Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.
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2025, Volume 46, Issue 7
publish date：July 01 2025
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2025, 46(7): 809-820.
doi: 10.21656/1000-0887.450316
Abstract:
Curvature, a fundamental geometric property that describes the bending of objects, plays a crucial role in biological and biophysical processes. The ubiquitous presence of curvatures in natural systems and its influence on the structures and behaviors of plants, animals, and microorganisms were investigated. In the human body, curvatures are evident at multiple scales, from microscopic cellular structures to the macroscopic organic morphologies, shaping cellular functions, mechanical homeostasis, and overall biomechanical efficiency. Curvatures significantly affect cell behaviors, particularly in processes like adhesion, migration, and intercellular communication, offering insights with implications for tissue engineering. Pathologically, alterations in curvature are associated with a range of diseases including cancers and neurodegenerative disorders, influencing disease progression and providing potential therapeutic targets. Additionally, curvature has diverse biomedical applications, such as in bioimaging, tissue engineering, and targeted drug delivery. A deeper understanding of curvature's role in biological systems not only enhances our comprehension of fundamental life processes but also opens new avenues for medical innovation and therapeutic development.
Curvature, a fundamental geometric property that describes the bending of objects, plays a crucial role in biological and biophysical processes. The ubiquitous presence of curvatures in natural systems and its influence on the structures and behaviors of plants, animals, and microorganisms were investigated. In the human body, curvatures are evident at multiple scales, from microscopic cellular structures to the macroscopic organic morphologies, shaping cellular functions, mechanical homeostasis, and overall biomechanical efficiency. Curvatures significantly affect cell behaviors, particularly in processes like adhesion, migration, and intercellular communication, offering insights with implications for tissue engineering. Pathologically, alterations in curvature are associated with a range of diseases including cancers and neurodegenerative disorders, influencing disease progression and providing potential therapeutic targets. Additionally, curvature has diverse biomedical applications, such as in bioimaging, tissue engineering, and targeted drug delivery. A deeper understanding of curvature's role in biological systems not only enhances our comprehension of fundamental life processes but also opens new avenues for medical innovation and therapeutic development.
2025, 46(7): 821-835.
doi: 10.21656/1000-0887.450140
Abstract:
The ultrasonic wave, owing to its non-invasiveness, precise targeting, and minimal side effects, has found extensive applications in clinical therapy. In recent years, tumor treatment utilizing ultrasonic exciting to induce vibration behaviors in cancer cell nuclei has drawn much attention. However, the dynamical characteristics and resonance mechanisms of cell nuclei, particularly under forced vibration, remain unclear. A model for cell nuclei was established to investigate the vibration responses under low-intensity ultrasonic excitations. Typical lymphocytes (suspended cells), glial cells, and chondrocytes with different substrate stiffnesses were taken as examples. The results indicate that, the higher the frequency and intensity of ultrasonic excitation are, the larger the acoustic force acting on the cell nucleus will be. Under certain frequency and intensity of ultrasonic excitation, the acoustic force acting on the cell nucleus will increase with the cell matrix stiffness. Ultrasonic excitation on cells can cause cell nuclear resonance, and the greater the cell matrix stiffness is, the higher the cell nuclear resonance frequency will be. The relative vibration amplitude of the cell nucleus decreases with the matrix stiffness, with lymphocytes having the largest resonance amplitudes, glial cells the next largest, and chondrocytes the smallest. This study provides a theoretical and analytical framework for ultrasound-excited cell nucleus vibration, and is conducive to promoting the development of ultrasound-based tumor mechanotherapy.
The ultrasonic wave, owing to its non-invasiveness, precise targeting, and minimal side effects, has found extensive applications in clinical therapy. In recent years, tumor treatment utilizing ultrasonic exciting to induce vibration behaviors in cancer cell nuclei has drawn much attention. However, the dynamical characteristics and resonance mechanisms of cell nuclei, particularly under forced vibration, remain unclear. A model for cell nuclei was established to investigate the vibration responses under low-intensity ultrasonic excitations. Typical lymphocytes (suspended cells), glial cells, and chondrocytes with different substrate stiffnesses were taken as examples. The results indicate that, the higher the frequency and intensity of ultrasonic excitation are, the larger the acoustic force acting on the cell nucleus will be. Under certain frequency and intensity of ultrasonic excitation, the acoustic force acting on the cell nucleus will increase with the cell matrix stiffness. Ultrasonic excitation on cells can cause cell nuclear resonance, and the greater the cell matrix stiffness is, the higher the cell nuclear resonance frequency will be. The relative vibration amplitude of the cell nucleus decreases with the matrix stiffness, with lymphocytes having the largest resonance amplitudes, glial cells the next largest, and chondrocytes the smallest. This study provides a theoretical and analytical framework for ultrasound-excited cell nucleus vibration, and is conducive to promoting the development of ultrasound-based tumor mechanotherapy.
2025, 46(7): 836-854.
doi: 10.21656/1000-0887.450234
Abstract:
Head-direction cells are present in several brain regions, including the mammalian medial entorhinal cortex, and respond selectively to specific head directions, and constitute a compass system in the brain. This system can update internal direction representations in a self-organized manner, and can receive inputs from the external environment to calibrate direction encoding. Currently, many computational models for head-direction cells only consider head directions encoding in the horizontal plane. Whereas experiments show that neurons encoding both horizontal azimuth and vertical pitch angles exist in the brains of mammals, there is a lack of computational modeling of their neural mechanisms. A continuous attractor network model was constructed to encode 3D direction features such as azimuth and pitch angles at the same time, realizing both the specific direction preference encoding of 3D-head-direction cells at the single-neuron level and the accurate tracking of head direction changes in 3D space at the population level. The torus topology used in the model, compared with the spherical topology, can more reasonably explain the neuronal tuning data for azimuth recorded by bats. The proposed neurodynamic model reproduces the phenomena encoded by electrophysiological experiments recorded in 3D head directions and gives a mechanistic explanation of the dynamical angles of the activity patterns of head-direction cells in the 3D space.
Head-direction cells are present in several brain regions, including the mammalian medial entorhinal cortex, and respond selectively to specific head directions, and constitute a compass system in the brain. This system can update internal direction representations in a self-organized manner, and can receive inputs from the external environment to calibrate direction encoding. Currently, many computational models for head-direction cells only consider head directions encoding in the horizontal plane. Whereas experiments show that neurons encoding both horizontal azimuth and vertical pitch angles exist in the brains of mammals, there is a lack of computational modeling of their neural mechanisms. A continuous attractor network model was constructed to encode 3D direction features such as azimuth and pitch angles at the same time, realizing both the specific direction preference encoding of 3D-head-direction cells at the single-neuron level and the accurate tracking of head direction changes in 3D space at the population level. The torus topology used in the model, compared with the spherical topology, can more reasonably explain the neuronal tuning data for azimuth recorded by bats. The proposed neurodynamic model reproduces the phenomena encoded by electrophysiological experiments recorded in 3D head directions and gives a mechanistic explanation of the dynamical angles of the activity patterns of head-direction cells in the 3D space.
2025, 46(7): 855-866.
doi: 10.21656/1000-0887.450093
Abstract:
A chaotic response surface method was proposed to improve the computational efficiency and accuracy of the traditional response surface method for stochastic analysis of structural responses involving non-Gaussian random variables. Firstly, the non-Gaussian response variable was expanded by a hybrid generalized polynomial chaos constructed according to the probability distribution function types of the basic random variables. Secondly, the candidate probability collocation points in the non-Gaussian probability space were determined through the combination of the roots of the 1D generalized polynomial chaos with the next higher order, then the probability optimal collocation points in the non-Gaussian probability space were picked out based on the full row rank principle of the coefficient matrix. Finally, the unknown coefficients of the proposed response surface were determined by means of the least squares method. Comparison of examples shows that, the proposed method requires fewer collocation points and lower expansion orders, and achieves higher calculation accuracy and efficiency than those of the traditional response surface methods.
A chaotic response surface method was proposed to improve the computational efficiency and accuracy of the traditional response surface method for stochastic analysis of structural responses involving non-Gaussian random variables. Firstly, the non-Gaussian response variable was expanded by a hybrid generalized polynomial chaos constructed according to the probability distribution function types of the basic random variables. Secondly, the candidate probability collocation points in the non-Gaussian probability space were determined through the combination of the roots of the 1D generalized polynomial chaos with the next higher order, then the probability optimal collocation points in the non-Gaussian probability space were picked out based on the full row rank principle of the coefficient matrix. Finally, the unknown coefficients of the proposed response surface were determined by means of the least squares method. Comparison of examples shows that, the proposed method requires fewer collocation points and lower expansion orders, and achieves higher calculation accuracy and efficiency than those of the traditional response surface methods.
2025, 46(7): 867-881.
doi: 10.21656/1000-0887.450139
Abstract:
Due to the excellent properties of materials and structures, composite laminated cylindrical shells are widely used in such key fields as chemical, marine and aerospace engineering. However, the local mechanical responses near the interfaces and boundaries are complex and affect the performances of the structures. As an effective method to obtain the exact solutions of the laminated structures, the state space method needs the numerical simulation to deal with the non-simply supported boundaries. Based on the state space framework for laminated cylindrical shells, the boundary displacement functions at the non-simply supported ends were introduced into the state equations as state variables, and homogeneous state equations were established to strictly satisfy the boundary conditions. Then, the variable coefficients in the state equations were converted to constants with the lamination approximate method, and the transfer relations of the mechanical quantities along the thickness of the laminated cylindrical shell were established. Finally, the loading conditions on the surfaces of the cylindrical shells were introduced with the Fourier series, and the exact solutions to the axisymmetric bending problems were obtained. The examples show that, the present solutions are consistent with the finite element ones, and give the exact distributions of the stresses and displacements along the axial and radial directions of the laminated cylindrical shells. In addition, the displacement and stress distributions near the clamped and free ends help illustrate the end effects of the two constraints.
Due to the excellent properties of materials and structures, composite laminated cylindrical shells are widely used in such key fields as chemical, marine and aerospace engineering. However, the local mechanical responses near the interfaces and boundaries are complex and affect the performances of the structures. As an effective method to obtain the exact solutions of the laminated structures, the state space method needs the numerical simulation to deal with the non-simply supported boundaries. Based on the state space framework for laminated cylindrical shells, the boundary displacement functions at the non-simply supported ends were introduced into the state equations as state variables, and homogeneous state equations were established to strictly satisfy the boundary conditions. Then, the variable coefficients in the state equations were converted to constants with the lamination approximate method, and the transfer relations of the mechanical quantities along the thickness of the laminated cylindrical shell were established. Finally, the loading conditions on the surfaces of the cylindrical shells were introduced with the Fourier series, and the exact solutions to the axisymmetric bending problems were obtained. The examples show that, the present solutions are consistent with the finite element ones, and give the exact distributions of the stresses and displacements along the axial and radial directions of the laminated cylindrical shells. In addition, the displacement and stress distributions near the clamped and free ends help illustrate the end effects of the two constraints.
2025, 46(7): 882-892.
doi: 10.21656/1000-0887.450202
Abstract:
Spherical particles non-filled with water as the phase change material were fabricated. A rotating drum experimental setup was built. the influences of the motion of the phase interface inside the particles on the dynamic angles of repose of the particles in the rotating drum were investigated with varying particle diameters, volume fractions of the phase change material inside the particles, filling ratios of the rotating drum, and rotation speeds. The dynamic angle of repose was obtained through image capture and the MATLAB image processing. The results indicate that, the motion of the phase interface can cause some particles to slip, enhancing particle flowability and resulting in a fluctuating change in the resting angle with an increasing rotational speed. As the volume fraction increases, the flowability of the particles will improve, and the resting angle will decrease, while the effect of the rotational speed on the particles will gradually diminish. Furthermore, as the filling rate decreases and the particle size increases, the dynamic resting angle of the particle bed layer will decrease, the particle flow capacity will heighten, and the particle bed layer will be more susceptible to the phase interface motion.
Spherical particles non-filled with water as the phase change material were fabricated. A rotating drum experimental setup was built. the influences of the motion of the phase interface inside the particles on the dynamic angles of repose of the particles in the rotating drum were investigated with varying particle diameters, volume fractions of the phase change material inside the particles, filling ratios of the rotating drum, and rotation speeds. The dynamic angle of repose was obtained through image capture and the MATLAB image processing. The results indicate that, the motion of the phase interface can cause some particles to slip, enhancing particle flowability and resulting in a fluctuating change in the resting angle with an increasing rotational speed. As the volume fraction increases, the flowability of the particles will improve, and the resting angle will decrease, while the effect of the rotational speed on the particles will gradually diminish. Furthermore, as the filling rate decreases and the particle size increases, the dynamic resting angle of the particle bed layer will decrease, the particle flow capacity will heighten, and the particle bed layer will be more susceptible to the phase interface motion.
2025, 46(7): 893-903.
doi: 10.21656/1000-0887.450179
Abstract:
The complex parameters of functionally graded materials (FGMs) lead to the complicated stress fields, which brings some difficulties for numerical analysis of their fatigue fracture. The complicated fracture problems such as crack propagation can be simulated with the phase-field model without additional fracture criteria. The hybrid phase-field model for FGMs was extended to fatigue fracture problems through introduction of the fatigue function to degrade the fracture energy. The phase-field model for fatigue fracture of FGMs was developed and the driving force for crack propagation was analyzed. The fatigue fracture mechanism that the crack propagation is controlled by the strain energy history, the critical energy release rate and the fatigue degradation function, was revealed. This work offers some guidance for the design of FGM structures.
The complex parameters of functionally graded materials (FGMs) lead to the complicated stress fields, which brings some difficulties for numerical analysis of their fatigue fracture. The complicated fracture problems such as crack propagation can be simulated with the phase-field model without additional fracture criteria. The hybrid phase-field model for FGMs was extended to fatigue fracture problems through introduction of the fatigue function to degrade the fracture energy. The phase-field model for fatigue fracture of FGMs was developed and the driving force for crack propagation was analyzed. The fatigue fracture mechanism that the crack propagation is controlled by the strain energy history, the critical energy release rate and the fatigue degradation function, was revealed. This work offers some guidance for the design of FGM structures.
2025, 46(7): 904-915.
doi: 10.21656/1000-0887.450221
Abstract:
The inverse problem of reconstructing spatial heat sources in the thermal wave diffusion model for biological organisms, was Investigated. Unlike traditional parabolic models for biological heat transfer, this work was focused on a more complex and practical hyperbolic model, particularly suitable for biomedical engineering applications. Firstly, the optimal control theory was employed, and the inverse problem was formulated as an optimal control problem. To address the challenge of non-uniqueness in the optimal solution due to the non-differentiability of total variation functions, a carefully designed and polished total variation regularization term was introduced. Subsequently, the existence of the optimal solution and its necessary conditions were thoroughly discussed. Secondly, under the assumption of a small terminal time, the uniqueness and stability of the optimal solution were proven with the Sobolev embedding theory. Last, a gradient-based optimization algorithm was developed based on these necessary conditions, and its effectiveness was demonstrated through several numerical examples.
The inverse problem of reconstructing spatial heat sources in the thermal wave diffusion model for biological organisms, was Investigated. Unlike traditional parabolic models for biological heat transfer, this work was focused on a more complex and practical hyperbolic model, particularly suitable for biomedical engineering applications. Firstly, the optimal control theory was employed, and the inverse problem was formulated as an optimal control problem. To address the challenge of non-uniqueness in the optimal solution due to the non-differentiability of total variation functions, a carefully designed and polished total variation regularization term was introduced. Subsequently, the existence of the optimal solution and its necessary conditions were thoroughly discussed. Secondly, under the assumption of a small terminal time, the uniqueness and stability of the optimal solution were proven with the Sobolev embedding theory. Last, a gradient-based optimization algorithm was developed based on these necessary conditions, and its effectiveness was demonstrated through several numerical examples.
2025, 46(7): 916-925.
doi: 10.21656/1000-0887.450171
Abstract:
A self-adaptive alternating direction multiplier method was proposed for a class of contact problems defined in 2 domains. A minimization problem constrained by inequalities was obtained for the variational problem in 2 domains, then the problem was equivalent to a saddle-point problem through introduction of an auxiliary unknown on the contact boundary. The alternating direction multiplier method was applied to the saddle point problem for the numerical solution, with each iteration successively determining the auxiliary variable explicitly, solving a linear problem and updating the Lagrange multiplier. The self-adaptive alternating direction multiplier method was proposed to select the penalty parameter automatically, by means of a self-adaptive rule and iterative functions. The results prove the convergence and demonstrate the effectiveness of the proposed method.
A self-adaptive alternating direction multiplier method was proposed for a class of contact problems defined in 2 domains. A minimization problem constrained by inequalities was obtained for the variational problem in 2 domains, then the problem was equivalent to a saddle-point problem through introduction of an auxiliary unknown on the contact boundary. The alternating direction multiplier method was applied to the saddle point problem for the numerical solution, with each iteration successively determining the auxiliary variable explicitly, solving a linear problem and updating the Lagrange multiplier. The self-adaptive alternating direction multiplier method was proposed to select the penalty parameter automatically, by means of a self-adaptive rule and iterative functions. The results prove the convergence and demonstrate the effectiveness of the proposed method.
2025, 46(7): 926-938.
doi: 10.21656/1000-0887.450273
Abstract:
The Hadamard well-posedness of a set optimization problem (P) and an infinite set optimization problem (ISOP) under upper set order relation was studied. Firstly, in the case of the gamma convergence of the set-valued mapping sequence, the definitions of the generalized Hadamard well-posedness and the ε-generalized Hadamard well-posedness for (P) were given, the relationship between these 2 types of well-posednesses were established, and the sufficient conditions for the Hadamard well-posedness of (P) were obtained. Then the sufficient conditions for the Hadamard well-posedness of (ISOP) were studied with the concept of Hausdorff cone-continuity under functional perturbations of both constraint sets and objective maps. The results improve those in the relevant previous references, enriching the study of set optimization problems.
The Hadamard well-posedness of a set optimization problem (P) and an infinite set optimization problem (ISOP) under upper set order relation was studied. Firstly, in the case of the gamma convergence of the set-valued mapping sequence, the definitions of the generalized Hadamard well-posedness and the ε-generalized Hadamard well-posedness for (P) were given, the relationship between these 2 types of well-posednesses were established, and the sufficient conditions for the Hadamard well-posedness of (P) were obtained. Then the sufficient conditions for the Hadamard well-posedness of (ISOP) were studied with the concept of Hausdorff cone-continuity under functional perturbations of both constraint sets and objective maps. The results improve those in the relevant previous references, enriching the study of set optimization problems.
2025, 46(7): 939-946.
doi: 10.21656/1000-0887.450191
Abstract:
The finite-time synchronization and energy consumption problems for a class of T-S fuzzy multi-layer networks were discussed. First, a T-S fuzzy control strategy was given for the multi-layer networks to deal with the flexible relationship between multi-layer networks. Second, based on the fuzzy theory, a finite-time controller was designed and a criterion for achieving finite-time synchronization between the drive system and the response system was proposed. In addition, based on the energy theory, the upper limits of the energy consumption and synchronization time of the T-S fuzzy multi-layer network were estimated to evaluate the working time of the controller. Finally, the correctness of the obtained results was verified by a numerical example.
The finite-time synchronization and energy consumption problems for a class of T-S fuzzy multi-layer networks were discussed. First, a T-S fuzzy control strategy was given for the multi-layer networks to deal with the flexible relationship between multi-layer networks. Second, based on the fuzzy theory, a finite-time controller was designed and a criterion for achieving finite-time synchronization between the drive system and the response system was proposed. In addition, based on the energy theory, the upper limits of the energy consumption and synchronization time of the T-S fuzzy multi-layer network were estimated to evaluate the working time of the controller. Finally, the correctness of the obtained results was verified by a numerical example.
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Founded in 1980 ( monthly )
Supervisor：Chongqing Jiaotong University
Founder：CHIEN Weizang
Honorary Chief Editor：ZHONG Wanxie
Editor-in-Chief：LU Tianjian
ISSN 1000-0887
CN 50-1060/O3
