-resolved imaging and high-throughput screening.

Influence of Strength Mismatch on Microstructural Evolution and Mechanical Behaviors for Q390/Q690 Ferritic Steel Dissimilar Welded Joints

For the structural integrity of weldments, it is necessary to ascertain acceptable strength mismatch mode when dissimilar parent materials are welded together. Herein, multilayer and multi‐pass CO2 gas shielded welding is carried out to manufacture two dissimilar welded joints of Q390 and Q690 steels using two filler materials with different strength levels. A comparative assessment of both strength mismatch modes is done based on microstructural characterization and mechanical testing. The results show that the weld metal (WM) with predominantly fine acicular ferrite (about 80 pct) and granular bainite has a more excellent combination of strength and toughness compared to the WM mainly composed of polygonal ferrite and degenerated pearlite, and the weakest link of the welded joint has transferred from the WM to the Q390‐side heat‐affected zone. The acceptable strength mismatch relationship of the dissimilar welded structures is revealed, e.g., the hardness in the welded joint should present a uniform gradient distribution. Herein, the gradient difference in the equivalent yield strength (calculated from their hardness) between adjacent areas is ≈170 MPa.

Optimal design of a novel crash box with functional gradient negative Poisson’s ratio structure

Crashworthiness and anti-vibration performance play critical roles in the performance of passenger cars. Aiming at enhancing the crash resistance and vibration resistance of vehicles thus providing good protection for passengers and drivers, a novel crash box with three-dimensional double arrow type negative Poisson’s ratio structure with functional gradient filling inner core (FGNPR crash box) is introduced in this paper and its performance is studied in detail through the comparison with the conventional crash box and the crash box filled with the uniform gradient negative Poisson’s ratio structure (NPR crash box) in crashworthiness and vibration resistance. Furthermore, range analysis is used to screen out the design variables that have little influence on the evaluation indexes and eliminate them. Based on these, neighborhood cultivation genetic algorithm (NCGA) and non-dominated sorting genetic algorithm-ii (NSGA-II) are selected as the optimization algorithms to carry out optimization design respectively and a comparison is made between the two suboptimal results screened out based on the normal boundary intersection (NBI) method to determine the overall optimal solution. Results show that the optimized FGNPR crash box has better crashworthiness and vibration resistance over the other crash boxes and its performance is further verified based on the peak acceleration of B-pillar in full vehicle crash condition. This paper provides some theoretical reference support for the development and exploration of automobile crash box systems.

A 3D numerical study on tsunamis ascending a river

ABSTRACT Three-dimensional numerical simulations were generated for tsunamis ascending processes with different river topographies. As tsunamis propagated in a narrow river, the radius of curvature around the first wave peak decreased, increasing the tsunami height with wave disintegration until the second tsunami height peak appeared. The diffracted waves also entered the river channel, causing an increase in tsunami height in the vicinity of the riverbank at the estuary. The tsunami height increased in a uniform riverbed gradient and narrower river width toward the upstream, based on the shallowing and energy concentration. As the angle between the riverbank line and coastline at the estuary was acute, the tsunami height was reduced because the diffracted waves were difficult to enter the river. The tsunami height in the rivers increased as the ratio of representative wavelength to river width was increased. The maximum tsunami height in the bore-shaped wave was larger than in the solitary wave with the same incident wave height. In the case of tsunami propagation in the compound cross-section river, multiple crestlines appeared because the tsunamis traveling diagonally in the flood channel showed multiple reflections both on the riverbank and between the flood and main channels.

Numerical study of droplet thermocapillary migration behavior on wettability-confined tracks using a three-dimensional color-gradient lattice Boltzmann model

Thermocapillary migration describes the phenomenon whereby liquid droplets move from warm to cold regions on a nonuniformly heated hydrophilic surface. Surface modifications can be applied to manipulate this migration process. In the present study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the droplet migration behavior on a series of wettability-confined tracks subject to a uniform temperature gradient. The model is validated by simulating the thermocapillary-driven flow with two superimposed planar fluids in a heated microchannel and the capillary penetration of a wetting fluid in a capillary tube. An in-depth study of the wettability-confined tracks confirms the capacity to manipulate the droplet migration process, that is, the wettability-confined tracks can accelerate thermocapillary migration compared with a smooth surface. The effects of changes in the viscosity ratio and interfacial tension are investigated, and it is found that a lower viscosity ratio and larger interfacial tension cause the droplet to migrate faster. Moreover, a systematic study of the track vertex angle is conducted, and the mechanism through which this parameter influences the droplet migration is analyzed. Then the effect of the track wettability on droplet migration is explored and analyzed. Finally, a serial wettability-confined track is designed to realize long-distance droplet migration, and the narrow side width of the connection region is found to play a key role in determining whether the droplets can migrate over long distances. The results provide some guidance for designing tracks that enable precise droplet migration control.

Dynamics of patchy vegetation patterns in the two-dimensional generalized Klausmeier model

<p style='text-indent:20px;'>We study the dynamical and steady-state behavior of self-organized spatially localized patches or "spots" of vegetation for the Klausmeier reaction-diffusion (RD) system of spatial ecology that models the interaction between surface water and vegetation biomass on a 2-D spatial landscape with a spatially uniform terrain slope gradient. In this context, we develop and implement a hybrid asymptotic-numerical theory to analyze the existence, linear stability, and slow dynamics of multi-spot quasi-equilibrium spot patterns for the Klausmeier model in the singularly perturbed limit where the biomass diffusivity is much smaller than that of the water resource. From the resulting differential-algebraic (DAE) system of ODEs for the spot locations, one primary focus is to analyze how the constant slope gradient influences the steady-state spot configuration. Our second primary focus is to examine bifurcations in quasi-equilibrium multi-spot patterns that are triggered by a slowly varying time-dependent rainfall rate. Many full numerical simulations of the Klausmeier RD system are performed both to illustrate the effect of the terrain slope and rainfall rate on localized spot patterns, as well as to validate the predictions from our hybrid asymptotic-numerical theory.</p>

Thermomechanical behavior of polymeric periodic structures

Additive manufacturing (AM) enables the fabrication of periodic structures with regular repeat units and tailorable mechanical properties. Polymer-based AM processes, such as fused filament fabrication (FFF), permit rapid, low-cost fabrication of periodic structures from a wide range of materials. However, the mechanical properties of polymers are strongly affected by temperature, especially near the glass transition temperature (T g ), which has a significant impact on the design and application of the structures. Herein, we utilize a coupled experimental and computational approach to evaluate the mechanical behavior of polymeric periodic structures (PPS) with uniform and spatially varying temperatures that span T g . Individual unit cells (square, auxetic, and honeycomb) are additively manufactured from polylactic acid (PLA) (T g = 54 °C) and experimentally evaluated by dynamic mechanical analysis (DMA) using a tension test fixture and thermal chamber. The unit cells are subjected to sequential tension and compression tests, up to a maximum of +/−20% strain, which are repeated from 40 °C to 65 °C in 5 °C increments. Maximum forces vary by two orders of magnitude when temperature varies across T g , and a hysteresis loop is observed for temperatures 14 °C below T g . This indicates that viscoelasticity has a significant impact on the mechanical properties of the structure below T g and that the structures are capable of dissipating energy. Experimental force-displacement and energy dissipation results agree favorably with results from a multiphysics finite element framework, which utilizes bulk material properties as inputs. The computational framework is then applied to structures comprising tessellated unit cells to evaluate the effects of uniform temperatures and temperature gradients on mechanical properties. The results demonstrate that non-uniform temperature fields can produce spatial variation of mechanical properties, such as Poisson’s ratio, throughout the structure. Insight obtained in this investigation provides guidelines for the design, fabrication, and implementation of PPS operating across a range of temperatures that passively modifies their mechanical properties and energy dissipation characteristics. • Thermomechanical analysis of square, honeycomb, and auxetic periodic structures. • Experimental and computational analysis of 3D printed PLA across glass transition. • Thermal gradients spatially affect array mechanical properties (Poisson’s ratio). • Square unit cell and honeycomb array dissipate highest energy per unit mass. • Applicable to other polymers and structures by updating bulk finite element inputs.

Mechanical design of uniform strain-gradient schemes for transverse and longitudinal flexoelectricity

Flexoelectricity is an electro-mechanical coupling effect in which dielectric materials polarize in response to deformation gradients. Typical models—including bending beams, trapezoidal terraces, and torquing bars—are adopted to generate strain gradients for studying flexoelectricity. Also, non-uniformities are introduced, which can induce possible problems related to electric polarization induced by higher-order components of the non-uniform strain gradient. Mechanical design is proposed to solve the problem of higher order components. Specifically, we propose mechanical design of two uniform strain-gradient schemes for transverse and longitudinal flexoelectricity—a special-designed beam and a circular terrace. Theoretical and numerical analysis support the uniformity of strain gradients of these designs. Experiments were conducted to obtain the two types of flexoelectric response of uniform strain-gradient schemes. By proposing a way to achieve uniform strain gradient through mechanical design, this work promotes research on flexoelectricity by eliminating possible impacts of non-uniform strain gradients. A uniform strain-gradient beam is an ideal tool for studying uniform strain gradient, and is applicable to various avenues of research besides flexoelectricity.

Dynamic response of density-graded foam subjected to soft impact

The density-graded foam materials are gaining traction due to their enhanced impact and blast resistance capacities. However, current knowledge in the impact response of density-graded foam is limited to rigid impact, which narrows the design space of target materials. In particular, three main issues remain unclear, i.e., (1) how to quantify soft impact response, (2) what is the reduction of deformation and transferred stress from soft impact as compared to rigid impact, (3) whether density-graded foam can reduce the transferred stress from soft impact. To address these knowledge gaps, an analytical model based on the double shock wave theory is established by using a deformable projectile impinging onto a density-graded foam target. The dynamic stress at the supported end is analyzed for uniform, positive, and negative density gradients. The results indicate that the deformation process due to impact from deformable projectile is vastly different from that of traditional rigid projectile, with the former causing 27.42% smaller deformation and 9.87% stress reduction of the graded foam target, and three separate velocities can be observed throughout the soft impact process. The findings indicate lower mechanical requirements of target materials for soft projectile impact protections, potentially leading to weight and cost savings.

Hydrogen nitrogening in great discharge with AC power

The paper substantiates and experimentally shows the possibility of anhydrous nitriding in a glow discharge (BATR) with AC power supply (AC), as well as the possibility of switching the shape of pulses, changing their polarity, which is solved by introducing a glow discharge nitriding device with a power source alternating current of a given frequency. The analysis of the results of metallographic studies of the modified layer indicated the presence of a more uniform gradient of hardness in depth (gradient decreased by 1.7 - 3.5 times), which increases the wear resistance of parts and quality indicators of strengthening parts while reducing processing costs and installation costs. At BATR in CCR with supply of current of industrial frequency the installation for realization of process becomes cheaper. The latter factor will contribute, among other aspects, to the wider introduction of BATR technologies. The use of alternating current affects the course and results of nitriding, as periodic changes in the polarity of the electrodes of the chamber contributes to the cleaning of the surface from the adsorption layer, which positively affects the nature of nitrogen saturation (gradient of microhardness times), contributes to a significant change in the phase composition of the surface modified layer and allows to expand the technological capabilities of nitriding in the direction of obtaining the required performance characteristics of working surfaces, in particular tribological characteristics

Efficient numerical model for effective thermal conductivity of concrete with aggregates of different morphologies and imperfect interfaces

The existing numerical model for predicting the effective coefficient of thermal conductivity (CTC) of concrete usually ignores its mesostructure such as the three dimensional (3D) irregular aggregate morphology, imperfect interface, phase in voids, and spatial distribution of aggregates. Meanwhile, most numerical models adopt the uniform temperature gradient in the homogenisation process, resulting in the larger model size required for convergence and lower post-processing efficiency. An algorithm to generate concrete with aggregates of different morphologies and imperfect interfaces was proposed. Subsequently, a simple method of imposing the periodic boundary conditions and an efficient post-processing method were proposed, thereby reducing the time consumption in the numerical homogenisation substantially. In addition, based on the mesomechanical analytical model, DIGIMAT, and experimental data, the rationality of the proposed method and established models was validated, and the effect of the 3D mesostructure of concrete on its effective CTC was analysed. Results show that the concrete exhibits imperfect interfaces in its service life, especially in the dried working condition. The concrete gradation, phase in voids, and aggregate orientation have different degrees of influence on the effective CTC of concrete, and the effect of aggregate morphology can be ignored.

Structural performance of cold-formed steel built-up section beams under non-uniform bending

The experimental investigation and numerical analyses are presented in this paper on cold-formed steel built-up open and closed section beams under either uniform or non-uniform minor axis bending. To the best knowledge of the authors, this is the first study devoted to exploring the effect of non-uniform bending on the behaviour of cold-formed steel built-up section flexural members. In the experimental investigation, the built-up section specimens were assembled by fastening two individual channels as press-braked from G500 and G550 steel sheets. Four-point bending tests of eighteen specimens with varying moment distributions were conducted to examine the flexural performance of the built-up section members experiencing uniform bending and moment gradients. In the numerical simulation, the finite element models were established for the built-up section flexural members and calibrated against the experimental results in terms of moment-deflection response, failure mode and moment capacity. Based on the validated finite element models, additional 300 numerical data of the built-up section beams under uniform and non-uniform minor axis bending were generated through a parametric study. Subsequently, the comparison of moment capacities obtained from the 18 tests and 300 numerical predictions with nominal strengths was carried out to evaluate the appropriateness of the current direct strength method as prescribed in the North American Specification for the built-up section flexural members. Aimed to achieve more suitable strength predictions, the modified design rules were recommended in this study and proven to be generally reliable as well as accurate for the design of cold-formed steel built-up section beams.

Parametric study on the influence of material properties and geometry on the thermally induced bistability of composite laminates

This paper presents a parametric study on the key parameters that control the thermally induced bistability of cross-ply laminates. The influence of the material properties including the moduli of elasticity and the thermal expansion coefficients and the laminate’s geometry including the aspect ratio (AR) and the width-to-thickness ratio are investigated. The unsymmetric [Formula: see text] and the antisymmetric [Formula: see text] cross-ply laminates are investigated. Five key parameters are varied: the number of plies, the width-to-thickness ratio, the laminate’s aspect ratio, the ratio of the moduli of elasticity, and the ratio of the thermal expansion coefficients of the lamina. The laminate is assumed flat at the cured temperature and a uniform temperature gradient is applied until it is reduced to the room temperature. For each set of parameters, the stable equilibrium shapes of the laminate are obtained using a Ritz model. The ABAQUS finite element package is used to validate the model and an excellent agreement is obtained. Results that show the variation of the curvatures with the width-to-thickness ratio and the onset of the bistability for a variety of parameters are presented. The ratio of the moduli of elasticity and the thermal expansion coefficients significantly affect the critical width-to-thickness ratio at which the laminates become bistable. The unsymmetric laminates show bistability at a lower width-to-thickness ratio compared with the antisymmetric laminates. The results also show that the higher the aspect ratio, the lower the critical width-to-thickness ratio for stability for both laminates.

Analysis of the electrostatic field distribution in the hemispherical internal cell of radon monitors to estimate the collection efficiency of Po-218

The collection efficiency of the hemispherical internal cell of radon monitors depends on many factors, with the distribution of the electric field and the relative humidity of the air being particularly important. COMSOL is used to simulate an internal cell with a plastic upper surface. Simulation results show a relatively uniform gradient of the electric field. Assuming that the electric field felt by the positively charged Po-218 ions in the internal cell is a linear function of its radial coordinate, a mathematical model of the collection efficiency is proposed. From this model, we obtained the following: 1) under the same neutralization rate and potential, the electric field gradient has little effect on the collection efficiency; 2) under the same neutralization rate, the collection efficiency increases with the potential on the cell wall. If the neutralization rate is small, then the potential value for the maximum collection efficiency is also small. At a relative humidity of 6%–10%, the collection efficiency saturates for values of the electric potential on the cell wall larger than 5 kV; 3) under the same potential, a large neutralization rate corresponds to reduced collection efficiency. At high potential, the collection efficiency is relatively less affected by the neutralization rate. Higher collection efficiency can be achieved under high potential and low humidity conditions. This study provides a theoretical foundation to design the internal cell of radon monitor for improving the collection efficiency of Po-218.

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.

Hydrodynamic force acted on a solid translating in nonuniform stream

To predict the effect of the uniform gradient stream, the hydrodynamic force acting on a translating solid is studied following the Newman method. Some new hydrodynamic force formulas that are valid in both two-dimensional and three-dimensional flow are proposed. A new and efficient velocity-vector based method is proposed to compute the added mass that is required in the new formulas. Abundant numerical examples are designed to check the correctness of the new formulas and the validity of the Newman hypothesis adopted during the proof. Comparison with classical results shows that the formula proposed by Taylor and Newman are only two special cases of the present study. Comparison with some recent studies are also studied and their rationality is analyzed.

A comprehensive framework for hard-magnetic beams: Reduced-order theory, 3D simulations, and experiments

Thin beams made of magnetorheological elastomers embedded with hard-magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite element modeling (FEM), to describe the behavior of hard-MRE beams under both uniform and constant gradient magnetic fields. First, based on the Helmholtz free energy of bulk (3D) hard-MREs, we perform dimensional reduction to derive a 1D description and obtain the equilibrium equation of the beam through variational methods. In parallel, we extend the existing 3D continuum theory for hard-MREs to the general case of non-uniform fields by incorporating the magnetic body force induced by the field gradient and implementing it in FEM. Then, we validate the beam model and FEM using experiments on a cantilever beam in either a uniform or a constant gradient field, and identify the dimensionless parameters governing the magneto-elastic coupling. Further, a set of comparative numerical studies for different field configurations and magnetization profiles yields additional insight into the beam response. Our study builds on previous work on hard-MRE beams, while providing a more complete framework, both in terms of the methodologies used and the broader range of configurations considered, serving as a valuable predictive toolbox for the rational design of beam-like hard-magnetic structures.

On the effect of porosity and functional grading of 3D printable triply periodic minimal surface (TPMS) based architected lattices embedded with a phase change material

Triply Periodic Minimal Surface (TPMS) topologies have recently gain widespread attention due to their promising performance in several areas like structural strength enhancement, heat transfer augmentation, scaffold and tissue engineering, etc. to name a few. Evolution in 3D printing technology has realized the manufacturing of these complex topologies in an extremely simplistic and straightforward manner. Recent research progress has shown that upon impregnations with phase change material (PCM), lattices based on TPMS topologies exhibited better heat transfer performance than the conventional metal foam in Latent Heat Thermal Energy Storage (LHTES) systems. However, the effect of lattice's porosity and functional grading is not understood and requires further investigation. In order to bridge this gap. This numerical study aims at studying the effect of porosity and functional grading of TPMS-PCM lattices on heat transfer performance. Three TPMS structures namely Primitive, Gyroid and IWP are considered in this study. The porosity study analyzes the heat transfer performance of TPMS structures at three distinct levels of porosity i.e., 60%, 75% and 90% with the 75% porosity case being the benchmark. Furthermore, to study the effect of functional grading, 75% uniform porosity configuration of each TPMS configuration was compared with 75% overall porosity configurations having first a positive and then a negative functional gradient in the porosity. It was found that both porosity and functional grading have a significant effect on both conductive and convective heat transfer enhancement. A reduction in porosity significantly reduces the PCM melting time owing to enhancement in the heat transfer. On the other hand, a positive gradient in the porosity outperforms both uniform porosity and negative porosity gradient cases. Moreover, in both porosity and functional grading studies, the extent of heat transfer enhancement is topology-dependent i.e., each TPMS structure exhibits a different extent of heat transfer enhancement that can be traced back to its topology. This study may therefore serve as a guideline for design and selection of a suitable TPMS candidate according to the applied boundary conditions/problem constraints of the respective LHTES system.