搜索结果：Mathematical Physics

Physics-informed machine learning (PIML) is emerging as a potentially transformative paradigm for modeling complex biomedical systems by integrating parameterized physical laws with data-driven methods. Here, we review three main classes of PIML frameworks: physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs), highlighting their growing role in biomedical science and engineering. We begin with PINNs, which embed governing equations into deep learning models and have been successfully applied to biosolid and biofluid mechanics, mechanobiology, and medical imaging, among other areas. We then review NODEs, which offer continuous-time modeling, especially suited to dynamic physiological systems, pharmacokinetics, and cell signaling. Finally, we discuss deep NOs as powerful tools for learning mappings between function spaces, enabling efficient simulations across multiscale and spatially heterogeneous biological domains. Throughout, we emphasize applications where physical interpretability, data scarcity, or system complexity make conventional black-box learning insufficient. We conclude by identifying open challenges and future directions for advancing PIML in biomedical science and engineering, including issues of uncertainty quantification, generalization, and integration of PIML and large language models.

Accurate simulation of biomass pyrolysis in fixed-bed reactors is crucial for optimizing this promising thermochemical conversion pathway. This review systematically consolidates and critically evaluates contemporary mathematical models that describe the intrinsically coupled phenomena of heat transfer, reaction kinetics, and fluid dynamics within such systems. Employing an enhanced paper-ranking methodology (NIRP 2.0), a curated portfolio of 54 key studies was established and analyzed through integrated bibliometric and systematic content analysis. The synthesis delineates prevailing modeling paradigms, spanning from continuum approaches to advanced discrete particle-resolved methods like computational fluid dynamics-extended discrete element method (CFD-XDEM), and provides a detailed discussion of their governing equations, submodel formulations, and numerical solution strategies. Particular emphasis is placed on scrutinizing common assumptions in critical subprocesses (drying, devolatilization, and char conversion) and on identifying persistent challenges in representing intraparticle gradients, bed shrinkage dynamics, and secondary reaction networks. The analysis reveals significant research gaps and emerging trends, underscoring the pressing need for more integrated, experimentally validated multiscale models. Consequently, this review serves not only as a comprehensive reference for current modeling practices but also as a strategic roadmap for developing next-generation simulation tools to advance the design, scale-up, and operation of industrial-scale pyrolysis reactors.

Collaborative operation of heterogeneous UAV swarms in dense urban environments remains challenging because right-of-way allocation is often rigid, frequent replanning consumes considerable onboard computation, and paths obtained by purely mathematical optimization may not be easy to execute under real dynamic constraints. This paper presents a physics-informed, event-triggered path planning and control framework, termed Physics-Informed SSA-MPC. Its global search layer is built on the Sparrow Search Algorithm (SSA), whose search mechanism originates from sparrow foraging and anti-predatory behaviors. On this basis, the method combines an event-triggered Stackelberg game for airspace coordination, a physically constrained SSA for global path generation, and an event-triggered MPC for local replanning. Battery State of Health (SoH) is incorporated into the adaptive search process, while Lévy-flight updates are limited by the maximum available acceleration to avoid infeasible path mutations. Local replanning is activated only when predicted safety ellipsoids overlap or tracking errors exceed prescribed thresholds, which helps reduce redundant computation. Simulations in a digital twin of Lujiazui, Shanghai, show that the proposed method shortens path length by 3.3% to 14.9%, reduces obstacle-avoidance latency to 45 ms, and achieves a 100% engineering feasibility rate.

This study aims to examine the nonlinear features of electromagnetic pulses that propagate obliquely to an external magnetic field within the nonlinear Zakharov Kuznetsov modified equal-width equation. This research will contribute to understanding the complicated dynamical nature of the presented model that implies different areas of research. Our objective is to show the traveling wave solution and stability analysis of the dynamic system. A modified Sardar sub equation technique is applied to find the traveling wave solution of the underlying problem. The traveling wave solution is obtained in a broad variety including solitons, kinks, periodic solutions, rational solutions, and many others. The dynamical analysis starts with phase portraits which provides information to the qualitative dynamics of the system and its stability features. The sensitivity analysis will examine the influence of parameters on the model to provide insights that demonstrate the effectiveness of the model and to examine the behavior of the dynamical system under different initial conditions. We also investigate the chaotic dynamics to identify the stability and categorize periodic, quasi-periodic, and chaotic dynamics of the perturbed dynamical system. These analyses demonstrate the potential application and enhance the underlying mechanics in the field of optical and nonlinear physics. This dynamical analysis improves understanding of nonlinear models and develops efficient mechanisms to manage the complex nonlinear model. Furthermore, Poincare map and Lyapunov exponent are used to find qualitative behavior and visualize the phase space to illustrate the various dynamical regimes. These contributions enhance the improvement in the field of optical soliton and help to analyze the complex dynamical system in the field of engineering and mathematical physics.

Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as "black boxes". In contrast to standard regression models that require a prescribed functional form, SR constructs expressions from a user-defined set of mathematical primitives, enabling the automated discovery of compact formulas that fit the data and reveal underlying physical relationships. In fluid mechanics, where understanding the underlying physics is as crucial as predictive accuracy, this study applies SR to model three-dimensional (3D) laminar flow in a rectangular channel, focusing on the axial velocity and pressure fields. Compact symbolic equations were derived from numerical simulation data, accurately reproducing the expected parabolic velocity profile and linear pressure drop, and showing excellent agreement with analytical solutions from the literature. To address the limitation that purely data-driven SR models may overlook domain-specific constraints, an innovative hybrid framework that integrates SR with Answer Set Programming (ASP) is also introduced. This integration combines the generative power of SR with the declarative reasoning capabilities of ASP, ensuring that derived equations remain both statistically accurate and physically plausible. The proposed SR/ASP methodology demonstrates the potential of combining data-driven and knowledge-representation approaches to enhance interpretability, reliability, and alignment with physical principles in fluid dynamics and related domains.

The application of chaos theory has positive results in different fields of science. Its nonlinear modeling properties and its vision of dynamic systems have enabled it to capture complex relationships in fields such as physics, financial econometrics, social systems and mathematical demography. This paper reviews the implication of chaos theory in the medical sciences. We carried out a systematic literature review under Cochrane’s international standards. A search strategy was executed with indexed terms (MeSH, DeCS and Emtree) that varied according to each database (Embase, MEDLINE, SciELO, LILACS). The PROSPERO registration number was CRD42023491407. In total, 2598 articles were retrieved, of which 20 were included. Algorithmic applications of chaotic systems were diverse. The medical fields with the largest studies were cardiology, neurology and oncology. The most used software was Matlab, however, in all cases, except one, we did not find open-source codes related to the studies. We found a wide heterogeneity in the studies reviewed, and this was reflected in the scope of research results. While some papers focus on proving the existence of chaotic behavior or understanding the nature of the phenomena being studied, others propose practical implications, such as in prescribing medicines and organizing health units. Not applicable. The online version contains supplementary material available at 10.1186/s42490-026-00111-0.

We present a novel acceleration scheme capable of accelerating electrons and ions in an underdense plasma. Transversely Pumped Acceleration (TPA) uses multiple arrays of counter-propagating laser beamlets that focus onto a central acceleration axis. Tuning the injection timing and the spacing between the adjacent beamlets allows for precise control over the position and velocity of the intersection point of the counter-propagating beam arrays. This results in an accelerating structure that propagates orthogonal to the direction of laser propagation. We present the theory that sets the injection timing of the incoming pulses to accelerate electrons and ions with a tunable phase velocity plasma wave. Simulation results are also presented which demonstrate 1.12 GeV proton beams accelerated in 3.6 mm of plasma and electron acceleration gradients on the order of 1 TeV/m in a scheme that circumvents dephasing. This work has potential applications as a compact accelerator for medical physics and high energy physics colliders.

Magnesium oxide (MgO) is a prototypical ionic solid with a well-defined rock-salt lattice and is frequently used as a reference structure in materials science and theoretical modeling. In this work, we present a rigorous graph-theoretical characterization of an idealized MgO lattice, formulated as a periodic point-lattice for analytical purposes. The structure is treated as a two-dimensional topological projection of the three-dimensional rock-salt lattice, enabling exact symbolic analysis without incorporating surface relaxation, reconstruction, or energetic considerations. Using edge partitioning and degree-based methods, we derive closed-form analytical expressions for a class of irregularity topological indices (ITIs) associated with the resulting periodic graph. These indices quantify degree asymmetry and structural heterogeneity purely in a combinatorial sense and serve as mathematical descriptors of connectivity patterns in finite lattice graphs. The primary contribution of this study is the exact derivation of these irregularity indices for an ideal rock-salt lattice, which, to the best of our knowledge, has not been previously reported. It is emphasized that the present work is formulated entirely within a graph-theoretical framework and does not establish direct correlations with experimentally measured physical properties. The observed scaling behavior of the indices reflects topological boundary effects inherent to finite periodic graphs and should not be interpreted as physical disorder in real crystalline materials. Instead, the results provide a foundational mathematical framework for future studies on non-ideal lattices, such as defective, doped, or reconstructed systems, where irregularity-based descriptors may be meaningfully related to material properties.

Understanding flight evolution requires quantifiable metrics. The complex flight dynamics and the vast morphological space insects have explored make it extremely challenging to define and understand what combinations of traits lead to these successful flyers. In this work, we constructed a mathematically tractable free-flight model, including the nonlinear wing-body coupling, to elucidate the effect of morphology on flight stability. Using this model to simulate almost a million different forms, we identified a region of passively stable upward flight, in addition to generic unstable flight. Analyzing the stability boundary in the 5D morphological and kinematic space, we found a set of explicit criteria that approximate the stability transitions, and expressed them in terms of two physically interpretable constraints. These two stability criteria provide a succinct metric for stability, quantifying the distance of an insect from the stable region directly from morphology, thus organizing a complex flight trait in a reduced and physically interpretable space. As such, they provide a framework for designing stable flapping-wing robots and for quantification of a critical phenotypic flight trait on top of the established phylogenetic relationships among insects.

Chronic inflammation perturbs hematopoietic homeostasis, promoting aberrant myelopoiesis and clonal expansion of mutated stem cells. Here, we develop a mathematical model that integrates both local (bone marrow-intrinsic) and global (systemic/peripheral) inflammation-driven feedback mechanisms to investigate their roles in hematopoietic regulation and disease progression. Our model captures the nonlinear interplay between self-renewal, progenitor proliferation, and inflammatory cues, enabling classification of healthy, myelodysplastic, and leukemic states based on stem cell population dynamics. We show that global inflammatory feedback enhances the resilience of hematopoiesis, while excessive feedback on progenitor cells under chronic inflammation drives instability and clonal dominance. Using sensitivity analysis and parameter space mapping, we identify critical feedback thresholds governing transitions between hematopoietic states and reveal how mutated clones exploit inflammation to outcompete wild-type cells. This systems-level framework offers mechanistic insights into the emergence of myeloid malignancies and provides a computational platform for exploring potential anti-inflammatory therapeutic strategies.

Targeted delivery of drugs and hyperthermia in cardiovascular disease demand the accurate delivery of nanoparticles in complex arterial geometries. This paper introduces combined hybrid computational model that concomitantly examines the combined impact of nanoparticle radius and interparticle spacing on the thermal and mass transport characteristics of ternary bio-nanofluid flow under magnetohydrodynamic (MHD) effect. The ternary fluid is composed of blood fluid with suspended nanoparticles such as gold (Au), silver (Ag) silica (SiO2). The mathematical model accounts for geometric properties of nanoparticles such as nanoparticles radius and interparticle spacing for their practical utility for several medical interventions. The numerical analysis is based on hybrid computational strategy, where the solutions are determined through the bvp4c numerical solver and then a novel supervised multi hidden layers Artificial neural network (ANN) is integrated. The proposed model has a high predictive capability with an exceptionally high accuracy with the lowest Mean squared error and ideal regression coefficient MSE=9.6327×10-11, Gradient=9.5681e-08, Mu=1e-09, and R2=1.0. Some of the main findings indicate that less spacing between particles (h=0.1) leads to continuous networks of thermal percolation, which enhance the thermal conductivity by up to 35% to improve the efficiency of hyperthermia, whereas the larger nanoparticles (radius ≥1.5) offer a higher drug-loading capacity, yet the rate of heat transfer decreases by 15-20%. Optimization of the magnetic parameter (M=0.1-0.7) also decreases flow velocity by 28% and extends the nanoparticle residence time at the stenosis by 35% which allows sustained drug delivery, results directly applicable to clinical-strength (1.5-3T) MRI-guided interventions. Radiation parameter (Rd=0.5-2.5) increases temperature of the arteries by 15-20% giving controllable thermal modulation to applications of hyperthermia. The proposed model predicts that optimal nanoparticle preparations (50 nm radius, 20 nm spacing) have to potential to lower the rate of restenosis by 30-40% in relation to traditional drug-eluting stents. The purpose of such an integrated computational-machine learning systems is to give quantitative advice to stent coating design, nanoparticle formulation, and optimization of treatment protocols, and has been directly used in biomedical interventions. The results can be used to offer practical advice to stent manufactures, interventional radiologist and pharmaceutical developers to create evidence-based cardiovascular therapy of the next generation.

After COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020, global responses relied on nonpharmaceutical interventions such as physical distancing and mask mandates. These measures were guided by mathematical models built on empirical data. Although traditional methods such as surveys and observational studies provide high-quality data, they are often slow and resource-intensive. Social media polls (SMPs) offer a faster, more cost-effective alternative. This study aims to evaluate the reliability and biases of SMPs as a rapid supplementary tool for epidemiological data collection and to compare their representativeness and data quality with conventional approaches. In this cross-sectional observational study in Germany, we used SMPs to collect data on infections and demographic attributes via Twitter and Mastodon. We collected data directly on the social media platforms as well as through forwarding to an external survey via post. The time frame covered was from 2019 to 2024. Data were analyzed for infection rates, sociodemographic representativeness, and overall data quality. SMPs demonstrated viability as a rapid data collection tool. Based on a sample of 6127 answers on social media and 867 responses from the external survey, the self-reported frequency of infection aligned well with conventional sources. Across all 4 studies, approximately one-third of respondents reported having never been infected, half reported having had 1 infection, and one-sixth reported having had 2 or more infections. Statistical analyses of differences between data from Twitter, Mastodon, the external survey, and conventional data showed only small effect sizes (Cohen w=0.105-0.188). Spearman rank correlation demonstrated strong positive associations between infection dates in the external survey and conventional data (&#x3c1;=0.883, P<.001), as well as between the external survey and the Robert Koch Institute (&#x3c1;=0.640, P<.001). However, demographic analyses revealed biases in the external survey. By design, SMPs do not provide detailed demographic data, limiting options for subgroup analyses. We found SMPs to be a practical and cost-effective method for quickly gathering epidemiological insights. In particular, self-reported infection frequency can aid during periods of high availability of self-testing during epidemics. We demonstrate that, even with a nonrepresentative and biased sample, we were able to closely match infection numbers with Multilocal and Serial Prevalence Study of Antibodies Against Respiratory Infectious Diseases in Germany data and produce incidence trends comparable to those in official Robert Koch Institute data. One can argue that SMPs alone are insufficient for public health modeling, as they do not allow real-time monitoring of, for example, population infection rates based on serological data. They are also limited with regard to inherent demographic bias related to recruitment and the inability to collect individual-level covariates. However, they can complement traditional approaches by offering rapid, low-cost insights.

In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to effectively represent both smooth functions and functions with singularities. This is important not only for function approximation but also for solving the partial differential equations with physics-informed neural networks. Through a series of experiments, we show that SincKANs provide better results in almost all of the examples we have considered. The codes are public at https://github.com/DUCH714/SincKAN.

Recent investigations into exercise-induced tumor suppression suggest that higher exercise frequency enhances tumor control when the total duration of exercise within a specified time window is not constrained. An equally compelling avenue for exploration is the effect of increased exercise frequency under the condition of a fixed total exercise duration within the same time frame. Using a mathematical model of IL-6-mediated interactions between natural killer (NK) cells and tumor cells, here we explore how different combinations of exercise and rest intervals -while maintaining a constant overall exercise volume -affect tumor suppression. Our results reveal a nonmonotonic tumor response and key metrics such as the time of maximum tumor suppression and the duration of tumor suppression are found to decrease with increasing exercise frequency. Interestingly, unlike earlier study where increasing exercise frequency leads to increase in tumor suppression, here we find that under fixed exercise volume constraints, increased frequency diminishes therapeutic efficacy of exercise, suggesting exercise bouts with longer duration are more effective in suppressing tumors. These findings highlight the importance of considering total exercise volume when designing exercise-based cancer interventions.

Background: Contemporary dentistry increasingly relies on tools and methods derived from the exact sciences, particularly mathematics and physics, to better understand the complexity of biological processes. One such tool is fractal analysis (FA), which enables the characterization and quantification of irregular, complex, self-similar structures commonly observed in nature in the form of the fractal dimension (FD). In oral radiology, it has been found useful for describing structural changes in bone tissue. Objective: The aim of this review is to present the current state of knowledge regarding the application of fractal analysis in the management of patients with, or at risk for, medication-related osteonecrosis of the jaw (MRONJ), with particular emphasis on its diagnostic and prognostic potential. This paper summarizes key research findings, and discusses the principal challenges and limitations associated with the use of this method of analysis in MRONJ cases. Materials and Methods: The inclusion criteria were as follows: original papers, the presence of MRONJ, and fractal analysis. In order to find relevant studies, international databases, including PubMed and Google Scholar, were searched. The last search was performed on 29 November 2025. Six articles were included in the systematic review. Results: The majority of the review studies show lower FD values for MRONJ patients and healthy control groups. The values are the lowest for necrotic lesions and highest for perinecrotic bone tissue. Conclusions: FD values calculated from radiological images of the jaws can be used to differentiate healthy and MRONJ-affected patients and to describe necrotic lesions. Fractal analysis has potential to be used in the diagnosis and monitoring of MRONJ after further studies and standardization of methodology.

In this paper we explore the coupled fractional Schr&#xf6;dinger-KdV system, which is relevant in the modeling of the interaction of short dispersive waves with long nonlinear waves in a wide range of physical phenomena, such as in plasma physics and nonlinear optics. The use of fractional derivatives enables the model to reproduce the effects of memory and non-local dynamics which cannot be sufficiently captured by classical integer-order formulations. Residual power series transform Method (RPSTM) and the Iterative Transform Method (ITM) are two semi-analytical methods that are used in the context of the Mohand transform in order to obtain effective analytical approximations. The methods are systematically implemented to obtain the approximate solutions of the coupled system and the performance of this system is studied using convergence behavior and error analysis. Moreover, the effect of the fractional-order parameter on the mechanism of the system is examined, which reveals that the effects of fractional-order have a tremendous impact on the properties of the wave propagation, such as attenuation of the amplitude and the speed of the propagation. The paper also highlights the relevance of the fractional modeling in the representation of complex physical phenomena, which then forms a solid foundation of future studies in the nonlinear wave theory and the applied sciences.

Feedforward loops (FFLs) and feedback loops (FBLs) are ubiquitous network motifs that mediate signal filtering, pulse generation, and state switching; yet, how coupling FBLs to FFLs produces robust multistability-a key mechanism for cellular decision-making-remains unclear. Here, we systematically investigate coupled FFL-FBL architectures by focusing on two prevalent FFL types, each with AND or OR logic, yielding four distinct frameworks. For each framework, we enumerate all 36&#x2009;=&#x2009;729 possible circuits, corresponding to three possible states (activation, inhibition, or absence) for each of six feedback edges, formulate each circuit as a system of ordinary differential equations, and quantify robustness as the proportion of 100,000 randomly sampled parameter sets exhibiting multistability. Our results reveal two key principles. First, positive self-activation is a primary driver of multistability, but the identity of the critical node(s) depends on the FFL type and logic. Second, coherent FFLs support multistability more readily than incoherent ones, whereas the choice between AND and OR logic has a comparatively weaker effect. Notably, we identify representative high-performing circuits within each framework and find that a small set of circuit designs remain robustly multistable across all four frameworks. These findings advance the theoretical understanding of motif design and provide practical guidelines for engineering synthetic multistable circuits.

Artificial vision systems are increasingly central to edge intelligence, yet they often suffer from high data latency and energy consumption due to sensor-processor separation. In-sensor computing (ISC) provides a promising solution by integrating sensing and computation. However, current ISC devices remain constrained by scalability, uniformity, and processability. Here, we address these limitations via a reconfigurable perovskite-photovoltaic platform that can be facilely processed from solutions. This architecture allows precise, reconfigurable photoresponsivity tuning with ultra-low variability and supports fabrication on both rigid and flexible substrates. The device exhibits up to &#xb1;1120&#xa0;mA&#xa0;W- 1 photoresponsivity and 1000 programmable states, with excellent air stability (30 days) and thermal reliability (80&#xb0;C). The scalability of these devices is demonstrated via a proof of concept 32 &#xd7; 32 array. The excellent uniformity and programmability of the array are utilized in energy-efficient face detection applications (achieving 95.2% sensitivity and 4.51 &#xd7; speedup for subsequent computation) in addition to image feature extraction and MNIST digit recognition tasks (96.97% accuracy). Compared to previous ISC implementations, our system offers enhanced tunability, fabrication scalability, and functional stability. These results establish a practical perovskite-based ISC platform, offering new avenues for intelligent computing systems in robotics, wearable electronics, and neuromorphic vision.

This study presents a novel surface plasmon resonance (SPR) biosensor composed of silver (Ag), bismuth ferrite (BiFeO3), nickel (Ni), and perovskite nanomaterial (MAPbBr3). Different ethanol concentrations (ECs) could be detected thanks to the hybrid structure. The transfer matrix technique (TMM) is used to assess the suggested surface plasmon resonance (SPR) structure. To compare the angular sensitivity of the EC&#x2009;=&#x2009;0% sample with the EC&#x2009;=&#x2009;10% to 40% sample, a comparative analysis was carried out. The BiFeO3, Ni, and MAPbBr3 layer thicknesses must be changed in order to maximize the surface plasmon resonance (SPR) structure's performance. Additionally, precise measurements of the resonance angle (&#x3b8;_res), minimum reflectance (Rmin), full width at half maximum (FWHM), and figure of merits (FOM) have been made. In comparison to the conventional structure (BK7/Ag/SM) with a matching FOM of 149.12 RIU-1, the ideal angular sensitivity was found to be 55&#xa0;nm for Ag, 5&#xa0;nm for BiFeO3, 20&#xa0;nm for Ni, and 3&#xa0;nm of MAPbBr3 with a sensitivity of 428 Degree RIU-1, which improved by 268.96%. Furthermore, the impacts of four sensor structures-conventional (BK7/Ag/SM), with BiFeO3 (BK7/Ag/BiFeO3/SM), with Ni (BK7/Ag/BiFeO3/Ni/SM), and our suggested sensor structure (BK7/Ag/BiFeO3/Ni/MAPbBr3/ SM) on sensitivity were examined in this work. The proposed structure shows better angular sensitivity compared to the existing surface plasmon resonance (SPR) biosensor. The biosensor in question shows promise for identifying a broad variety of chemical molecules and biological analytes because of its increased sensitivity.