Physical Solution Research Articles

AI-Driven Rehabilitation Robots: Enhancing Physical Therapy for Stroke and Injury Recovery

AI-driven rehabilitation robots are transforming physical therapy by providing personalized, precise, and adaptive support for patients recovering from strokes and injuries. This research explores the integration of Artificial Intelligence (AI) into robotic systems to enhance physical rehabilitation outcomes, focusing on key areas such as motor skill recovery, real-time performance tracking, and patient engagement. Utilizing machine learning algorithms and biomechanical data, these robots can tailor therapy sessions to individual needs, dynamically adjusting resistance, movement patterns, and feedback. Advanced sensor technology enables the robots to monitor patient progress, ensuring accurate assessments and adaptive interventions. This study also examines the role of AI in promoting neuroplasticity through repetitive, task-specific training, a critical component of stroke recovery. Ethical considerations, including data privacy and accessibility, are analyzed to address barriers to widespread adoption. By bridging robotics, AI, and clinical practice, this research highlights the potential of AI-driven rehabilitation robots to revolutionize physical therapy, offering scalable and effective solutions that improve recovery rates and enhance the quality of care.

The importance of boundary evolution for solar-wind modelling

The solar wind is a continual outflow of plasma and magnetic field from the Sun’s upper atmosphere—the corona—that expands to fills the solar system. Variability in the near-Earth solar-wind conditions can produce adverse space weather that impacts ground- and space-based technologies. Consequently, numerical fluid models of the solar wind are used to forecast conditions a few days ahead. The solar-wind inner-boundary conditions are supplied by models of the corona that are, in turn, constrained by observations of the photospheric magnetic field. While solar eruptions—coronal mass ejections (CMEs)—are treated as time-dependent structures, a single coronal “snapshot” is typically used to determine the ambient solar-wind for a complete model run. Thus, all available time-history information from previous coronal-model solutions is discarded and the solar wind is treated as a steady-state flow, unchanging in the rotating frame of the Sun. In this study, we use 1 year of daily-updated coronal-model solutions to comprehensively compare steady-state solar-wind modelling with a time-dependent method. We demonstrate, for the first time, how the SS approach can fundamentally misrepresent the accuracy of coronal models. We also attribute three key problems with current space-weather forecasting directly to the steady-state approach: (1) the seemingly paradoxical result that forecasts based on observations from 3-days previous are more accurate than forecasts based on the most recent observations; (2) high inconsistency, with forecasts for a given day jumping significantly as new observations become available, changing CME propagation times by up to 17 h; and (3) insufficient variability in the heliospheric magnetic field, which controls solar energetic particle propagation to Earth. The time-dependent approach is shown to alleviate all three issues. It provides a consistent, physical solution which more accurately represents the information present in the coronal models. By incorporating the time history in the solar wind along the Sun-Earth line, the time-dependent approach will provide improvements to forecasting CME propagation to Earth.

Approximation of the Absorption Spectrum of Indium Phosphide in the Context of Simulation of the Process of Sensitivity Enhancement

Examines the fundamental rights of Phosphide of India, legitimized by Tellur and, in the last resort, compensated for. Data on the composition of four high-quality images of the InP: Cu photoelectronic spectrum are presented in the individual layers. The work is characterized by the semi-empiric approach to photoconduction of InP: Cu oxide films. It is concluded that the photoresistance Iph (α(ћω)) was analytically approximated as the function of the experimental-complete spectral distribution of the coefficiency phosphorus india. It is proposed to use five approximating functions with the aim of analyzing the coefficient of absorption of Indian phosphorus α(ћω). Completed 5 locations with different signs of median isolation. On the basis of analytical amplitudes, the complete analytical amplitude Iph(α(ћω)) is modelled. Analogously, five conclusions were drawn that indicate a sign of median isolation. Five non-stationary measures of IF photometry have been taken (as two functions: co-efficiency of exposure, as photo energy functions, and time-consuming observations) in normal situations. The answer to the question is the most mathematical and physical solution of the proximate function α(ћω). Obviously, it shows that this the degree of variance is optimal for its implementation (inclusion of this degree of variance in the structure Iph = f(α) and α = f(ћω)) of the complete analytical description of the process photoconductivity. It should be noted that subsequent research may be based on the establishment of physical bases of photoconductivity in the short wave of fundamental transfers of phosphorus from India, as well as research into the properties of air on the high InP: Cu layer, with its stability and stability.

Ion-Specific Surface Tension of Aqueous Electrolyte Solutions: Analytical Insights from a Restricted Primitive Model.

The ion-specific surface tension of aqueous electrolyte solutions is of fundamental importance in physical chemistry, solution chemistry, electrochemistry, and biochemistry, yet it remains a challenge to be qualitatively predicted. In this work, an analytical theory of ion-specific surface tension is developed. By modeling the solution to a restricted primitive model (RPM), the surface tension increment of the electrolyte solution reduces to the surface tension of the RPM, which is further determined analytically by using the integral equation theory and the morphological thermodynamics theory. According to our formula, the surface tension increment of the electrolyte solution consists of a dominant and positive hard sphere contribution, which depends on the salt concentration, and a secondary electrostatic contribution, which depends on the inverse Debye length and the salt concentration. Our theory is applied to 1:1, 2:2, 1:2, 2:1, 3:1, and 3:2 electrolyte solutions with typical salt concentrations up to several mol/L and compared with experimental data. Without introducing any adjustable parameters, our theory leads to a good prediction of the surface tension increment of more than 50 kinds of aqueous solutions. Such a good agreement demonstrates the great potential of our theory for a fundamental understanding of specific ion effects in a variety of electrolyte solutions.

Unveiling air sparging analysis in flow cells through the continuum approach

We present various analytical solutions for a two-dimensional steady air source that demonstrate classical flow physics’ usefulness in air-sparging evaluation. These solutions capture different flow geometry and setup effects while offering accuracy, speed, and a deeper understanding of governing physics. Compared to empirical models, they excel with fewer physical parameters. We validate their accuracy by comparing these solutions to experimental air-sparging data from two-dimensional flow cells. This comparison underscores the applicability of the physical model and establishes a relationship between grain size and a key model parameter. Furthermore, this analysis enables predictive capabilities for scaled-up systems with diverse setup geometries.Plain Language Summary Air-sparging refers to the injection of air below the groundwater table, that is, to the water-saturated section of the aquifer. Air-sparging is used to facilitate the volatilization of organic pollutants (e.g., solvents, gasoline) and their extraction to the soil surface. However, evaluating and modeling the flow and distribution of air is limited by the complicated physics of unstable multiphase flow. These complexities drive researchers to search for empirical relations and rules of thumb to design air-sparging systems. In this research, we use previously published experimental data to demonstrate the capabilities and discuss the limitations of the classical physical solutions of steady single-phase flow to evaluate air flow through wet porous media such as aquifers.

Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation

In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the generalized hydrodynamic equations of Eu, and aims to describe rarefied flows. In the non-equilibrium regime, the NCCR equations are more reliable than the Navier-Stokes equations. And the NCCR equations have an advantage of efficiency over the discrete velocity methods and stochastic particle methods. However, the NCCR model is a complicated nonlinear system. Many assumptions have been used in the schemes for solving the NCCR equations. The corresponding numerical methods may be associated with unphysical solution and instability. At the same time, it is hard to analyze the physical accuracy and stability of NCCR model due to the uncertainties in the numerical discretization. In this study, a new numerical method for solving NCCR equations is proposed and used to analyze the properties of NCCR equations. More specifically, the nonlinear equations are converted into the solutions of an objective function of a single variable. Under this formulation, the multiple solutions of the NCCR system are identified and the criteria for picking up the physical solution are proposed. Therefore, a numerical scheme for solving NCCR equations is constructed. A series of flow problems in the near continuum and low transition regimes with a large variation of Mach numbers are conducted to validate the numerical performance of proposed method and the physical accuracy of NCCR model.

On the soliton-type and other physical solutions for the space–time fractional Kraenkel–Manna–Merle model

On the soliton-type and other physical solutions for the space–time fractional Kraenkel–Manna–Merle model

Bound-preserving OEDG schemes for Aw–Rascle–Zhang traffic models on networks

Physical solutions to the widely used Aw–Rascle–Zhang (ARZ) traffic model and the adapted pressure ARZ model should satisfy the positivity of density, the minimum and maximum principles with respect to the velocity v and other Riemann invariants. Many numerical schemes suffer from instabilities caused by violating these bounds, and the only existing bound-preserving (BP) numerical scheme (for ARZ model) is random, only first-order accurate, and not strictly conservative. This paper introduces arbitrarily high-order provably BP discontinuous Galerkin (DG) schemes for these two models, preserving all the aforementioned bounds except the maximum principle of v, which has been rigorously proven to conflict with the consistency and conservation of numerical schemes. Although the maximum principle of v is not directly enforced, we find that the strictly preserved maximum principle of another Riemann invariant w actually enforces an alternative upper bound on v. At the core of this work, analyzing and rigorously proving the BP property is a particularly nontrivial task: the Lax–Friedrichs (LF) splitting property, usually expected for hyperbolic conservation laws and employed to construct BP schemes, does not hold for these two models. To overcome this challenge, we formulate a generalized version of the LF splitting property, and prove it via the geometric quasilinearization approach (Wu and Shu, 2023 [47]). To suppress spurious oscillations in the DG solutions, we incorporate the oscillation-eliminating technique, recently proposed in (Peng et al., 2024 [34]), which is based on the solution operator of a novel damping equation. Several numerical examples are included to demonstrate the effectiveness, accuracy, and BP properties of our schemes, with applications to traffic simulations on road networks.

Generative model-based framework for parameter estimation and uncertainty quantification applied to a compartmental model in epidemiology

We propose a new method in which a generative network (GN) set within a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. We train the GN using only unconditional simulations of the discretized PDE model. A GN is used here to exploit the ability of these methods to generate realistic outputs from complex probability distributions, such as the ones that represent the possible states and parameters of a physical problem. We compare the proposed method with the gold standard Markov chain Monte Carlo (MCMC). Additionally, we suggest the use of a novel type of time-stepping regularization to improve the representativeness of the physical solution, and we present a new way of evaluating the GN training, taking advantage of the real/generated sample structure. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the gold standard. This is achieved using only a limited number of unconditional simulations from the full-order numerical PDE model (40 simulations). The GN-based ROM operates 60 times faster than the gold standard (MCMC), while producing uncertainties that closely match those generated by the MCMC approach. The proposed method is a general framework for quantifying uncertainties in numerical physical simulations and is not restricted to the specific physics of this application.

Analysis of the application of natural circulation of cooling media in shipboard reactor installations

In projects of floating facilities with a nuclear power plant, great importance is attached to the formation of a set of properties of the internal self-protection of the reactor, i. e. the development of properties that ensure its safety based on natural feedbacks, processes and characteristics. To do this, the RU project is based on physical patterns and technical solutions that prevent or minimize possible consequences from emergency situations. In particular, the natural circulation of the coolant in case of loss of power supply by the circulation pumps of the first round allows cooling the core after its transfer to a subcritical state. However, in order for a natural circulation to occur sufficient to ensure nuclear and radiation safety, certain conditions must be met in a particular case. The paper notes that the most important property of reactor installations of nuclear vessels is their ability to ensure natural circulation of the coolant in emergency situations, as well as when operating at capacity. This makes it possible to reduce the dependence of reactor plant safety on the technical condition of power supplies. Currently, natural circulation of auxiliary cooling media in passive safety systems is also widely used in reactor installations. These include emergency reactor cooling systems using an emergency cooling system, including using intermediate heat exchangers; reducing emergency pressure in the protective shell in case of an accident with a large coolant leak; cooling the reactor vessel in an out-of-design accident with the formation of corium. The paper proposes a method for preliminary analysis of the reactor plant’s ability to ensure natural circulation of the coolant, which allows us to compare various design solutions that contribute to an increase in coolant consumption during natural circulation. It is shown that for the operation of the reactor plant in stand-down mode and at energy power levels with natural circulation of the coolant, it is advisable to switch to boiling reactors. Passive safety systems using natural circulation have received special development on new nuclear vessels of projects 20870, 22220, 10510. Further development of safety systems using natural circulation to move cooling media is predicted.

The common solution space of general relativity

We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de Sitter-Schwarzschild geometry, which includes a cosmological constant; the Reissner-Nordström geometry, which accounts for the presence of charge. Additionally we consider the homogenenous and anisotropic locally rotational Bianchi II spacetime in the vacuum. Our analysis reveals that the field equations for these scenarios share a common three-dimensional group of point transformations, with the generators being the elements of the D⊗sT2 Lie algebra, known as the semidirect product of dilations and translations in the plane. Due to this algebraic property the field equations for the aforementioned gravitational models can be expressed in the equivalent form of the null geodesic equations for conformally flat geometries. Consequently, the solution space for the field equations is common, and it is the solution space for the free particle in a flat space. This approach open new directions on the construction of analytic solutions in gravitational physics and cosmology.

Natural ventilation and acoustic privacy in settlement cores: a review of window technology and night-time economy planning policy

This study reviewed the potential of partially open windows to address the challenges of natural ventilation and night-time airborne noise within settlement cores. These areas, which often feature historic buildings, require sensitive interventions to balance the conservation of heritage with the need for liveable, sustainable cities. The 'night-time economy' (NTE) encompasses a diverse range of businesses, services, and events that operate beyond traditional daytime hours, such as restaurants, bars, nightclubs, entertainment venues, cultural events, and 24-hour services. Night-time noise disturbances can be detrimental to residents' health and well-being. A case study examined the solutions proposed by contemporary NTE planning policy to address night-time noise in settlement cores, particularly in instances where the expansion of NTE areas and extended trading hours are considered. No physical solution mitigation strategies for noise reduction were identified in the NTE policy, and only a management approach was proposed. This study examines the potential of innovative acoustically attenuated partially open windows as a strategic solution to airborne night-time noise pollution from a night-time economy. This solution may improve energy efficiency and sustainability in cities while allowing the night-time economy and residential areas to coexist more harmoniously.

Wall, Wall in the Mirror: Which Is the Sturdiest of Them All?

This research examines the comparative effectiveness of physical versus virtual border walls in managing illegal border crossings along the U.S.-Mexico border, focusing on Yuma, Arizona, and Laredo, Texas. It addresses the question of which type of infrastructure is more efficient in reducing migration and how these approaches influence crossing patterns. Previous studies have largely concentrated on other factors of migration such as economic conditions, overlooking the role of evolving border security systems. This gap in the literature calls for a deeper analysis of these evolving strategies. Utilizing U.S. Customs and Border Protection data from 2020 to 2024, the study analyzes border encounters in these regions, employing time series analysis to investigate shifts in crossing rates and demographic trends. Our findings reveal that physical barriers are effective when properly maintained but lose deterrence power when consistent maintenance and construction is absent. Conversely, virtual walls provide consistent monitoring but are less effective in significantly deterring crossings. Both methods present significant ethical concerns, as physical walls drive migrants to more dangerous routes, while virtual walls amplify surveillance and privacy issues. We conclude that a hybrid approach, integrating physical and technological solutions, could better balance migration management with ethical border enforcement.

Plant protein, fibre and physical activity solutions to address poor appetite and prevent undernutrition in older adults: study protocol for the APPETITE randomised controlled trial.

Reduced appetite with ageing is a key factor that may increase risk of undernutrition. The objective of this study is to determine the impact of innovative plant protein fibre (PPF) products within a personalised optimised diet (PD), a physical activity (PA) programme, and their combination on appetite, and other nutritional, functional and clinical outcomes in community-dwelling older adults in a multi-country randomised controlled intervention trial. One hundred and eighty community-dwelling adults (approximately sixty per trial centre in Germany, Ireland and Italy) aged 65 years and over will be recruited to participate in a 12-week, parallel-group, controlled trial. Participants will be randomised into one of four groups: 1, PD (incorporating two PPF products): 2, PA; 3, PD + PA; and 4, no intervention (control). The primary outcome is appetite measured by visual analogue scales and energy intake from an ad libitum test meal. Secondary outcomes include fasting and postprandial appetite-related gut hormones, Simplified Nutritional Appetite Questionnaire score, body composition, cardiorespiratory fitness, muscle strength, physical function and PA. In addition, self-efficacy, cognitive status, dietary restraint, depressive symptoms and compliance and acceptability of the intervention will be assessed. Metabolomic profiles, RMR, muscle motor unit properties and gut microbiome will also be assessed to explore potential underlying mechanisms. This multi-centre randomised controlled trial will advance knowledge on how PD (incorporating PPF products), PA and their combination influence appetite, nutritional status and related health outcomes in community-dwelling older adults and contribute to the prevention of undernutrition. Trial registration: Clinical Trials.gov Registry NCT05608707 (registered on 2 November 2022). Protocol Version: NCT05608707 Version 4 (registered on 29 September 2023).

Thermodynamic properties and geometries of bardeen black hole surrounded by string clouds

In this work, we investigate the thermodynamic properties of Bardeen black hole which is coupled with cloud of strings and minimally coupled to nonlinear electrodynamics. The modified entropy in the form of Sharma–Mittal entropy is used to discuss these properties which include mass, temperature, pressure, Gibbs free energy and trace of Hessian matrix. We obtain stable behavior along with physical solution for some specific values of parameters a and q. Furthermore, our work provides a thermodynamic metric using the Hessian matrix of black hole mass, changing the conformal connection between Quevedo and Ruppeiner’s geometries. Investigating the first principle of thermodynamics for regular black holes, such as the Bardeen AdS black hole, exposes significant behavior changes during phase transitions in an extended phase space.

112 Promoting Physical Activity in Workplaces: The Integral Role of Well-being Management

Abstract Purpose The primary purpose of the research was to find out how employers in Finland support physical activity at workplaces and how physical activity is related to the management of well-being at work. In the new government program in Finland, physical activity is integrated as a part of developing work ability and well-being at work. Methods The Adults on the Move program conducted the Finnish barometer on physical activity at workplaces. The research was carried out by interviewing 300 employers representing five industries and 1100 employees. The role of the management practices on activity of worksite physical activity was analyzed using regression analysis. Indicators were formed from the data. Results In the barometer, questions were related to physical activity as well as to the management of well-being at work. The basic decisions of well-being management are setting the goal, making the plan, and deciding the responsibility of the supervisors. The results showed that the implementation of physical activity at workplaces is strongly linked to the quality of well-being management. When all three basic decisions of well-being management are implemented, the action to increase physical activity is carried out most effectively: • Most diverse task-specific physical activity solutions are in use, • Physical activity is taken into account in remote work, • Physical activity suppors recovery, • Physical activity is part of the cooperation with occupational health care, • Physical activity is included in supervisor coaching and training and further in personnel development discussions. Conclusions The level of well-being management is thus related to the implementation and diversity of physical activity at workplaces. Basic management decisions were more commonly made in large organizations. The management of small and medium-sized companies needs training on physical activity and well-being at work, so that the means of physical activity for the personnel would be optimal and high-quality. In this way, work ability and well-being at work are increased through physical activity. Funding Adults on the Move Program, Ministry of Education and Culture.

Comment on “Which is greater: eπ or πe? An unorthodox physical solution to a classic puzzle” [Am. J. Phys. 92(5), 397–398 (2024)]

Comment on “Which is greater: eπ or <i>πe</i>? An unorthodox physical solution to a classic puzzle” [Am. J. Phys. <b>92</b>(5), 397–398 (2024)]

Exploring New Traveling Wave Solutions to the Nonlinear Integro-Partial Differential Equations with Stability and Modulation Instability in Industrial Engineering

In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for two types of nonlinear models in this present investigation. These analyses have several applications including analyzing control systems, engineering, biomedical engineering, neural networks, optical fiber communications, signal processing, nonlinear imaging techniques, oceanography, and astrophysical phenomena. To study nonlinear PDEs analytically, exact traveling wave solutions are in high demand. In this paper, the (1 + 1)-dimensional integro-differential Ito equation (IDIE), relevant in various branches of physics, statistical mechanics, condensed matter physics, quantum field theory, the dynamics of complex systems, etc., and also the (2 + 1)-dimensional integro-differential Sawda–Kotera equation (IDSKE), providing insights into the several physical fields, especially quantum gravity field theory, conformal field theory, neural networks, signal processing, control systems, etc., are investigated to obtain a variety of wave solutions in modern physics by using the mentioned method. Since abundant exact wave solutions give us vast information about the physical phenomena of the mentioned models, our analysis aims to determine various types of traveling wave solutions via a different integrable ordinary differential equation. Furthermore, the characteristics of the obtained new exact solutions have been illustrated by some figures. The method used here is candid, convenient, proficient, and overwhelming compared to other existing computational techniques in solving other current world physical problems. This article provides an exemplary practice of finding new types of analytical equations.

Study of a combined Kairat-II-X equation: Painlevé integrability, multiple kink, lump and other physical solutions

PurposeThis study aims to explore a novel model that integrates the Kairat-II equation and Kairat-X equation (K-XE), denoted as the Kairat-II-X (K-II-X) equation. This model demonstrates the connections between the differential geometry of curves and the concept of equivalence.Design/methodology/approachThe Painlevé analysis shows that the combined K-II-X equation retains the complete Painlevé integrability.FindingsThis study explores multiple soliton (solutions in the form of kink solutions with entirely new dispersion relations and phase shifts.Research limitations/implicationsHirota’s bilinear technique is used to provide these novel solutions.Practical implicationsThis study also provides a diverse range of solutions for the K-II-X equation, including kink, periodic and singular solutions.Social implicationsThis study provides formal procedures for analyzing recently developed systems that investigate optical communications, plasma physics, oceans and seas, fluid mechanics and the differential geometry of curves, among other topics.Originality/valueThe study introduces a novel Painlevé integrable model that has been constructed and delivers valuable discoveries.

A triple emulsion droplet in a uniform flow

The fluid mechanics problem of a triple emulsion droplet in a uniform creeping flow is theoretically studied. The triple emulsion, submerged in an external fluid 1, is composed of an inner spherical drop (fluid 4), covered by a spherical shell (fluid 3), which is subsequently covered by another spherical shell (fluid 2). In the absence of a body force, eight parameters are governed: the Capillary number (Ca), three viscosity ratios (λ21, λ32, λ43), two radii ratios (K, k), and two-surface tension ratios (M, m). If all surfaces remain spherical and concentric, five parameters (λ21, λ32, λ43, K, k) are sufficient. Expressions for the stream functions and the drag forces were obtained to calculate the terminal velocity of the triple emulsion falling or rising in a stagnant fluid under the influence of gravity. With gravity, four additional parameters are needed: the ratio of the buoyancy force to the external viscous force (B), and three density ratios (γ21, γ31, γ41). To remain concentric, all surfaces must have the same velocity (magnitude and direction). This results in two restricted parameters, but even then, not every combination of parameters leads to a physical solution. Our findings suggest that the terminal velocity of a triple emulsion is equal to or lower than that of a double emulsion, which is subsequently equal to or lower than that of a single drop. Similar to single and double emulsion droplets, no deformation takes place in a concentric spherical triple emulsion subjected to a gravitational field under creeping flow conditions.