Quantitative Mathematical Model Research Articles

A thermal conductivity model for alpine meadow soils on the Tibetan Plateau and validation analysis

Under the background of global warming, natural disasters such as landslides and mudslides are becoming more frequent on the Tibetan Plateau. It is important to study the thermal behavior of alpine meadow soils, which are widely distributed on the Tibetan Plateau due to the high altitude and extreme climate. In this paper, a quantitative mathematical model of thermal conductivity for alpine meadow soils is presented, which successfully describes the influence of plant roots and organic matter on the thermal behavior of alpine meadow soils. A series of thermal conductivity experiments are carried out on thirty alpine meadow soils collected from Nangqian district, located east of Tibetan Plateau, China. The results of the proposed model are compared with the experimental measured data to validate the model efficiency and satisfactory agreement is achieved. Furthermore, Root mean square error (RMSE) and bias are also used to evaluate the performance of the proposed model and other available models. The results of the validation analysis show that the proposed model, with an RMSE of 0.041 W m−1 K−1 and a bias of 0.005 W m−1 K−1, provides reliable and accurate estimated values of thermal conductivity for alpine meadow soils. This study is beneficial for understanding the thermal behaviors of soil-root system on the Tibetan Plateau.

Interfacial cohesion model of ultra‐high performance concrete wet joints under the influence of multiple factors

AbstractThe interfacial cohesion between precast normal concrete (NC) and cast‐in‐place ultra‐high performance concrete (UHPC) is an important index to evaluate their interfacial bond strength, which is of great importance for the application of UHPC as a connection material for precast structural bridges. Interfacial cohesion is related to several influencing factors. However, there needs to be more research on the interrelationship model between multiple influencing factors and interfacial cohesion. This study took the UHPC wet joint in a precast concrete structure as the object. First, the relationship between the interface cohesion of UHPC wet joint and substrate strength, UHPC age, interfacial roughness, interfacial moisture content, and curing method was studied; The result shows that the key factors affecting interfacial cohesion include UHPC age, interface roughness, and substrate strength, with interfacial moisture content potentially playing a secondary role. Second, the failure types of the interface zone surface by using digital image correlation (DIC) are divided into three categories. Finally, the quantitative mathematical model of interfacial cohesion under the coupling effect of multiple factors was established based on the above four factors. The model is in good agreement with the experimental data.

Study on the variation regularities of minimum explosion concentration of moist magnesium dust/derived hydrogen hybrids under multiple working conditions

Magnesium is widely used but often accompanied by frequent magnesium powder explosion accidents. If the variation regularity and mechanism of the minimum explosion concentration (cm) of magnesium powder under the multi-factor coupling effect can be understood, the occurrence of magnesium powder explosion accidents can be fundamentally avoided, and intrinsic safety can be achieved. In this paper, experiments were conducted using a self-made 20 L explosion device to explore the effects of particle size, initial temperature, and equilibrium relative humidity (ERH) coupling on the cm of magnesium powder. The study found that an increase in ERH of moist magnesium powder would lead to easier agglomeration of the dust, making it less prone to activation. Additionally, excessive moisture also absorbed more heat, reducing the ignition sensitivity of the dust cloud and resulting in a continuous increase in cm. However, increasing the initial temperature and decreasing the dust particle size both decreased the cm of moist magnesium powder, weakening the effect of ERH on cm. Furthermore, using the analysis methods of orthogonal experimental range and AHP model, it was determined that the influence weights of the factors coupling effects on the cm of magnesium powder, from highest to lowest weight, were: particle size > ERH > initial temperature.Furthermore, in order to deeper understand the mechanism of the action process that affect the cm of moist magnesium powder, additional experiments were conducted to further confirm that the addition of hydrogen derived from the erosion reaction of moist magnesium powder to the explosion system can reduce the cm of magnesium dust clouds. Moreover, a quantitative mathematical model for predicting the cm of magnesium powder/hydrogen two-phase system was also established.

Measurement technology based on a Stokes parametric polarization system

Structured light measurement systems often use polarization filters to reduce image interference from highly reflective areas. This method can be effective, but it may also reduce the brightness of specific areas, particularly overly dark portions, which can affect the accuracy of the measurement results. This paper proposes a measurement method for a polarization system based on Stokes parameters to solve the problem. After adjusting the polarization filter to angles of 0°, 45°, and 90°, the camera captures an image of the object and calculates the corresponding Stokes parameters to generate the expected polarization angle histogram. Then, based on the detailed information on the angle distribution, the accurate mathematical model is used to screen the interval, and the optimal polarization angle is determined by orthogonal processing while ensuring the signal-to-noise ratio and image quality. Finally, an image fusion technology synthesizes a set of fringe projection images with the preferred polarization angles. Experiments have shown that this new method effectively addresses the issue of interference in the highlighted region when using conventional polarization filters. Additionally, it significantly improves the quality of the fringe pattern. The polarization angle selection in the experimental process is made more rapid and accurate through the quantitative mathematical model calculation of the polarization angle, significantly improving the system’s measurement efficiency.

Post-COVID breathlessness: a mathematical model of respiratory processing in the brain.

Breathlessness is among the most common post-COVID symptoms. In a considerable number of patients, severe breathlessness cannot be explained by peripheral organ impairment. Recent concepts have described how such persistent breathlessness could arise from dysfunctional processing of respiratory information in the brain. In this paper, we present a first quantitative and testable mathematical model of how processing of respiratory-related signals could lead to breathlessness perception. The model is based on recent theories that the brain holds an adaptive and dynamic internal representation of a respiratory state that is based on previous experiences and comprises gas exchange between environment, lung and tissue cells. Perceived breathlessness reflects the brain's estimate of this respiratory state signaling a potentially hazardous disequilibrium in gas exchange. The internal respiratory state evolves from the respiratory state of the last breath, is updated by a sensory measurement of CO2 concentration, and is dependent on the current activity context. To evaluate our model and thus test the assumed mechanism, we used data from an ongoing rebreathing experiment investigating breathlessness in patients with post-COVID without peripheral organ dysfunction (N = 5) and healthy control participants without complaints after COVID-19 (N = 5). Although the observed breathlessness patterns varied extensively between individual participants in the rebreathing experiment, our model shows good performance in replicating these individual, heterogeneous time courses. The model assumes the same underlying processes in the central nervous system in all individuals, i.e., also between patients and healthy control participants, and we hypothesize that differences in breathlessness are explained by different weighting and thus influence of these processes on the final percept. Our model could thus be applied in future studies to provide insight into where in the processing cascade of respiratory signals a deficit is located that leads to (post-COVID) breathlessness. A potential clinical application could be, e.g., the monitoring of effects of pulmonary rehabilitation on respiratory processing in the brain to improve the therapeutic strategies.

Design of a Biohybrid Materials Circuit with Binary Decoder Functionality.

Synthetic biology applies concepts from electrical engineering and information processing to endow cells with computational functionality. Transferring the underlying molecular components into materials and wiring them according to topologies inspired by electronic circuit boards has yielded materials systems that perform selected computational operations. However, the limited functionality of available building blocks is restricting the implementation of advanced information-processing circuits into materials. Here, a set of protease-based biohybrid modules the bioactivity of which can either be induced or inhibited is engineered. Guided by a quantitative mathematical model and following a design-build-test-learn (DBTL) cycle, the modules are wired according to circuit topologies inspired by electronic signal decoders, a fundamental motif in information processing. A 2-input/4-output binary decoder for the detection of two small molecules in a material framework that can perform regulated outputs in form of distinct protease activities is designed. The here demonstrated smart material system is strongly modular and can be used for biomolecular information processing for example in advanced biosensing or drug delivery applications.

Time dependent performance analysis of a Smart Trash bin using state-based Markov model and Reliability approach

In this paper, the authors have developed a quantitative mathematical model to assess the performance of a smart trash bin. This model takes into account six hardware components of the trash bin, including Arduino Uno, ultrasonic sensor, servo motor, switch, battery, jumper wires utilizing Markov modelling and reliability-based approach. The objective of this model is to facilitate timely planning of repair and maintenance activities, ensuring prolonged availability of the smart trash bin after identifying the weakest component/components of the system.The efficient functioning of all components in the smart trash bin is imperative for the timely transmission of the garbage level data to the municipal corporation. To achieve this, the paper focuses on evaluating key reliability metric for smart trash bin system, specifically reliability, unreliability, and Mean time to Failure (MTTF). The modelling approach employs a state-based Markov model, from which Kolmogorov differential equations are derived and subsequently solved using Laplace transformation. After collecting data from organization and experts of the field explicit expression for system reliability, unreliability and MTTF have been obtained.Furthermore, this study includes sensitivity analysis of the system to pinpoint critical components which is switch and servo motor, requiring attention for proper maintenance. The research finding indicates that reliability and MTTF of the system diminish as the failure rate of the components increase under certain conditions.

Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities.

A 19F-qNMR-Guided Mathematical Model for G Protein-Coupled Receptor Signaling.

G protein-coupled receptors (GPCRs) exhibit a wide range of pharmacological efficacies, yet the molecular mechanisms responsible for the differential efficacies in response to various ligands remain poorly understood. This lack of understanding has hindered the development of a solid foundation for establishing a mathematical model for signaling efficacy. However, recent progress has been made in delineating and quantifying receptor conformational states and associating function with these conformations. This progress has allowed us to construct a mathematical model for GPCR signaling efficacy that goes beyond the traditional ON/OFF binary switch model. In this study, we present a quantitative conformation-based mathematical model for GPCR signaling efficacy using the adenosine A2A receptor (A2AR) as a model system, under the guide of 19F quantitative nuclear magnetic resonance experiments. This model encompasses two signaling states, a fully activated state and a partially activated state, defined as being able to regulate the cognate Gα s nucleotide exchange with respective G protein recognition capacity. By quantifying the population distribution of each state, we can now in turn examine GPCR signaling efficacy. This advance provides a foundation for assessing GPCR signaling efficacy using a conformation-based mathematical model in response to ligand binding. SIGNIFICANCE STATEMENT: Mathematical models to describe signaling efficacy of GPCRs mostly suffer from considering only two states (ON/OFF). However, research indicates that a GPCR possesses multiple active-(like) states that can interact with Gαβγ independently, regulating varied nucleotide exchanges. With the guide of 19F-qNMR, the transitions among these states are quantified as a function of ligand and Gαβγ, serving as a foundation for a novel conformation-based mathematical signaling model.

Risk assessment of rain-induced debris flow in the lower reaches of Yajiang River based on GIS and CF coupling models

Abstract In order to reduce the adverse impact of debris flow disasters on engineering construction facilities and social security in the lower reaches of the Yajiang River, this article selected 11 risk assessment factors such as elevation, aspect, profile curvature, Relief, and rainfall to study the occurrence rule of debris flow in this area. The data of disaster factors caused by debris flow points were derived and analyzed in ArcGIS. Then, factor correlation test and factor sensitivity level were established. The coupling model of qualitative mathematical model (analytic Hierarchy Process, AHP), quantitative mathematical model (binary logistic regression [LR]), machine learning model (random forest RF), and certainty factor (CF) were, respectively, used to predict the risk of debris flow disaster in the study area. After comparison, it was found that the CF–LR model had the highest accuracy. The results show that the areas with high debris flow risk are mainly concentrated in the first half of the lower reaches of the Yajiang River and distributed along both sides of the river bank. The annual rainfall range of 600–700 mm is the critical water source saturation value of debris flow in the study area.

New conceptualization and quantification method of first-flush in urban catchments: A modelling study

A major challenge for runoff pollution control lies in the quantification and identification of the first-flush. At present, there is a lack of reasonable theoretical methods to guide engineering practices. To remedy this deficiency, a novel method of cumulative pollutant mass vs. cumulative runoff volume (M(V)) curve simulation is proposed in this study. Subsequently, the first-flush phenomenon was redefined based on the M(V) curve simulation and demonstrate that the first-flush exists until the derivative of the simulated M(V) curve is equal to 1 (Ft′ = 1). Consequently, a mathematical model for first-flush quantification was developed. The Root-Mean-Square-Deviation (RMSD) and Pearson's Correlation Coefficient (PCC), as objective functions, were used to evaluate the performance of the model and the Elementary-Effect (EE) method was used to analyze the sensitivity of the parameters. The results indicated the satisfactory accuracy of the M(V) curve simulation and first-flush quantitative mathematical model. The NSE values exceeding 0.8 and 0.938, respectively, were obtained by analyzing 19 rainfall-runoff data for Xi'an, Shaanxi Province, China. The wash-off coefficient “r” was demonstrably the most sensitive factor influencing the model performance. Therefore, interactions between “r” and the other model parameters should be focused on to highlight the overall sensitivities. Overall, this study posits a novel paradigm shift from the traditional dimensionless definition criterion to redefine and quantify first-flush, which has significant implications for urban water environment management.

Mathematical Modeling of Seepage–Temperature Field for Earth Dam Using Experimental Test

Monitoring the seepage field is essential to characterize the operation of the earth dam. However, conventional seepage monitoring typically involves the use of a piezometer tube or pressure sensor for point distribution. A mathematical model incorporating the feedback of the temperature field on the seepage field was proposed based on experimental test observations. First, a theoretical analysis of the mathematical model is conducted, which includes examining the relationship between the variation of temperature field and factors, such as hydraulic gradient, water and soil temperature difference, hydraulic conductivity, thermal conductivity, specific heat, and time. Second, a homogeneous earth dam model is constructed in the laboratory with a distributed temperature sensor system to obtain synchronous information of the seepage–temperature field. Finally, the parameters of the mathematical model are quantified using observations from experimental tests, demonstrating good agreement between calculated and measured values. The experimental results indicate the feasibility of inferring seepage field monitoring information from the temperature field and elucidation of the interaction mechanism of the coupled fields. The quantitative mathematical model of the temperature field feedback on the seepage field is validated for its applicability in earth dams.

Predicting Effective Adaptation to Breast Cancer to Help Women BOUNCE Back: Protocol for a Multicenter Clinical Pilot Study.

BackgroundDespite the continued progress of medicine, dealing with breast cancer is becoming a major socioeconomic challenge, particularly due to its increasing incidence. The ability to better manage and adapt to the entire care process depends not only on the type of cancer but also on the patient’s sociodemographic and psychological characteristics as well as on the social environment in which a person lives and interacts. Therefore, it is important to understand which factors may contribute to successful adaptation to breast cancer. To our knowledge, no studies have been performed on the combination effect of multiple psychological, biological, and functional variables in predicting the patient’s ability to bounce back from a stressful life event, such as a breast cancer diagnosis. Here we describe the study protocol of a multicenter clinical study entitled “Predicting Effective Adaptation to Breast Cancer to Help Women to BOUNCE Back” or, in short, BOUNCE.ObjectiveThe aim of the study is to build a quantitative mathematical model of factors associated with the capacity for optimal adjustment to cancer and to study resilience through the cancer continuum in a population of patients with breast cancer.MethodsA total of 660 women with breast cancer will be recruited from five European cancer centers in Italy, Finland, Israel, and Portugal. Biomedical and psychosocial variables will be collected using the Noona Healthcare platform. Psychosocial, sociodemographic, lifestyle, and clinical variables will be measured every 3 months, starting from presurgery assessment (ie, baseline) to 18 months after surgery. Temporal data mining, time-series prediction, sequence classification methods, clustering time-series data, and temporal association rules will be used to develop the predictive model.ResultsThe recruitment process stared in January 2019 and ended in November 2021. Preliminary results have been published in a scientific journal and are available for consultation on the BOUNCE project website. Data analysis and dissemination of the study results will be performed in 2022.ConclusionsThis study will develop a predictive model that is able to describe individual resilience and identify different resilience trajectories along the care process. The results will allow the implementation of tailored interventions according to patients’ needs, supported by eHealth technologies.Trial RegistrationClinicalTrials.gov NCT05095675; https://clinicaltrials.gov/ct2/show/NCT05095675International Registered Report Identifier (IRRID)DERR1-10.2196/34564

Probabilistic seismic demand model of UBPRC columns conditioned on Pulse-Structure parameters

Unbonded prestressed reinforced concrete (UBPRC) column has attracted the attention of many researchers in bridge seismic design because of its small residual displacement. However, the research on the mechanism and quantitative method of its seismic response under near-fault impulse ground motions is still insufficient. On this basis, a quantitative probabilistic mathematical model was established to evaluate the seismic demand of UBPRC columns with different structural parameters subjected to earthquakes with varying pulse parameters. Firstly, in order to describe the seismic response of UBPRC columns under pulse-like ground motions accurately and conveniently, a new parameter (xT) composed by fundamental period (T1) and pulse period (Tp) was proposed. It is found that Gaussian function can well describe the relationship between the newly defined parameter and seismic demand, based on a set of seismic response databases of UBPRC columns with different heights under impulse ground motions. Secondly, considering that the peak pulse velocity (Vp) has a significant impact on the seismic response of bridge structures, the influence of Vp on the parameters of Gaussian function was studied, and the functional relationship between these parameters and Vp was established. Finally, a novel probabilistic seismic demand model (PSDM) considering structure parameters and pulse parameters was established, and its accuracy is verified. The quantitative mathematical model with multi pulse-structure coupled parameters can be adopted to conduct the seismic fragility analysis of UBPRC columns. The verification and application indicate that the proposed PSDM model can quickly and accurately estimate the seismic demand of UBPRC column under different near-fault impulse ground motions.

Analysis of Grid Response Strategies for the Safety Behavior Risk Events of Transportation System Based on System Dynamics—“the Assistant Watchman Does Not Appear as Required”

Employees are the most important and dynamic elements in the railway transportation system. How to achieve accurate control of inertial violation of “key person, key matter, key period”, and formulate more personalized risk response strategy is a thorny problem that faced by safety managers. The existing risk response usually takes control measures from the perspective of the system as a whole, ignoring the heterogeneity of risk, and the selection of response strategies only considers the target risks to be dealt with, ignoring the secondary risks that may occur in the process of risk response, or the residual risks formed by changing the existing risk, coupled with the lack of quantitative evaluation of risk response effect, resulting in poor risk response effect. By introducing the grid theory and taking the risk event of “the assistant watchman does not appear as required” at Huangyangcheng station of Shenshuo Railway as an example, this study constructs a grid response model of the assistant watchman risk events based on system dynamics. Through the grid division, the model accurately locates and classifies the assistant watchman on duty. Then, during the system dynamics simulation process, the hazard factor is regarded as a bridge, and the traditional virtual boundary of system simulation is transformed into accurate grid definition. By improving the response strategy of safety behavior risk event of the assistant watchman on duty in cell grid and using Vensim-PLE software for personalized simulation, the intervention of “the assistant watchman does not appear as required” risk event is transformed from qualitative analysis to dynamic quantitative mathematical model, so as to realize the personalized response simulation analysis of employees in the grid.

Measurement, Evaluation, and Model Construction of Mathematical Literacy Based on IoT and PISA

“Mathematics Curriculum Standard for Ordinary Senior High School” points out that mathematical modelling literacy is the literacy of abstracting real problems mathematically, expressing problems with mathematical language, and building models with mathematical methods to solve problems. It assesses the amount to which students who are about to finish compulsory schooling have the knowledge and aptitude to deal with future life issues, based on the notion of lifelong learning. The usage of a local integrated development environment requires a number of complex processes, including installation and setup, as well as the procurement of necessary hardware. In reality, in order to nurture students, the core literacy of mathematics is to completely execute quality education, further identify the training and development direction of talents, and infiltrate the core literacy material into junior high school mathematics classroom instruction. For such a large-scale international education measurement project, the research and development of test questions is very important. Therefore, detailed technical consideration has been carried out and test volumes have been designed that are relatively suitable for different countries. The test questions are closely related to life, while there are few questions related to real situational problems in the test, which are mathematically processed first. Due to the international background of evaluation, it is a great challenge for researchers to realize the localization of evaluation on the basis of adapting to the domestic situation. At the same time, there is no scientific and perfect mathematical modelling literacy evaluation system in China’s basic education research. How can middle school front-line teachers better evaluate students’ mathematical modelling literacy? As a result, it is critical to develop a scientific and quantitative mathematical literacy measurement model that will aid in the teaching and research of mathematical modelling by middle school front-line teachers, as well as contributing theoretically to the evaluation and research of mathematical modelling literacy in China. Therefore, based on mathematics literacy evaluation, this paper studies the hierarchy of the IoT and the measurement and evaluation model of mathematics literacy based on the IoT, as well as its enlightenment to the compilation of mathematics academic test questions in China.

Establishment, Analysis, and Application of the Information Transmission and Response Model for Students of Vocational Colleges under Public Health Emergencies.

To provide a basic quantitative mathematical model for data analysis, decision-making support, and application of information systems oriented to emergency research, this paper established an information transmission response model for school students under such system mathematically based on actual school information transmission data during COVID-19 prevention. This paper proposes an emergency information management method—a two-step emergency information management method. It can be referenced for promotion of the development of IT-based school management, enhancement of IT application in school emergency information management, and improvement of the speed and accuracy of information transmission.

Prediction of birefringence for polymer optical products based on a novel molecular chain orientation model

Optical polymer materials are widely used in aerospace, electronics, and other engineering fields, which have strict requirements on optical properties such as the birefringence of products. The present birefringence calculation method is based on the stress-birefringence law and is still difficult in accurate prediction, owing to extremely difficulty in predict residual stress. Actually, the birefringence of polymer optical products is essentially caused by the molecular chain orientation. Thus, a quantitative mathematical model between molecular orientation and birefringence is proposed in this study. The coupling simulation of the macroscopic flow field and microscopic orientation is realized through internal stress. The accuracy of the proposed model is verified by the polarized Raman and birefringence distribution experimental results. Compared with the stress-birefringence method, the proposed model and numerical method can more accurately simulate molecular orientation and birefringence. Meanwhile, the simulated average orientation degree in the thickness direction under different melt and mold temperatures are compared with the measured results, which verifies the effectiveness of the proposed model and simulation method at different process conditions.

AI Predicted Competency Model to Maximize Job Performance

Human resources are concerned with recruiting, training and keeping talent. The correct selection of personnel is key to the success of a business because regardless of the outstanding business strategy, those who put it into practice are most important. A carefully developed strategy is as bad as having no strategy if the wrong person is placed in the wrong position. There are no studies to predict the competency of job applicants based on dimensional values such as level of knowledge, self-motivation, self-concern and role perception. This study proposes a prediction model that uses AI (Artificial Intelligence), this includes a quantitative mathematical model that identifies the level of personnel competency to optimize job performance. The model verifies the discrete and continuous relationship between competency dimensions and their synergetic effects. Four AI algorithms are used to train a data set that contains 362 data elements, consisting of two optimized combinations of dimensional values in step 1, and 360 data elements that are derived from the dimensional relationship that produces the synergetic effects. The proposed model predicts the competence of job applicants and compares this competence with the value gives optimized job performance to optimize the selection of human resources.

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.