Relaxation Method Research Articles

Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity

The rotating shaft-hydrodynamic bearings systems operated with high speed and/or heavy load conditions expose serious rotor-dynamics instability problems due to characteristics of the supporting bearings. The stability and the dynamics of these systems, directly relate to the lubricant properties that are directly affect by the heat generation. In this study, the dynamic characteristics of a shaft-hydrodynamic journal bearing and its stability were investigated under variable viscosity. The equations of lubricant flow were derived by Dowson’s equation under variable viscosity, and the perturbation equations were obtained for 2 degrees-of-freedom system. The heat transfers between oil and the journal surface was modelled in a 3-dimensional energy equation, and the heat transfer on the journal structure was also modelled with heat conduction equation. An algorithm based on finite difference scheme with successive over relaxation method was developed to solve the theoretical models, simultaneously, and a serial simulation was performed to investigate the variations of the dynamic coefficients of the bearing-shaft system concerning the rotating speed for different radial clearance values. It was determined that the high speed increases the lubricant temperature, and so the static and dynamic performance characteristics decrease, moreover, this effect is more dominant for the smaller radial clearance.

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

A global method for relaxation for multi-levelled structured deformations

We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation problems are also provided.

Continuous heating aging characteristics of Al-Cu-Mg-Ag alloy based on stress relaxation method

Clarifying the aging characteristics of aluminum alloys during continuous heating is crucial for formulating isothermal and non-isothermal aging (continuous heating aging) processes. This paper investigates the stress relaxation characteristics of an Al-Cu-Mg-Ag alloy under three-point bending during continuous heating. Taking into account the mechanical properties and precipitate analysis, it demonstrates the feasibility of using the stress relaxation method to determine the peak aging temperature during continuous heating. This approach is efficient, requires minimal sample, and yields continuous data. The peak aging temperature of the sample increases from 260 °C to 305 °C when the heating rate increases from 1 to 3 °C/min with the same initial load (3 N). The peak aging temperature is around 280 ℃, when the initial load increases from 1 N to 9 N with the same heating rate (2 °C/min). Under low temperatures (25 ℃∼ 200 ℃), the sample displays the presence of GP zones, and a few Ω precipitates during the continuous heating process of 2 ℃/min. As the temperature increases, the GP zones dissolve and transform into the Ω precipitates. A large number of Ω precipitates appear in the matrix in a continuous precipitation manner when the temperature reaches 235 °C. The precipitation strengthening effect is strongest at 280 °C, and the Ω precipitates begin to coarsen as the temperature exceeds 280 °C.

A comprehensive optimization mathematical model for wind solar energy storage complementary distribution network based on multi-regulatory devices under the background of renewable energy integration

In the context of global energy transformation and sustainable development, integrating and utilizing renewable energy effectively have become the key to the power system advancement. However, the integration of wind and photovoltaic power generation equipment also leads to power fluctuations in the distribution network. The research focuses on the multifaceted challenges of optimizing the operation of distribution networks. It explores the operation and control methods of active distribution networks based on energy storage and reactive power compensation equipment. The stable operation of the distribution network is analyzed under the conditions of wind and photovoltaic integration, with a particular focus on precise regulation to address the limitations of existing methods. Afterwards, the study proposes an improvement plan that combines on load tap changer transformers and reactive power compensation equipment to solve complex power balance problems through second-order cone programming relaxation method. The results of numerical analysis show that the constructed mathematical model maintains a stable voltage of 1 to 1.1 pu at distribution network nodes within 24 h. Especially during peak hours from 15:00 to 24:00, it remains normal without any abnormal fluctuations when the control equipment is not added. These results confirm that precise regulation of multiple devices ensures voltage stability and avoids low or high voltage issues.

The impact of complementary therapies on dysmenorrhea in young women

HIGHLIGHTS Complementary treatments have been shown to greatly reduce the intesity of dysminorrhea pain. The use of medicinal plants, herbal concoctions, or compresses might reduce dysmenorrhea discomfort more effectively than taking medications like mefenamic acid, ibuprofen, piroxicam, etc. ABSTRACT Objective: The study's objective was to obtain latest data on alternative therapy for dysmenorrhea in adolescent females of reproductive age. Materials and Methods: A scoping review was conducted using the PRISMA ScR protocol. A search was conducted on PubMed, Science Direct, and Wiley, yielding 848 studies. Ten literature studies were identified that satisfied the criteria for population, exposure, and outcome. The studies also incorporated inclusion criteria, focusing on women of reproductive age who had dysmenorrhea. Results: Out of 848 articles, 32 were considered potentially relevant and met the inclusion criteria. The articles indicated that teenagers commonly used warm compresses and herbal drinks as supplementary therapies to alleviate dys-menorrhea due to their perceived effectiveness and comfort. Other complement-ary therapies for the condition included massage, relaxation, herbal products, self-care practices, acupuncture, and therapeutic methods. Conclusion: Herbal and warm water compress are the most commonly applied alternative therapies for treating dysmenorrhea.

Teaching stress reduction techniques including biofeedback for managing stress in medical students

IntroductionMedical students have been under immense pressure throughout their studies, impacting their mental health and academic performance. Stress reduction is a fundamental skill that all students require to manage their studies and lives efficiently. Biofeedback devices providing information about physiological states have been shown to aid stress reduction. Methods to reduce stress should be taught to medical students to help them tackle the challenges of medical school.ObjectivesOur goal was to teach stress reduction methods such as extracurricular activities and paced breathing aided by biofeedback training and its application in simulated healthcare situations to medical students.Methods15 medical students who completed medical physiology were recruited for an elective course of 7 sessions on practical techniques in stress management. One credit was offered to those who completed the course requirements consisting of participation in sessions and individual biofeedback training. Sessions (classes) consisted of presentations on good sleeping and eating patterns, group simulations of stressful hospital environments, visiting a science centre with interactive displays, an orchestra performance, and nature walks. Before biofeedback training, heart and respiration rates were taken individually by a biofeedback device during the first week of the course. Data was processed using a code created in statistical software. Heartbeats per minute and heart rate variability (HRV) for every 10 seconds were calculated and plotted on a graph. Two measurements were taken with each student: a baseline measurement for 10 minutes and another measurement during controlled breathing paced at 6 breaths per minute for 15 minutes, of which the first 10 minutes were used for calculation and plotting. Students provided narrative feedback in an essay submitted after the course was completed.Results5 males and 10 females from years 2-5 registered for the elective, and 12 participated in individually scheduled sessions. Heart beats per minute decreased, whereas HRV increased during paced breathing sessions in 83% of them. Most students reported feeling calm and drowsy during the sessions, and 2 students fell asleep by the end.Feedback from 11 students showed that the music session and the science centre visit were the highlights throughout the elective. Improvements recommended were to have a consistent time slot for all sessions and fewer simulations.Conclusions In concert with the literature, biofeedback training seems to be a feasible and effective method for relaxation in medical students. This method could be offered as part of mental health services for students. Data could be used to follow students’ progress and identify those requiring extra support. Providing them with avenues to de-stress while emphasizing activities outside medicine could boost their confidence and improve their coping skills.Disclosure of InterestNone Declared

Linearization Method for Large-Scale Hydro-Thermal Security-Constrained Unit Commitment

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

Стационарное протекание несжимаемой вязкой жидкости сквозь двухмерный разветвленный канал

The results of a numerical experiment for the problem of an incompressible viscous fluid stationary flow through a branched planar (two-dimensional) channel are presented. The region in which the flow occurs simulates either blood vessels or a river delta. The finite element method and a modification of the penalty method, as well as the splitting method, are used for calculations. The implementation of the calculation algorithm is using with the help the package FreeFem++. The main goal, in addition, of course, to study the properties and structure of the stationary flow, is to demonstrate the effectiveness of the proposed modification of the penalty method. It is assumed that the region has one input boundary section through which the liquid flows into the region, and several (five) boundary sections through which the liquid flows out of the region. The remaining sections of the region boundary are considered impermeable to liquid. The boundary condition corresponding to the Poiseuille flow in a plane rectilinear channel is set at the input section. Three types of boundary conditions are considered on the output boundary secctions. 1. The boundary conditions correspond to the conditions of conservation of motion of luid particles i. e. the material derivative of the velocity is zero. 2. The boundary conditions correspond to the setting of the flow velocity. 3. The boundary conditions correspond to the setting of the same pressure. The stationary solution is constructed by the relaxation method. In fact, a non-stationary problem is solved over a sufficiently large time interval. As an initial condition for a non-stationary problem, a flow is chosen that is a Poiseuille flow in some region near the input boundary. The dependence of the convergence rate of the relaxation method on the initial data is investigated. It is found that the Poiseuille flow, given at the input section of the boundary of the region, induces similar Poiseuille flows at the output boundaries sections of the region in all these cases of boundary conditions. For a region with five sections of the output boundaries for some configuration of the region, the presence of stationary vortex flows (‘maelstorm’) is found.

Exact solution for minimization of root mean square deviation with G-RMSD to determine molecular similarity

Abstract Generalized root mean square deviation (G-RMSD) is an optimization method for three-dimensional molecular similarity determination. It calculates the minimum value of RMSD among all the possible one-to-one matchings between the atoms and positions of the molecules. The first paper on G-RMSD introduced two approaches called alternating optimization (AO) and tangent space relaxation (TSR) methods, which give local optimum solutions. We propose here a new method of G-RMSD using a branch-and-bound method (BnB) on isometric transformations, called IsometryOpt, which is mathematically proven to give an exact G-RMSD index, i.e. this method can reach the global optimum solution. The performance of IsometryOpt was compared to AO and TSR, as well as the MatchFastOpt method. IsometryOpt shows better performance than MatchFastOpt for molecules with the same number of atoms. AO and TSR fail to reach exact values in some cases. We also have developed two improved methods to search for all possible matches of a substructure in one or more molecules. One is called IsometrySearch, which uses BnB on isometric transformations. The other is a variant version of MatchFPT, called MatchFPT-delta. Computer experiments indicate that MatchFPT-delta performs better than MatchFPT and IsometrySearch.

Predictive modelling of flow dynamics in micropolar hybrid nanofluids subjected to magnetic dipole influence using nonlinear autoregressive artificial neural networks with exogenous input

In the present research article, we explore the intelligence-based numerical computation of a nonlinear autoregressive artificial neural network with exogenous input using the Levenberg-Marquardt algorithm (ANN-LMA) trained to analyze the unsteady two-dimensional micro-polar flow of an incompressible hybrid nanofluid (Al 2 O 3−Fe 3 O 4/Ethylene Glycol) under the impact of the magnetic field introduced by the magnetic dipole on a nonlinear stretched sheet. In the first step of the research, partial differential equations are converted into nonlinear ordinary differential equations using appropriate transmission and then solved numerically via the Successive Over Relaxation method after applying the finite difference method. The impact of numerous emerging parameters on the solutions is displayed graphically, and the physical significance is discussed. The results show that the concentration profile displays a dwindling trend for the Brownian motion parameter, and the opposite trend is witnessed for the thermophoretic parameter. Moreover, for increasing values of the dimensionless distance parameter and ferromagnetic interaction parameter, the temperature and velocity profiles exhibit the opposite tendency. In the second step of the study, we validated the Successive Over Relaxation outcomes with an ANN-LMA. For this purpose, the suggested ANN-LMA is trained for six different scenarios of the reference dataset points of the given flow model. The analysis shows that Successive Over Relaxation and LM-SNNs yield similar results, with a decreasing trend for the Brownian motion parameter and an opposite trend for the thermophoretic parameter.

The thixotropic characteristics of rheological parameters of waste stone-tailings cemented paste backfill and the time effect of pipeline resistance

The cemented paste backfill (CPB) involves the optimal combination of one or more solid materials with water to prepare a paste-like slurry with certain stability, fluidity, and plasticity. The paste flows as a piston flow under external force (pumping pressure) or gravity through pipelines into the underground goaf to complete backfilling operations. In order to improve the performance of the CPB, coarse aggregate is added to the CPB to form a coarse aggregate cemented paste backfill (C-CPB). The C-CPB belonged to non-Newtonian fluids and exhibited thixotropic behavior as its rheological parameters determined its flow characteristics. During the initial stage of pipeline transportation, the rheological parameters of the paste material were influenced by its thixotropic behavior and exhibited a certain degree of time dependence. The present study employed the stress relaxation method for thixotropy test to ascertain the rheological parameters of the C-CPB with respect to shear time. The results indicated that the yield stress decreased with increasing shear time with a negative exponential growth trend. A mathematical function describing the variation of yield stress with time for the paste material was established, and an estimation method for thixotropic equilibrium time of the yield stress was proposed. A Gaussian distribution function describing the variation of plastic viscosity with shear time was developed, and the thixotropic stabilization time of plastic viscosity was estimated. On this basis, a pipeline transportation resistance model considering the time-dependent rheological parameters of the C-CPB was established. Subsequently, a formula for calculating the boundary layer thickness during the initial stage of pipeline transportation was derived. The establishment of the model enables a better understanding of the resistance characteristics of the paste during the initial stage of pipeline transportation, as well as the process and patterns of boundary layer formation, which is of great significance.

Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II

This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.

Pengaruh Pemberian Hipnotis Lima Jari Terhadap Ansietas Pada Lansia Hipertensi di Wisma Assisi Kota Sukabumi

Pengaruh Pemberian Hipnotis Lima Jari Terhadap Ansietas Pada Lansia Hipertensi di Wisma Assisi Kota Sukabumi

Energy optimal scheduling strategy considering V2G characteristics of electric vehicle

in recent years, large-scale electric vehicles connected to the power grid has a significant impact on demand-side resources. In addition, the vehicle-to-grid technology of electric vehicles introduces more uncertainties, which brings great challenges to the optimal scheduling of integrated energy systems. To solve this problem, this paper fully considers the uncertainty and fluctuation of wind power. Firstly, the objective function of joint configuration is constructed to maximize the utilization of wind power and minimize the planned generation cost of the system. Secondly, the linearized power flow equations are used to represent the relations among the state variables, and the second-order cone relaxation method is applied to deal with the branch power flow constraints, which is transformed into a solvable mixed-integer second-order cone programming model. Finally, the validity of the model is verified by an example. The system achieves obvious peak-shaving and valley-filling effect and improves the economic benefit of the system.

Методика циклических испытаний образцов-моделей коленчатого вала судового двигателя внутреннего сгорания на изгиб с кручением

It is proposed to consider the bending fatigue strength of the crankshaft as the main criterion of its operability during operation. It is noted that thermomechanical straightening with heating by stress relaxation method is most acceptable for straightening critical shafts that have received a curvature of the longitudinal axis during operation. Bending fatigue tests of round samples with a diameter of 20 mm in a dangerous section were carried out to substantiate the correction technology, test modes and evaluate the results of the correction. It was found that an increase in diameter leads to a decrease in the endurance limit of structural steels. The loading scheme of the experimental sample is adopted – transverse bending with torsion. A semicircular notch in the sample was used to focus the fracture site, and the radius of the notch was calculated. The size of the sample tuck is determined by the formula based on the similarity criterion adopted in the statistical theory of similarity of fatigue failure of parts, proposed by V. P. Kogaev. The requirements for the roughness of the surface of a circular groove of at least Ra 0.16 are established. The need for control of the manufacturing technology of the experimental sample is noted. An experimental installation for testing flexural fatigue strength is proposed. A cone cartridge was used to securely fasten and prevent the sample from turning during the experiment. Experimental samples were used-models with deflection arrows of 1, 2, 3, 4 and 5 mm. The method and equipment for obtaining samples with the necessary deflection arrows have been determined. Diagrams of a model sample for testing cantilever bending with torsion, an experimental installation for testing model samples, bending to a given deflection arrow, and a model sample with a curved longitudinal axis are presented.

Optimizing linear energy transfer distribution in intensity-modulated proton therapy using the alternating direction method of multipliers.

This study develop a novel linear energy transfer (LET) optimization method for intensity-modulated proton therapy (IMPT) with minimum monitor unit (MMU) constraint using the alternating direction method of multipliers (ADMM). The novel LET optimization method (ADMM-LET) was proposed with (1) the dose objective and the LET objective as the optimization objective and (2) the non-convex MMU threshold as a constraint condition. ADMM was used to solve the optimization problem. In the ADMM-LET framework, the optimization process entails iteratively solving the dose sub-problem and the LET sub-problem, simultaneously ensuring compliance with the MMU constraint. Three representative cases, including brain, liver, and prostate cancer, were utilized to evaluate the performance of the proposed method. The dose and LET distributions from ADMM-LET were compared to those obtained using the published iterative convex relaxation (ICR-LET) method. The results demonstrate the superiority of ADMM-LET over ICR-LET in terms of LET distribution while achieving a comparable dose distribution. More specifically, for the brain case, the maximum LET (unit: keV/µm) at the optic nerve decreased from 5.45 (ICR-LET) to 1.97 (ADMM-LET). For the liver case, the mean LET (unit: keV/µm) at the clinical target volume increased from 4.98 (ICR-LET) to 5.50 (ADMM-LET). For the prostate case, the mean LET (unit: keV/µm) at the rectum decreased from 2.65 (ICR-LET) to 2.14 (ADMM-LET). This study establishes ADMM-LET as a new approach for LET optimization with the MMU constraint in IMPT, offering potential improvements in treatment outcomes and biological effects.

Enhancing security for physical layer communication in RIS-aided MIMO-NOMA systems in the presence of an eavesdropper

This paper investigates the potential of leveraging a reconfigurable intelligent surface (RIS) in the multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) wireless communication systems. In fact, NOMA improves spectral efficiency (SE) through power domain utilization, and RIS enhances the system performance by manipulating the propagation environment. In this paper, we investigate the physical layer security (PLS) of a RIS-aided MIMO-NOMA system serving two users in the presence of an eavesdropper (EV), where the channel state information (CSI) of the EV is unknown for the BS. To address the security challenge, we utilize secrecy outage probability (SOP) and minimize it by optimizing the RIS’s phase shift matrix, the beamforming vector, and the power allocation coefficients. Due to the non-convexity of the main optimization problem, we decompose the initial problem into three subproblems, and then, we propose an iterative approach to determine the unknown parameters alternately. The first subproblem involves obtaining the optimal beamforming vector and phase shift matrix using the semidefinite relaxation (SDR) method, which introduces high complexity. As an alternative, another algorithm is proposed based on the duality of the optimization problem, offering lower complexity and better accuracy for high-dimensional optimization problems. In this algorithm, the successive convex approximation (SCA) technique is employed to achieve the optimum phase shift matrix, and the stochastic gradient (SG) approach is used to determine the beamforming vector. Furthermore, the paper establishes the optimal values of power allocation coefficients by minimizing the difference between the SOPs of the two users. Finally, the simulation results demonstrate that the proposed power allocation coefficients scheme significantly enhances system performance compared to the existing fixed power allocation coefficients scheme.

Target shape approximation of funicular surfaces by load control using RBF interpolation

Existing methods for form-finding prioritize discovering optimal shapes under design load conditions, often overlooking the designer’s shape preferences. To address this problem, this research relaxes the load condition and develops a user-friendly form-finding tool that encapsulates a new method for obtaining funicular surfaces that pass through user-prescribed points through load control. The method involves generating smooth load distributions via RBF interpolation of nodal loads, which are repeatedly adjusted so that the equilibrium shape is close enough to the target points. For faster convergence, the step size of the load adjustment is automatically determined through a coarse line search, and a warm start is introduced in form-finding with the dynamic relaxation method. Despite uneven load distributions, the method ensures high accuracy in approximating the surface shape to the desired points while preserving funicularity against the load distributions. Additionally, the resulting load distribution gives designers valuable feedback on the specified target points, as the degree of load non-uniformity indicates the deviation from the equilibrium shape for uniformly distributed loads.

Optimal Allocation Stochastic Model of Distributed Generation Considering Demand Response

Demand response (DR) can improve the accommodation of renewable energy and further affect the distributed generation (DG) allocation strategy. In this context, this paper proposes a stochastic optimal allocation model of DG, considering DR. Firstly, to address the uncertainty of wind and solar power outputs, a large number of scenarios of wind and solar power are generated based on the scenario method, which are then clustered into 10 typical scenarios by the k-means method. Secondly, with the goal of maximizing the total cost, the DR cost and corresponding constraints are introduced. Then, the stochastic planning model for DG is established, where the planning level aims to minimize the investment cost while the operation level minimizes the total operation expectation cost. For the non-linear term in the DR cost and power flow constraint, the Taylor expansion method and second-order conic relaxation method are both adopted to transform the original mixed-integer non-linear model to the mixed-integer second-order conic planning model. Finally, the whole planning model for DG is solved by CPLEX 12.6.0. The results show that DR can reduce the total cost and improve the accommodation of renewable energy in the DG planning process, which should be paid more attention to in the DG planning model.