The physical information neural networks(PINNs)are an important tool for solving partial differen-tial equations.In the numerical solution of partial differential equations,equations with discontinuous solutions are currently a research challenge.The PINNs and their existing improved algorithms often cannot capture the characteristics of discontinuities.However,many discontinuous problems need to be considered in the field of fluid mechanics.In response to the shortcomings of the PINNs in handling equations with discontinuous solu-tions,an adaptive gradient-annihilated PINNs(AGA-PINNs)method was proposed to solve the Burgers equa-tions and the Allen-Cahn equations with discontinuous solutions.The gradient related weight functions were uti-lized to optimize the loss function,and the training points were dynamically adjusted based on the current re-sidual distribution during the training process to gradually enhance the model's learning ability in discontinuous regions.The experimental results show that,the AGA-PINNs method significantly improves the accuracy of pre-dicted physical quantities compared to the traditional PINNs,the gradient-enhanced physics-informed neural networks(gPINNs),the gradient-annihilated physics-informed neural networks(GA-PINNs)method,and the high-order deep Galerkin(DG)method.In solving the Burgers equation and the Allen-Cahn equation,the mean square errors decrease by approximately 1 order of magnitude,accurately reproducing the characteristics of shock waves in the Burgers equation and the phase separation phenomena in the Allen-Cahn equation.
Core analysis is the cornerstone of reservoir evaluation.The digital rock physics(DRP)enables the quantitative characterization of reservoir microstructures and flow properties through 3D imaging and numerical simulation.The evolution of DRP paradigms was reviewed from the 1st-generation"What you see is what you get"(geometric characterization)and the 2nd-generation"What you calculate is what you get"(numerical simulation),to the emerging 3rd-generation"What you learn is what you get"(intelligent prediction).The 1st 2 paradigms face 2 core bottlenecks:the difficulty in determining the representative elementary volume(REV)and the prohibitive computational costs of numerical simulations.The progress of the 3rd-generation intelligent prediction paradigm was systematically summarized,with the focus on structural properties,single-phase per-meability,and multiphase flow properties(relative permeability,capillary pressure,and wettability).Centered on deep learning,this paradigm offers revolutionary pathways to overcome traditional limitations:on one hand,the generative adversarial networks(GANs)and the super-resolution(SR)techniques were employed for data-driven reconstruction to mitigate REV challenges;on the other hand,the efficient surrogate models,such as the convolutional neural networks(CNNs),were constructed to accelerate property prediction by orders of magnitude.Finally,the current challenges regarding data dependence,model generalization,and physical inter-pretability were discussed to outlines future directions,including integrating physical mechanisms into AI mod-els(physics-informed AI),promoting multi-scale data fusion,and constructing reservoir"digital twins"to support the development of smart oilfields.
The non-Fourier heat transfer characteristics of couple stress fluid in a microchannel were investiga-ted,and effects of the couple stress parameters,the Hartmann number,the Joule heating effect and the 2-phase lag time parameters on the temperature distributions and heat transfer characteristics of the fluid were analyzed through establishment of the relevant governing equations combined with the non-Fourier heat transfer model.The results show that,the above parameters significantly influence the fluidity and heat diffusion char-acteristics of the couple stress fluid.The increase of the couple stress parameter aggravates the temperature gra-dient;the Hartmann number enhances the magnetic field confinement and inhibits the heat conduction;the Joule heating effect promotes the temperature gradient and highlights the non-Fourier effect;and the change of the biphasic hysteresis time parameter has a significant modulation effect on the temperature peak and the re-sponse speed.
The modified Allen-Cahn equation with the mean curvature source term can effectively model curva-ture-driven physical processes.However,the nonlinear term and gradient magnitude make it difficult to design efficient numerical schemes.An efficient numerical scheme was proposed for solving the equation.Based on the Strang operator splitting method,the original equation was discretized in time into three subproblems:the non-linear equation was solved analytically;the mean curvature equation was discretized using the second-order Runge-Kutta method combined with central differences to establish a fully discrete explicit scheme,while the heat equation was discretized with the Crank-Nicolson method and solved via the alternating direction implicit(ADI)fast scheme.Theoretical analysis shows that,the proposed scheme achieves second order convergence accuracy.Finally,numerical experiments were presented to validate the convergence rate and effectiveness of the scheme.
With the widespread implementation of zero-output transformation of low-pressure cylinders in heat-ing units,the low-pressure cylinders of steam turbines often need to operate at extremely low flow rates.To get a deeper understanding of the flow behavior under this working condition,the low-pressure cylinder of a steam turbine in a certain power plant was studied,a numerical calculation model for the final-stage flow channel was constructed,and the structure of the final-stage flow field and the temperature changes on the surface of the moving blades were inspected through simulation analysis of the flow state and aerodynamic performance in the cylinder under variable working conditions,especially at low flow rates.The research results indicate that,at low flow rates,the gas separation and backflow will occur in the final stage of the low-pressure cylinder.The separation initially occurs at the moving blade root and gradually spreads to the blade top as the flow rate de-creases.Local vortices emerge in the channel,and a negative attack angle appears at the moving blade inlet,which significantly hinders the normal steam flow.When the load drops to 15％THA,a local high-temperature zone will appear at the steam outlet edge on the top of the last stage stator blade,showing the blower heating effect.As the flow rate further decreases,the high-temperature area will keep expanding and the maximum temperature will continue to rise.When the load decreases to 10％THA,the maximum surface temperature of the moving blade will rise by 40.29％compared with the rated working condition.This research provides a refer-ence basis for the safe operation of the low-pressure cylinder of the heating unit after the zero-output transfor-mation.
Based on the Biot-type wave equations for unsaturated soils,the transient responses of 1D unsatu-rated soil columns subjected to dynamic loading were investigated,to analyze wave propagation characteristics in unsaturated soils and derive analytical solutions to provide a theoretical basis for relevant engineering prob-lems.The effects of saturation on both the permeability coefficient and the dynamic shear modulus were incor-porated into the governing equations.With the separation of variables method plus the state space method,a systematic analytical solution of the transient response was obtained.The validity of the solution was verified through comparison with the finite element results from COMSOL's PDE module.The results indicate that,on-ly 1 compression wave occurs in unsaturated soil due to its relatively low permeability.As the intrinsic permea-bility increases,the peak transient pore water pressure response will gradually decreases.Furthermore,an in-crease in the saturation leads to a significant rise in the amplitude of the pore water pressure response.Both the saturation and the permeability considerably influence the wave-induced responses in unsaturated soils.The proposed analytical method effectively predicts transient response characteristics and provides a theoretical sup-port for analyzing the dynamic behaviors of unsaturated soils.
The actuation hysteresis effect caused by cable-hole sliding friction is one of the critical challenges limiting the multi-functional and multi-domain applications of cable-driven continuum robots.During trajectory tracking,the driving cables undergo frequent switching between winding and unwinding,leading to repeated re-versals of sliding friction within the guiding holes.As a result,the current configuration of the flexible arm va-ries significantly depending on the actuation history.A quasi-static model for the cable-driven continuum robot was developed based on the dynamics theory of flexible multibody systems.A nodal force equilibrium equation with decoupled rigid and flexible motions was established,and the tangent stiffness matrices for both nodal forces and cable driving forces were rigorously derived to enhance the convergence rate of the equilibrium equa-tion.The trajectory tracking problem was formulated as a servo constraint problem in multibody systems.A nonlinear least-squares solver incorporating the Newton-Raphson iterative algorithm was employed to conduct path tracking simulations under both loaded and unloaded end-effector conditions.The configuration evolution law of the continuum robot was thereby obtained.
Physics-informed neural network(PINN)are widely applied for solving both forward and inverse problems of differential equations.However,traditional PINNs exhibit limitations when solving differential e-quations over large domains,including insufficient accuracy,susceptibility to local optima,and a lack of theo-retical guarantees of convergence.To address these issues,a residual-based Fourier neural network(Res-FNN)was proposed.This network integrates residual Fourier layers into the traditional PINN framework,leveraging the periodicity property of trigonometric functions to enhance the model's accuracy in solving large-domain problems effectively.In particular,a theoretical convergence analysis was established for the Res-FNN applied to linear elliptic differential equations.Numerical experiments demonstrate that,the Res-FNN outperforms the traditional PINN in solving both forward and inverse problems,achieving higher accuracy and faster conver-gence speed.
The parameterized dual-continuum model plays a significant theoretical and practical role in various subsurface geological modeling applications.This model effectively captures the highly heterogeneous,high-contrast,and multiscale structural features of geological formations,while also exhibiting considerable uncer-tainty.To address the numerical challenges posed by such complex models,adopting appropriate model reduc-tion techniques has become a key approach to improving computational efficiency while maintaining solution ac-curacy.Herein an iterative solution strategy was proposed based on the uncoupled generalized multiscale finite element method(GMsFEM)for the parameterized dual-continuum model.The original parameter-dependent model was reformulated as a new one consisting of multiscale diffusion coefficients and transfer functions(both parameter-independent),along with a parameter-dependent source term.The proposed iterative method was divided into offline and online stages.In the offline stage,multiscale basis functions were constructed in each coarse grid block based on deterministic multiscale parameters to generate a reduced-order space.In the online stage,the model was solved efficiently within the reduced space with an iterative scheme.A major advantage of this method lies in the fact that,once the multiscale basis space is constructed offline,each online iteration can leverage efficient direct solvers and reuse matrix inverses,thus significantly reducing computational costs.Fur-thermore,the convergence of the proposed iterative method was analyzed.Finally,numerical experiments on the parameterized dual-continuum model were conducted to demonstrate the effectiveness and efficiency of the multiscale-based iterative approach,and validate the theoretical convergence results.
The mechanical properties of the cytoskeleton are crucial for maintaining cell morphology and enab-ling life processes such as cell movement and division.Actin filaments and microtubules,as core components of the cytoskeleton,are interconnected by cross-linking proteins to form a complex polymer network structure,of which the macroscopic mechanical behavior is closely related to the physical properties of cross-linking pro-teins.Based on a coarse-grained actin-microtubule composite network model,the effects of 2 key parameters of cross-linking proteins:the fracture distance threshold and the formation distance threshold,on the network's mechanical properties were systematically investigated.The simulation results show that,the fracture distance threshold of microtubule cross-linking proteins plays a dominant role in the network's mechanical responses:reducing this threshold leads to an overall downward shift of the stress-strain curve and a decrease in structural loading-bearing capacity.In contrast,changes in the fracture distance threshold of actin filament cross-linking proteins have a weak impact on the macroscopic mechanical behavior,and the formation distance threshold of cross-linking proteins has no significant effect on the network's mechanical properties.This study reveals that the macroscopic mechanical properties of the actin-microtubule composite network are mainly dependent on the fracture distance threshold of cross-linking proteins while being insensitive to the formation distance threshold,providing a new sight for understanding the role of dynamic cross-linking in the mechanical stability of the cy-toskeleton.
Under hypergravity conditions,the free surface of confined viscoelastic soft solids can become un-stable due to Rayleigh-Taylor instability,with the evolution behavior governed by both material rheology and geometric confinement.The confined cylindrical viscoelastic soft solids were studied,and a linear stability anal-ysis for free-surface perturbations was developed based on linear viscoelastic constitutive relations.The gover-ning equations were formulated and solved in the frequency domain,to deduce the dispersion relation between the perturbation growth rate and the wavenumber.Then,the roles of hypergravity,surface tension,material compressibility and viscous dissipation were systematically investigated in the instability process.Finite geomet-ric effects were incorporated through introduction of circumferential boundary conditions in a cylindrical coor-dinate system,to discretize the admissible wavenumbers and reveal the effects of finite confinement on the in-stability critical values and mode selections.Furthermore,the finite element method was used to verify the the-oretical predictions and to investigate the relationship between instability modes and the subsequent evolutions of surface patterns.This study provides a coherent theoretical and numerical approach for analyzing interfacial stability in confined viscoelastic soft solids under hypergravity,and offers a guidance for experiment design and pattern control of soft materials.
In response to the instability problem caused by the coupling of strong nonlinear factors such as time-varying mesh stiffness and backlash in high-speed heavy-duty gear systems,an external periodic excitation control strategy was introduced,to establish and numerically solve a dynamic model for single-degree-of-free-dom gear transmission systems.With the cell mapping method,the effects of control parameters on the erosion and bifurcation transition process of the system safety-attraction basin,as well as the evolution law of the at-traction domain proportion p,were quantitatively analyzed.Based on the Floquet multiplier analysis,a quantita-tive mapping relationship between the doubling coefficient,the excitation amplitude,and the bifurcation threshold,was established.Combined with the system phase diagram and the Poincaré mapping diagram,the stable control mechanism realized through reconstruction of the phase space topology under external excita-tion,was revealed,and the control mechanism of key control parameters on the global stability transition of the system was quantitatively elucidated.The results shows that,the low-frequency excitation can easily induce high period attractors,leading to motion boundary instability;the high frequency excitation can trigger safety-attraction basin erosion and bifurcation,where the P3S attractor is stable and the P2S attractor undergoes in-verse doubling bifurcation to transition to the P1S single period safe orbit;and the reverse excitation amplitude will destroy the system stability,while increasing the forward excitation amplitude can accelerate the stabiliza-tion process,ultimately achieving full coverage of the P1S attraction domain.The research provides a theoreti-cal support for vibration suppression,parameter optimization,and safety design of gear transmission systems.
The clearance in the cage pocket of cylindrical roller bearings influences the kinematic characteris-tics such as slip and collision between the rollers and the cage,as well as the overall vibration of the bearing.the limitation of traditional dynamic models solely considering viscous drag effects of lubricant on rollers for cy-lindrical roller bearings,was addressed.Instead,the lubricant was described as a time-varying friction coeffi-cient related to the contact force between the rollers and raceways,along with flow resistances and resistance torques on the cage.Additionally,nonlinear spring and damping elements were employed to simulate the colli-sion contacts between the rollers and the cage,highlighting the impacts of the pocket clearance.The accuracy of the proposed model was validated,and the influences of the cage pocket clearance on the kinematic charac-teristics of the roller-cage speed,slip,and collision,as well as the vibration characteristics of the bearing,were investigated.Simulation results indicate that,as the cage pocket clearance increases within the range of 0.1 mm to 0.7 mm,the cage slip rate rises,leading to more severe speed fluctuations and compromising cage stability.Simultaneously,the roller's spin slip rate decreases,which reduces the collision frequency between the roller and the front and rear ends of the cage pocket,while the collision force increases.Furthermore,the overall vibration of the bearing intensifies with the increasing pocket clearance.The study can provide valuable insights for the design and failure analysis of cylindrical roller bearings.
Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere and ocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalized β-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scale characteristics of wave processes simultaneously.In the case where the perturbation expansion is independent of secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalized β-effect is the key factor inducing the evolution of Rossby solitary waves.
In cold regions,the formation of ice covers over water bodies during winter is a common phenome-non.The continuous growth of ice covers significantly impacts human activities,making it practically important to understand and predict ice growth behavior for the prevention of ice-related hazards.Ice cover growth is in-fluenced by multiple factors,and the underlying mechanisms have not yet been fully elucidated.To investigate the complexity of ice cover growth,a finite element computational model was established,and the equivalent heat capacity method was employed to numerically simulate the ice growth process.The accuracy of the pro-posed model and method was validated through comparison with experimental data.A comparative analysis was conducted between numerical results considering and neglecting natural convection.Furthermore,both the pro-posed method and the freezing degree-day method were applied to estimate the ice thickness at a specific cross section of the Songhua River.The root mean square errors of the 2 methods were provided,further confirming the effectiveness of the equivalent heat capacity method in real river environments.The results demonstrate that,the established computational model and the numerical approach can effectively represent physical proces-ses such as heat transfer and fluid motion,and handle water-ice phase transition problems.This study provides an effective method for simulating ice cover growth under multi-physics coupling effects.
For leader-less multi-agent systems,the problem of distributed formation optimization in predefined time under unknown disturbances was studied,and the global cost function composed of local strongly convex functions for all agents was minimized.A class of formation optimization algorithms based on the sliding mode control was proposed to realize the formation control of multi-agent systems within the predefined time.The al-gorithm was divided into 3 parts:firstly,the integrated sliding mode control strategy was used to guide each a-gent to approach the sliding mode surface in the predefined time,and the external interference was effectively suppressed;then,the design protocol control was employed to guide each agent state to the minimum point of its local cost function;finally,the leaderless formation was realized for all agents to reach the minimum point of the global cost function.The algorithm does not require agents to share the gradients and Hessian matrix in-formation of neighbors,thus saving the information exchange cost,and can deal with highly nonlinear multi-valued strongly convex cost functions.Several examples of numerical experiments demonstrate the effectiveness and reliability of the design control protocol algorithm.
To accomplish long-duration and complex orbit flight missions,next-generation spacecrafts need to carry large flexible structures and high-capacity liquid fuel tanks.The nonlinear coupling problems between rigid body motion,liquid sloshing,and flexible structure vibrations become particularly significant during spacecraft maneuvering and control processes.A dynamic model for rigid-liquid-flexible coupling systems was presented,to first calculate the vibration of the flexible structure with the Kirchhoff-Love plate theory and the finite ele-ment methods.Then the flow theory was employed to model liquid fuel sloshing,and finally the overall dynamic model for the coupling system was derived with the Lagrange method.The study reveals the coupling dynamic interactions between rigid body motion,liquid sloshing,and flexible structure vibrations.The proposed model-ing approach for rigid-liquid-flexible coupling spacecrafts was validated by comparison with published experi-mental and analytical results.The coupling analysis of complex,liquid-filled spacecrafts with large,flexible structures shows that,the finite element method can accurately capture the dynamic responses of high-frequen-cy modes of the flexible structures.Additionally,due to the low-frequency characteristics of these large and complex space structures,the coupling effects with liquid fuel sloshing become even more pronounced.
Presently,scientific research is becoming increasingly active,interdisciplinary integration is deepe-ning,and artificial intelligence is rapidly entering knowledge production,reconsidering what truly constitutes high-quality research has become a matter of immediate practical relevance.This paper argues that scientific re-search should uphold four essential criteria:significance,necessity,originality,and feasibility.Significance asks whether a study is worth pursuing;necessity asks why it must be undertaken and why now;originality concerns what substantive advance it makes;and feasibility asks whether its outcomes can truly stand and be translated under scientific,technical,engineering,economic,and practical constraints.These four criteria are not isolated labels,but form a logical chain from problem formulation to the establishment of credible results.Several tendencies in current research practice deserve particular caution:replacing judgment on scientific problems with journal labels and impact factors,reversing research logic by chasing international trends and top-tier journals,packaging marginal variations as originality,and presenting ideas that lack object constraints,manufacturability,cost awareness,durability assessment,and application compatibility as"frontier break-throughs."In the age of artificial intelligence,big data,and automated research,results can be generated fas-ter,appearances of completeness can be produced more easily,and ideas can be packaged more persuasively;reiterating these four criteria is therefore not a conservative reaction against new tools,but a basic safeguard a-gainst the deviation of scientific judgment by formal abundance.For Applied Mathematics and Mechanics,reaf-firming the four criteria also means clarifying the journal's orientation:mechanics should remain the point of application,engineering goals the central guide,and applied mathematics a source of essential methodological support.
Viscoelastic materials are extensively utilized in civil engineering,aviation,and other domains owing to their superior vibration damping characteristics.The nonlinear stiffness Zener model was employed to replace the energy transfer elements in the conventional nonlinear energy trap,thereby making a novel viscoelastic en-ergy trap device.Furthermore,the bifurcation behavior of the model under simple harmonic excitation was in-vestigated.Initially,the nonlinear dynamic control equation for the coupled main structure-energy trap system was formulated based on the nonlinear stiffness Zener model.Subsequently,the slow-varying system's equation under the 1:1 resonance condition was analytical derived with the complex variable averaging method.On this basis,the effects of key parameters on the bifurcation behavior of the system's viscoelastic energy trap under slow-changing conditions were elucidated.Through integration of the numerical simulation approach and in view of the vibration reduction efficiency and energy transfer efficiency of the main structure as evaluation indi-cators,the vibration suppression effectiveness of the viscoelastic energy trap across different bifurcation re-gions was further explored.The results indicate that,the newly developed viscoelastic energy trap can effective-ly modulate saddle-node bifurcations and Hopf bifurcations through parameter adjustments,thereby significant-ly enhancing the system's vibration damping efficiency and energy transfer efficiency while effectively restrai-ning the displacement response of the main structure.This research provides a robust theoretical foundation for the engineering design and parameter optimization of the innovative viscoelastic energy trap.
The high-gravity reactor,renowned for its superior mass transfer efficiency,plays a pivotal role in carbon capture processes.The wire mesh packing serves as the primary structural element enhancing mass transfer.To fully comprehend the dispersion mechanism,it is essential to investigate the dynamics of droplets impacting on a single fiber.The volume of fluid method was employed to numerically examine the interaction between a droplet and a fiber.The effects of factors such as the initial velocity(u0),the initial diameter(D0),the impact eccentricity(e),and the impact angle(θ)on droplet deformation and dispersion characteristics were analyzed in detail.Vertical or central impacts were divided into 4 key stages:splitting,merging,stretc-hing,and breaking.In contrast,eccentric and non-vertical impacts exhibit asynchronous breaking,sliding split-ting,and oblique deformation stages.To quantitatively assess the post-impact dispersion characteristics,the di-mensionless time(t*)and the gas-liquid interfacial area growth rate(η)were introduced.The results indicate that,increasing the initial velocity,reducing the droplet diameter,minimizing the eccentric distance,and maxi-mizing the impact angle all enhance dispersion.A correlation was established to predict the maximum increase rate in gas-liquid interfacial area.
