Analysis of the Cicatricial Acceleration Method (MAC®) in Skin Repair in Wistar Rattus norvegicus with Induced Chemical Burns

Introduction: The cicatricial acceleration method (MAC®) promotes photobiological effects of an anti-inflammatory and healing nature. Its therapeutic radiation is emitted, producing photobiostimulant effects that result in rapid tissue repair and better tissue quality. The treatment of burns has always been a challenge, which involves both performing surgery and controlling and guiding scar regeneration, avoiding possible morbidities. Objective: To evaluate the effects of applying the MAC methodology with an AlGa (aluminum, gallium arsenide) laser on the time and quality of tissue repair in the skin of rats after induced chemical burns. Method: 22 adult male rats were subjected to a second-degree chemical burn on the back using 50% trichloroacetic acid. After the burns, the animals were randomly separated into 2 groups: control and experimental. The control group (G1) received placebo laser therapy and the laser group (G2) underwent laser irradiation with an energy density of 100 J/cm2. Histological analysis and macroscopic evaluation were carried out by means of the paper template method. Results: Group G1 showed (53%) of the necrosis area and group G2 showed (11%) necrosis area. Conclusion: The cicatricial acceleration method (MAC®) favored the repair of wounds caused by a 2nd-degree chemical burn, optimizing time and improving quality.

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

Stability of average acceleration method for structures with nonlinear damping

The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

A new type of quadratic acceleration method

The polynomial acceleration method for time history analysis is presented,in which accelerations between several equal neighboring time steps were assumed to be a polynomial function of time interval.With a higher order polynomial used,a higher accuracy can be obtained,but the stability field of the method becomes narrower.When stability field and computational accuracy are taken into account at the same time,the quadratic acceleration method is superior to linear and cubic acceleration methods in choosing the maximum acceptable time step size.It is also shown that the quadratic acceleration method has desirable arithmetic damp,amplitude decay rate and period elongation rate,though its conditional stability restricts its application in stiff structures.

Research and experimental analysis of precision degradation method based on the ball screw mechanism

As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.

Comparison of capability of time integration methods in capturing dynamic loading

Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

In this paper, we propose an accelerated search-extension method （ASEM） based on the interpolated coefficient finite element method, the search-extension method （SEM） and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

A Low-Complexity Signal Detection Utilizing AOR Iterative Method for Massive MIMO Systems

Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at the base stations. However, the excessively high computational complexity of the signal detection in massive MIMO systems imposes a significant challenge for practical hardware implementations. In this paper, we propose a novel minimum mean square error(MMSE) signal detection using the accelerated overrelaxation(AOR) iterative method without complicated matrix inversion, which is capable of reducing the overall complexity of the classical MMSE algorithm by an order of magnitude. Simulation results show that the proposed AOR-based method can approach the conventional MMSE signal detection with significant complexity reduction.

Arrhenius relationship and two-step scheme in AF hyperdynamics simulation of diffusion of Mg/Zn interface

The accelerating factor （AF） method is a simple and appropriate way to investigate the atomic long-time deep diffusion at solid-solid interface. In the framework of AF hyperdynamics （HD） simulation, the relationship between the diffusion coefficient along the direction of z-axis which is normal to the Mg/Zn interface and temperature was investigated, and the AF＇s impact on the diffusion constant （D0） and activation energy （Q^＊） was studied. Then, two steps were taken to simulate the atomic diffusion process and the formation of new phases： one for acceleration and the other for equilibration. The results show that： the Arrhenius equation works well for the description of Dz with different accelerating factors; the AF has no effect on the diffusion constant Do in the case of no phase transition; and the relationship between Q＊ and Q conforms to Q^＊=Q/A. Then, the new Arrhenius equation for AFHD is successfully constructed as Dz=Doexp[-Q/（ART）]. Meanwhile, the authentic equilibrium conformations at any dynamic moment can only be reproduced by the equilibration simulation of the HD-simulated configurations. Key words： accelerating factor method; Arrhenius equation; two-steps scheme; Mg/Zn interface; hyperdynamic simulation

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition,a unified gas-kinetic wave-particle(UGKWP)method has been developed for multiscale flow simulations.With the variation of the cell Knudsen number,the UGKWP method captures the transport process in all flow regimes without the kinetic solver’s constraint on the numerical mesh size and time step being determined by the kinetic particle mean free path and particle collision time.In the current UGKWP method,the cell Knudsen number,which is defined as the ratio of particle collision time to numerical time step,is used to distribute the components in the wave-particle decomposition.The adaptation of particles in the UGKWP method is mainly for the capturing of the non-equilibrium transport.In this aspect,the cell Knudsen number alone is not enough to identify the non-equilibrium state.For example,in the equilibrium flow regime with a Maxwellian distribution function,even at a large cell Knudsen number,the flow evolution can be still modelled by the Navier-Stokes solver.More specifically,in the near space environment both the hypersonic flow around a space vehicle and the plume flow from a satellite nozzle will encounter a far field rarefied equilibrium flow in a large computational domain.In the background dilute equilibrium region,the large particle collision time and a uniform small numerical time step can result in a large local cell Knudsen number and make the UGKWP method track a huge number of particles for the far field background flow in the original approach.But,in this region the analytical wave representation can be legitimately used in the UGKWP method to capture the nearly equilibrium flow evolution.Therefore,to further improve the efficiency of the UGKWP method for multiscale flow simulations,an adaptive UGKWP(AUGKWP)method is developed with the introduction of an additional local flow variable gradient-dependent Knudsen number.As a result,the wave-particle decomposition in the UGKWP method is determined by both the cell and gradient Knudsen numbers,and the use of particles in the UGKWP method is solely to capture the non-equilibrium flow transport.The current AUGKWP method becomes much more efficient than the previous one with the cell Knudsen number only in the determination of wave-particle composition.Many numerical tests,including Sod shock tube,normal shock structure,hypersonic flow around cylinder,flow around reentry capsule,and an unsteady nozzle plume flow,have been conducted to validate the accuracy and efficiency of the AUGKWP method.Compared with the original UGKWP method,the AUGKWP method achieves the same accuracy,but has advantages in memory reduction and computational efficiency in the simulation for flows with the co-existing of multiple regimes.

Stator-Flux Oriented Continuous Control of Torque in Induction Motors

This paper analyzes dynamic equivalent circuit of induction motor and the relationship among inner fluxes, then presents a direct stator flux oriented continuous torque control (DSFOCTC) scheme of induction motor , which uses stator current vector control instead of voltage vector control. As a combination of direct torque control (DTC) and flux oriented vector control, it achieves round stator flux and continuous dynamic torque control resulting in less torque ripple than that in DTC. It reduces the dependence on rotor parameters, and is especially insensitive to rotor resistance. Finally, an induction motor speed control system incorporating this novel scheme is given and checked by simulation.

Numerical simulation of superhalo electrons generated by magnetic reconnection in the solar wind source region

Superhalo electrons appear to be continuously present in the interplane- tary medium, even during very quiet times, with a power-law spectrum at energies above ～2 keV. Here we numerically investigate the generation of superhalo electrons by magnetic reconnection in the solar wind source region, using magnetohydrody- namics and test particle simulations for both single X-line reconnection and multiple X-line reconnection. We find that the direct current electric field, produced in the mag- netic reconnection region, can accelerate electrons from an initial thermal energy of T ～105 K up to hundreds of keV. After acceleration, some of the accelerated elec- trons, together with the nascent solar wind flow driven by the reconnection, propagate upwards along the newly-opened magnetic field lines into interplanetary space, while the rest move downwards into the lower atmosphere. Similar to the observed superhalo electrons at 1 AU, the flux of upward-traveling accelerated electrons versus energy dis- plays a power-law distribution at ～ 2-100 keV, f（E）～ E^-δ, with a 6 of ～1.5 - 2.4. For single （multiple） X-line reconnection, the spectrum becomes harder （softer） as the anomalous resistivity parameter a （uniform resistivity η） increases. These modeling results suggest that the acceleration in the solar wind source region may contribute to superhalo electrons.

Automated pavement horizontal curve measurement methods based on inertial measurement unit and 3D profiling data

Pavement horizontal curve is designed to serve as a transition between straight segments, and its presence may cause a series of driving-related safety issues to motorists and drivers. As is recognized that traditional methods for curve geometry investigation are time consuming, labor intensive, and inaccurate, this study attempts to develop a method that can automatically conduct horizontal curve identification and measurement at network level. The digital highway data vehicle （DHDV） was utilized for data collection, in which three Euler angles, driving speed, and acceleration of survey vehicle were measured with an inertial measurement unit （IMU）. The 3D profiling data used for cross slope calibration was obtained with PaveVision3D Ultra technology at 1 mm resolution. In this study, the curve identification was based on the variation of heading angle, and the curve radius was calculated with ki- nematic method, geometry method, and lateral acceleration method. In order to verify the accuracy of the three methods, the analysis of variance （ANOVA） test was applied by using the control variable of curve radius measured by field test. Based on the measured curve radius, a curve safety analysis model was used to predict the crash rates and safe driving speeds at horizontal curves. Finally, a case study on 4.35 km road segment demonstrated that the proposed method could efficiently conduct network level analysis.

BEM for wave interaction with structures and low storage accelerated methods for large scale computation

The boundary element method（BEM） is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required calculations and storage increase rapidly with the increase of the structure scale. Thus, an accelerated method with a low storage is desirable for the wave interaction with a very large structure. A systematic review is given in this paper for the BEM for solving the problem of the wave interaction with a large scale structure. Various integral equations are derived based on different Green functions, the advantages and disadvantages of different discretization schemes of the integral equations by the constant panels, the higher order elements, and the spline functions are discussed. For the higher order element discretization method, the special concerns are given to the numerical calculations of the single-layer potential, the double layer potential and the solid angle coefficients. For a large scale computation problem such as the wave interaction with a very large structure or a large number of bodies, the BEMs with the FMM and p FFT accelerations are discussed, respectively, including the principles of the FMM and the p FFT, and their implementations in various integral equations with different Green functions. Finally, some potential applications of the acceleration methods for problems with large scale computations in the ocean and coastal engineering are introduced.

Scalable Distributed Optimization Combining Conic Projection and Linear Programming for Energy Community Scheduling

In this paper, a new method to address the scheduling problem of a renewable energy community while considering network constraints and users' privacy preservation is proposed. The method decouples the optimization solution into two interacting procedures: conic projection(CP) and linear programming(LP) optimization. A new optimal CP method is proposed based on local computations and on the calculation of the roots of a fourth-order polynomial for which a closed-form solution is known. Computational tests conducted on both 14-bus and 84-bus distribution networks demonstrate the effectiveness of the proposed method in obtaining the same quality of solutions compared with that by a centralized solver. The proposed method is scalable and has features that can be implemented on microcontrollers since both LP and CP procedures require only simple matrix-vector multiplications.

Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems

The solution of minimum-time feedback optimal control problems is generally achieved using the dynamic programming approach,in which the value function must be computed on numerical grids with a very large number of points.Classical numerical strategies,such as value iteration(VI)or policy iteration(PI)methods,become very inefficient if the number of grid points is large.This is a strong limitation to their use in real-world applications.To address this problem,the authors present a novel multilevel framework,where classical VI and PI are embedded in a full-approximation storage(FAS)scheme.In fact,the authors will show that VI and PI have excellent smoothing properties,a fact that makes them very suitable for use in multilevel frameworks.Moreover,a new smoother is developed by accelerating VI using Anderson’s extrapolation technique.The effectiveness of our new scheme is demonstrated by several numerical experiments.

A New Algorithm for Total Variation Based Image Denoising

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.

A Combination Model for Image Denoising

In this paper, we propose an efficient combination model of the second-order ROF model and a simple fourth-order partial differential equation （PDE） for image denoising. The split Bregman method is used to convert the nonlinear combination model into a linear system in the outer iteration, and an algebraic multigrid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to analyze the parameter selection criteria and discuss the performance of ~he fourth-order PDE in the combination model. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.