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An extended FitzHugh–Nagumo model is developed to model the synaptic coupling of neurons and the associated dynamics. The neurons are coupled via chemical synapses, which can excite or inhibit the postsynaptic neuron. The neurotransmitter-receptor dynamics is governed with a gating dynamic, which allows for the distinction between fast and slow synapses. Detailed nonlinear dynamics analysis are performed for simple neural motifs of a self-synapsed neuron and two synaptically coupled neurons for the instabilities that lead to neural oscillations, and the associated phase diagrams are obtained. Interesting dynamics such as synchronization of fast and slow firing neurons, frequency enhancement, quiescent neurons coupled to oscillators, chaotic spiking, and periodic bursting are found.

In this paper, we study the dynamics of a three-species food chain model with two delays duo to fear. First we discuss the permanence of this delayed model, then we discuss dynamics under six cases: (1) τ 1 = τ 2 = 0 , (2) τ 1 > 0 , τ 2 = 0 , (3) τ 2 > 0 , τ 1 = 0 , (4) τ 1 = τ 2 > 0 , (5) τ 1 ∈ ( 0 , τ 10 ) , τ 2 > 0 , (6) τ 2 ∈ ( 0 , τ 20 ) , τ 1 > 0 . We shall study the Hopf bifurcation about case (5) by center manifold theorem and normal form. At last we shall give simulations which reveal the influence of delays and fear on the dynamics of this predator–prey system.

The paper discussed the dynamic model of a genetic algorithm (GA) with an adjustment of a search space size in a noisy environment. A linear pseudo-Boolean function with positive coefficients was used for modeling the GA with a search space size adjustment. The impact of an additive noise on the fitness value of the GA is assessed, and analytical expressions are derived that described how GA’s selection and size adjustment operators alter the macroscopic statistical properties of population. Calculations based on the theory are compared with experiments demonstrating the accurate predictions for the macroscopic statistical properties of population.

In this paper, we investigate the influence of the nonlocal intraspecific competition on the stability and spatialtemporal dynamics for a diffusive predator–prey system with generalist predator. The stability region and the possible bifurcation curves are determined in the plane consisting of diffusion coefficients of the prey and the predator. Spatially inhomogeneous steady states with different spatial profiles and spatially inhomogeneous periodic solutions with mode-1 as the parameters are varied acrossing the boundaries of the stability region.

The earlier smooth sliding control (SSC) is revisited. New global stability and chattering alleviation analysis is presented under the more general situation of simultaneous presence of plant uncertainty, unmodeled dynamics and external disturbance. Based on an appropriate prediction error loop, it delivers a smooth filtered control signal to the plant. New explicit conditions are presented for SSC to eliminate chattering. Considering numerical examples recently used in a lively debate between continuous and discontinuous sliding mode control options, the SSC is shown to overcome chattering arising in both classical first-order sliding mode (FOSM) control and the super-twisting algorithm (STA) in the presence of unmodeled dynamics. Besides the original theoretical contribution, one main purpose here is to stir new research about chattering avoidance in both classical and higher-order sliding mode algorithms for uncertain systems.

In this paper we study the effect of solvent potential interaction on the dynamics of Peyrard Bishop model of DNA. The potential energy in the Hamiltonian arises from the morse potential beacause of hydrogen bonding and solvent potential due to environmental interaction. We invoke the semi discrete approximation and the dynamics is found to be governed by the Nonlinear Schrodinger equation(NLS). The propagation of envelope soliton in DNA is analyzed for various contributing factors.

We study Boltzmann-Fermi-Dirac equation when quantum effects are taken into account in dilute gas dynamics. By employing new estimates on trilinear terms of collision kernels, we prove the global existence of the classical solution to Boltzmann-Fermi-Dirac equation near equilibrium. Furthermore, the limit from Boltzmann-Fermi-Dirac equation to incompressible Navier-Stokes-Fourier equations is justified rigorously. The corresponding formal analysis was given in the thesis of Zakrevskiy \cite{Zakrevskiy}, Comment: 32 pages

The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique and residual power series method are utilized to build new exact and analytical approximate solutions of the time-fractional potential Korteweg-de Vries equation. The dynamics of the solutions obtained are explored by drawing them in two and three dimensions. Comparisons between the new results and the solutions available in literature show that the presented approaches of nonlinear problem resolution are highly effective and reliable. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena.

Flow dynamics associated with open-channel confluences are highly three-dimensional (3D) with significant velocity gradients in the contraction zone downstream of junctions. The main objective of the present study was to investigate the impact of discharge ratio and junction angle on the non-uniformity of the velocity distribution within the contraction zone. A one-dimensional (1D) theoretical model and a 3D numerical model were developed to establish the relationships of the maximum values of energy and momentum correction coefficients ( α m and β m ) with discharge ratio (q) and junction angle (θ). The expressions of α m and β m were determined in terms of q and cosθ with the 1D theoretical model, and the constants were determined through regression analysis with the computed results from the 3D numerical model. The expressions show that α m and β m increased with an increase in junction angle or a decrease in discharge ratio due to the improved three-dimensionality of the flow structure. The expressions of α m and β m determined from the present study are consistent with the existing findings with θ = 90°.

This manuscript considers the homogeneous Neumann initial-boundary value problem for a three-component chemotaxis system describing the spatio-temporal Alopecia Areata dynamics. The model addresses the complex interactions between CD4+ T cells, CD8+ T cells and interferon-gamma (IFN-γ): Both types of immune cells secrete the chemical that diffuses and degrades; conversely, the T cells are activated by the chemical but decay due to density-dependent death. In addition to random motion, the T cells bias their movement toward the concentration gradient of IFN-γ. To compare with previous chemotaxis models, a distinctive feature of this system is that CD8+ T cells additionally proliferate in a nonlinear manner with the help of CD4+ T cells. Given suitably regular initial data, it is shown that either small logistic damping in the two-dimensional case or strong logistic damping in the three-dimensional setting can prevent any blow-up of classical solutions to the problem. Moreover, we find a specific parameter regime for which the unique coexistence equilibrium is globally convergent.

The paper deals with the attitude dynamics of CubeSats with flexible stabilizing panels in free molecular flow taking into account the aerodynamic damping. In addition to the operating position, characterized by zero angle of attack, aerodynamically stabilized satellites may have intermediate equilibrium positions. The presence of unstable equilibrium positions and small perturbations such as the oscillations of the flexible panels is the cause chaos in the attitude motion. An analysis of the chaotic motion is carried out using Poincare sections and Lyapunov exponents. Numerical simulations show that the chaos intensity is sensitive to the geometric and environmental parameters of the system.

Development of practical control approaches for the under-actuated chaotic systems such as the robot manipulators are challenging due to the unpredictable character of the chaotic dynamics, and the inevitable real-time application properties like delays, saturations, and uncertainties In this paper, we propose a model free digital adaptive control approach, which considers the time delay of the control signal, actuator saturation, and non-parametric uncertainties, for an under-actuated manipulator. We also develop a chaos control to learn the unbiased and smooth digital control policy inside the chaotic regions of the continuous time under-actuated manipulator. We perform real-time experiments in a dynamic environment with the proposed digital adaptive control. Then we compare the results of the learning and control with and without chaos control. We observe that the proposed model free adaptive control approach can accurately learn both the long-term predictor and unbiased control policy even in the chaotic regions of the under-actuated robot manipulator.

The D’Alembert solution is an important basic formula in linear partial differential theory due to that it can be considered as a general solution of the wave motion equation. However, the study of the D’Alembert wave is few works in nonlinear partial differential systems. In this paper, one construct the D’Alembert solution of a (2+1)-dimensional generalized breaking soliton equation which possesses the nonlinear terms. This D’Alembert wave has one arbitrary function in the traveling wave variable. We investigate the dynamics of the three soliton molecule, the soliton molecule by bound as an asymmetry soliton and one-soliton, the interaction between the half periodic wave and two-kink, and the interaction among the half periodic wave, one-kink and a kink soliton molecule of the (2+1)-dimensional generalized breaking soliton equation by selecting the appropriate parameters.

The dynamics of the gravitational lifting system of the deep sea mining industry is demonstrated in this article. A simplified dynamic model is obtained when gravity, buoyancy and drag force are the major concerns. By quantitative analysis, different variables like bucket size, distribution distance, and filling rate are considered to measure their influence on lifting speed and production rate, which ends up with that the most influential factor is the bucket size, and it has a positive correlation with both the two targets: lifting speed and production rate. Due to the breaking strength of the cable wire rope, a feasible design of such a lifting system should take the tension force into consideration. Hence, the feasibility is also examined and a conclusion is summarized that a combination of the bucket size and the distribution distance should be optimized according to the concrete working conditions.

The corpus callosum (CC) is a major interhemispheric commissure of placental mammals. Early steps of CC formation rely on guidance strategies, such as axonal branching and collateralization. Here we analyze the time-course dynamics of axonal bifurcation during typical cortical development or in a CC dysgenesis mouse model. We use Swiss mice as a typical CC mouse model and find that axonal bifurcation rates rise in the cerebral cortex from embryonic day (E)17 and are reduced by postnatal day (P)9. Since callosal neurons populate deep and superficial cortical layers, we compare the axon bifurcation ratio between those neurons by electroporating ex vivo brains at E13 and E15, using eGFP reporter to label the newborn neurons on organotypic slices. Our results suggest that deep layer neurons bifurcate 32% more than superficial ones. To investigate axonal bifurcation in CC dysgenesis, we use BALB/c mice as a spontaneous CC dysgenesis model. BALB/c mice present a typical layer distribution of SATB2 callosal cells, despite the occurrence of callosal anomalies. However, using anterograde DiI tracing, we find that BALB/c mice display increased rates of axonal bifurcations during early and late cortical development in the medial frontal cortex. Midline guidepost cells adjacent to the medial frontal cortex are significant reduced in the CC dysgenesis mouse model. Altogether these data suggest that callosal collateral axonal exuberance is maintained in the absence of midline guidepost signaling and might facilitate aberrant connections in the CC dysgenesis mouse model.

This work uses a recently developed MRI method to measure the solid fraction and velocity in three-dimensional (3D) hoppers quantitatively. We demonstrate that the measurements are quantitative by calculating the mass flow rate within the hopper using MRI and show good agreement with the mass flow rate measured gravimetrically. We study the velocity and solid fraction in hoppers with various angles and outlet sizes. We show that the solid fraction decreases smoothly from the bulk value above the outlet, indicating that the assumption of a “free-fall arch” used in some mass flow correlations is invalid. Furthermore, we show that the solid fraction, velocity and vertical evolution of the acceleration are all self-similar when normalised by the value at the centre of the outlet in a 3D hopper, in agreement with recent studies of 2D hoppers. Thus, these quantitative measurements enable evaluation of phenomenological models describing the flow rate from hoppers.

Segregation of the replicating chromosome from a single to two nucleoid bodies is one of the major processes in growing bacterial cells. The segregation dynamics is tuned by intricate interactions with other cellular processes such as growth and division, ensuring flexibility in a changing environment. We hypothesize that the internal stochasticity of the segregation process may be the source of cell-to-cell phenotypic variability, in addition to the well-established gene expression noise and uneven partitioning of low copy number components. We compare dividing cell lineages with filamentous cells, where the lack of the diffusion barriers is expected to reduce the impact of other factors on the variability of nucleoid segregation dynamics. The nucleoid segregation was monitored using time-lapse microscopy in live E. coli cells grown in linear grooves. The main characteristics of the segregation process, namely, the synchrony of partitioning, rates of separation, and final positions, as well as the variability of these characteristics, were determined for dividing and filamentous lineages growing under the same conditions. Indeed, the gene expression noise was considerably homogenized along filaments as determined from the distribution of CFP and YFP stochastically expressed from the chromosome. We find that 1) the synchrony of nucleoid partitioning is progressively decreasing during consecutive cell cycles, but to a significantly lesser degree in filamentous than in dividing cells; 2) the mean partitioning rate of nucleoids is essentially the same in dividing and filamentous cells, displaying a substantial variability in both; and 3) nucleoids segregate to the same distances in dividing and filamentous cells. Variability in distances is increasing during successive cell cycles, but to a much lesser extent in filamentous cells. Our findings indicate that the variability of the chromosome segregation dynamics is reduced upon removal of boundaries between nucleoids, whereas the remaining variability is essentially inherent to the nucleoid itself.

This paper is mainly concerned with the new types of entire solutions which are different from pulsating fronts of Lotka-Volterra competition systems with asymmetric dispersal in spatially periodic habitats. The asymmetry of kernel function leads to a great influence on the profile of pulsating fronts and the sign of wave speeds, which gives rise to the properties of the entire solution more complex and diverse. We first give a relationship between the critical speeds c ⁎ ( ξ ) and c ⁎ ( − ξ ) , corresponding to the minimal speeds of two pulsating fronts propagating in the direction of ξ and −ξ, respectively. Then, the exponential behavior of pulsating fronts as they approach their limiting states is obtained. Finally, by considering the interactions of two different pulsating fronts coming from two opposite/same directions and applying the super-/subsolutions techniques as well as the comparison principle, we establish the existence and various qualitative properties of some different types of entire solutions defined for all time and whole space. Moreover, we give some numerical simulations to describe intuitively these obtained entire solutions.

Coffee-ring patterns are typical phenomena in evaporation-driven nanoparticles suspended (NPs-laden) droplet. However, NPs motion in droplet fails to exhibit characteristic patterns such as coffee-ring formation in lattice Boltzmann (LB) framework. With features of density diffuse interface, new interfacial schemes composed of density gradient force and interfacial force are proposed and coupled in LB-LE model. They offer a solution to well modulate the NPs dynamics in liquid-vapor interface as droplet deforms and evaporates. In the following simulations of one droplet and multi-droplets evaporation, typical coffee-ring pattern is obtained for one droplet evaporation with hysteresis window 5°

A predator–prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium points in the first quadrant, one is always a saddle point and the other exhibits multi-stability phenomenon since the equilibrium point can be stable or unstable. The model with weak Allee effect has at most three positive equilibrium points in the first quadrant, one is always a saddle point and the other two can be stable or unstable node. In addition, when the parameters vary in a small neighbourhood of system parameters the model undergoes different bifurcations, such as saddle–node, Hopf and Bogdanov–Takens bifurcations. Moreover, numerical simulation is used to illustrate the impact in the stability of positive equilibrium point(s) by adding an Allee effect and an alternative food sources for predators.

This paper investigates the neural adaptive control problem for air-breathing hypersonic vehicles. For the velocity subsystem, a radial basis function neural network (RBFNN)-based adaptive controller is first designed, which employs the auxiliary variable to compensate for the saturation nonlinearity of the scramjet control command. For the altitude subsystem, an RBFNN-based controller addresses actuator constraints and dynamics using the model predictive control, as well as counteracts uncertainties and disturbances using the neural adaptive mechanism. The effectiveness of the proposed control is verified by simulations.

The dynamics of water droplets on fiber layers are investigated by fiber-scale simulation using volume of fluid (VOF) method. The effects of fiber spaces, contact angles at fibers and numbers of layers on droplet dynamics are investigated. Force analysis for the pinned and moving droplets on fiber layers shows that the resistant forces from the wetted fibers at the edge positions rather than middle positions are the dominant force to control the droplet mobility. Force analysis for droplets on the dual-layers fiber layer are also conducted. The results show that the second layer contributes little to hinder the droplet directly due to the insignificant resistant force they provided. However, the second fiber layer enhances the total resistant force from the first layer. Furthermore a simplified model is used to compare with the fiber model. The results indicate that the simplified model can also be used to predict the droplet mobility once the contact angle is given.

In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results.

An algorithm for regulation of the vertical penetration rate in rotary drilling systems is developed under the assumption that parameters of the rock-bit interaction as well as those of the translational dynamics are unknown. The control design utilizes a multi-step approach, where the vertical penetration velocity is regulated through an appropriate assignment of a reference rotational velocity signal, while the tracking of the latter is achieved using tracking with disturbance rejection scheme. In contrast with the existing results, the algorithm does not require real-time measurement and communication to the ground level of the downhole variables, such as angular position, rotational velocity, and torque-on-bit. This is achieved through the use of high-order sliding mode observers which estimate the required downhole variables based on measurements performed at the ground level. Simulation results are presented which confirm efficiency of the proposed control method.

The dynamics of a constrained three-vortex system, a pair of point vortices of arbitrary non-zero circulations in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized into two cases based on the zero and non-zero values of the constant of angular impulse. For each case, dynamical features of the vortex motion are studied analytically in the transformed plane to completely classify the vortex motions and understand the boundedness and periodicity of the inter-vortex distances. The theoretical predictions are also verified numerically and illustrated for various sets of initial conditions and circulations.

In this paper we consider a chemotaxis system coupling with the incompressible Euler equations in spatial dimension two, which describing the dynamics of chemotaxis in the inviscid fluid. We establish the regular solutions globally in time under some assumptions on the chemotactic sensitivity.

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. These properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV.

Single-molecule Förster resonance energy transfer (smFRET) of molecular motors provides transformative insights into their dynamics and conformational changes both at high temporal and spatial resolution simultaneously. However, a key challenge of such FRET investigations is to observe a molecule in action for long enough without restricting its natural function. The Anti-Brownian ELectrokinetic Trap (ABEL trap) sets out to combine smFRET with molecular confinement to enable observation times of up to several seconds while removing any requirement of tethered surface attachment of the molecule in question. In addition, the ABEL trap’s inherent ability to selectively capture FRET active molecules accelerates the data acquisition process. In this work we exemplify the capabilities of the ABEL trap in performing extended timescale smFRET measurements on the molecular motor Rep, which is crucial for removing protein blocks ahead of the advancing DNA replication machinery and for restarting stalled DNA replication. We are able to monitor single Rep molecules up to 6 s with sub-millisecond time resolution capturing multiple conformational switching events during the observation time. Here we provide a step-by-step guide for the rational design, construction and implementation of the ABEL trap for smFRET detection of Rep in vitro. We include details of how to model the electric potential at the trap site and use Hidden Markov analysis of the smFRET trajectories.

Na(+)/Ca(2+) exchangers (NCXs) are secondary active transporters that couple the translocation of Na(+) with the transport of Ca(2+) in the opposite direction. The exchanger is an essential Ca(2+) extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca(2+)-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca(2+) sensor called CBD12. Binding of intracellular Ca(2+) to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca(2+)-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR ((1)H-(15)N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca(2+)-bound state is less frequently sampled. These results are consistent with the view that Ca(2+) binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs’ allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.

We deal with the problem of the convergence of HCNNs (High-order Cellular Neural Networks) involving neutral type time-proportional delays and D operators in this paper. By combining Lyapunov function approach and differential inequality theory, we establish some novel assertions to check the global exponential convergence for the proposed model, which lay the foundation to devise a stable HCNNs and extend some known relevant results. Meanwhile, the outcomes of numerical simulations are highly consistent with the theoretical results.

This study investigated the rollover phenomenon of a self-propelled combine harvester during short-distance cross-region travel on a road. The mathematical model of the unsteady lateral multi-degree-of-freedom (multi-DOF) motion of the combine harvester was established with consideration to rear wheel steering, front wheel braking, wheel sideslip, and tyre lateral deflection. By carrying out complex kinematics analysis for the entire vehicle and rotational dynamics analysis for the wheels, the mathematical relationships among the lateral deflection angles of the tyres, the kinematic parameters of the combine harvester centroid, the steering angles of the rear wheels, and the speed components of the wheel centroids along their longitudinal directions were derived and used to transform the established mathematical model into a novel form that considers the steering angles and kinematic parameters as unknown quantities. The lateral load transfer ratio (LTR) model of the combine harvester was established to assess the harvester's rollover critical state. Finally, by considering the steering angles of the rear wheels and the braking torque of the front wheels as model inputs, the rollover mechanism and effects of the structural geometry, steering angles, and braking torque on the LTR of the combine harvester were revealed through numerical calculation, and the safety intervals of the parameters were obtained. The results obtained by this study can provide theoretical and technical support for the dynamic design, control, and rollover protection of combine harvesters.

Chemotactic migration of bacteria-their ability to direct multicellular motion along chemical gradients-is central to processes in agriculture, the environment, and medicine. However, current understanding of migration is based on studies performed in bulk liquid, despite the fact that many bacteria inhabit tight porous media such as soils, sediments, and biological gels. Here, we directly visualize the chemotactic migration of Escherichia coli populations in well-defined 3D porous media in the absence of any other imposed external forcing (e.g., flow). We find that pore-scale confinement is a strong regulator of migration. Strikingly, cells use a different primary mechanism to direct their motion in confinement than in bulk liquid. Furthermore, confinement markedly alters the dynamics and morphology of the migrating population-features that can be described by a continuum model, but only when standard motility parameters are substantially altered from their bulk liquid values to reflect the influence of pore-scale confinement. Our work thus provides a framework to predict and control the migration of bacteria, and active matter in general, in complex environments.

Female fertility in mammals requires iterative remodeling of the entire adult female reproductive tract across the menstrual/estrous cycle. However, while transcriptome dynamics across the estrous cycle have been reported in human and bovine models, no global analysis of gene expression across the estrous cycle has yet been reported for the mouse. Here, we examined the cellular composition and global transcriptional dynamics of the mouse oviduct along the anteroposterior axis and across the estrous cycle. We observed robust patterns of differential gene expression along the anteroposterior axis, but we found surprisingly few changes in gene expression across the estrous cycle. Notable gene expression differences along the anteroposterior axis included a surprising enrichment for genes related to embryonic development, such as Hox and Wnt genes. The relatively stable transcriptional dynamics across the estrous cycle differ markedly from other mammals, leading us to speculate that this is an evolutionarily derived state that may reflect the extremely rapid five-day mouse estrous cycle. This dataset fills a critical gap by providing an important genomic resource for a highly tractable genetic model of mammalian female reproduction.

Phagocytosis is an important part of innate immunity and describes the engulfment of bacteria and other extracellular objects on the micrometer scale. The protrusion of the cell membrane around the bacteria during this process is driven by a reorganization of the actin cortex. The process has been studied on the molecular level to great extent during the past decades. However, a deep, fundamental understanding of the mechanics of the process is still lacking, in particular because of a lack of techniques that give access to binding dynamics below the optical resolution limit and cellular viscoelasticity at the same time. In this work, we propose a technique to characterize the mechanical properties of cells in a highly localized manner and apply it to investigate the early stages of phagocytosis. The technique can simultaneously resolve the contact region between a cell and an external object (in our application, a phagocytic target) even below the optical resolution limit. We used immunoglobulin-G-coated microparticles with a size of 2 μm as a model system and attached the particles to the macrophages with holographic optical tweezers. By switching the trap on and off, we were able to measure the rheological properties of the cells in a time-resolved manner during the first few minutes after attachment. The measured viscoelastic cellular response is consistent with power law rheology. The contact radius between particle and cell increased on a timescale of ∼30 s and converged after a few minutes. Although the binding dynamics are not affected by cytochalasin D, we observed an increase of the cellular compliance and a significant fluidization of the cortex after addition of cytochalasin D treatment. Furthermore, we report upper boundaries for the length- and timescale, at which cortical actin has been hypothesized to depolymerize during early phagocytosis.

The radial basis reproducing kernel particle method (RRKPM) has been constructed by introducing the radial basis function (RBF) into the reproducing kernel particle method (RKPM). In this article, the RRKPM is extended to the elastic dynamic analysis of the functionally graded material (FGM), and the elastic dynamics governing equation of the FGM based on the RRKPM is obtained. Then, the influence of the penalty factor, the scaling parameter and the shaped parameter are discussed. Finally, numerical examples of the FGM verify that the RRKPM has a smaller calculation error than the RKPM, and prove the correctness of the RRKPM for solving the elastic dynamics problems of the FGM.

Analytical and numerical solutions are developed to compute the threshold stress for the initiation of motion of sediment particles, from spherical to ellipsoidal, on inclined beds under boundary layer flows. The numerical model is based on the discrete element method and simulates the micro-mechanics of the sediment as an aggregate of rigid ellipsoids interacting by contact, while analytical solution establishes the basic dynamics for initiation of motion. In both models the coupling of grain motion with the flow dynamics is accomplished via drag, lift, buoyancy and seepage forces under turbulent velocity fluctuations by a one-way technique, since incipient motion does not modify substantially the flow. The comparison of both models and their extension to compute the threshold stress in terms of seepage, turbulent velocity fluctuations, bed inclination and particle orientations provide a better understanding of the onset of sediment particles. The parametric analyses cover a wide range of natural and usual conditions for incipient motion, showing that most of results fall within the variability range of the experiments. Additionally, these models are able to compute the initiation of motion for configurations not still tested in laboratory.

The dynamin-related protein 1 (Drp1) and its homologs in various eukaryotes are essential to maintain mitochondrial morphology and regulate mitochondrial division. Several mutations in different domains of Drp1 have been reported, which result in debilitating conditions. Four such disease-causing mutations of the middle domain of Drp1 were mimicked in the yeast dynamin-related GTPase (Dnm1) and were characterized in this study. Mitochondrial morphology and protein function were observed to be altered to a variable extent in cells expressing the mutated variants of Dnm1. Several aspects related to the protein such as punctate formation, localization to mitochondria, dynamic behavior and structure were analyzed by microscopy, biochemical studies and molecular dynamics simulations. Significant effects on the protein structure and function were observed in cells expressing A430D and G397D mutations. Overall, our data provide insight into the molecular and cellular alterations resulting from middle domain mutations in Dnm1.

Using Chiral Perturbation Theory to properly account the dynamics of nonleptonic K → 2 π decays, we found the Standard Model prediction for the CP violating ratio Re (e′/e) = (14 ± 5) × 10−4, where isospin breaking effects are included, in perfect agreement with the current experimental world average. Similar results has been reported by a recent release of improved lattice data.

Cell migration, which can be significantly affected by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays a crucial role in many physiological and pathological processes. The efficiency of cell migration, which is typically modeled as a persistent random walk (PRW), depends on two critical motility parameters, i.e., migration speed and persistence. It is generally very challenging to efficiently and accurately extract these key dynamics parameters from noisy experimental data. Here, we employ the normalized Shannon entropy to quantify the deviation of cell migration dynamics from that of diffusive/ballistic motion as well as to derive the persistence of cell migration based on the Fourier power spectrum of migration velocities. Moreover, we introduce the time-varying Shannon entropy based on the wavelet power spectrum of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which is typically resulted from complex and time-varying intra or extra-cellular mechanisms. We employ our approach to analyze trajectory data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the combination of Shannon entropy and wavelet transform offers a simple and efficient tool to estimate the persistence of cell migration, which may also reflect the real-time effects of ICSP-ECM to some extent., 20 pages, 9 figures

The motion in the cytosol of microorganisms such as bacteria and yeast has been observed to undergo a dramatic slowing down upon cell energy depletion. These observations have been interpreted as the motion being "glassy", but whether this notion is useful also for active, motor protein-driven transport in eukaryotic cells is less clear. Here we use fluorescence microscopy of beads in human (HeLa) cells to probe the motion of membrane-surrounded structures that are carried along the cytoskeleton by motor proteins. Evaluating several hallmarks of glassy dynamics, we show that at short length scales the motion is heterogeneous, is non-ergodic, is well-described by a model for the displacement distribution in glassy systems and exhibits a decoupling of the exchange and persistence times. Overall, these results suggest that the short length scale behaviour of objects that can be transported actively by motor proteins in human cells shares features with the motion in glassy systems.

This paper introduces a novel concept of flap-type wave energy device named the Hull Reservoir Wave Energy Converter (HRWEC). The device is a hybrid of the Pendulum type wave energy converter (PeWEC) and the Pendulor wave energy converter. The device mainly consists of a floating reservoir and a top hinged flap that hangs inside the reservoir. The flap motion is triggered by both the float motion and the fluid motion inside the reservoir and the energy take-off happens through the relative motion between the flap and the float. Because this concept closely resembles the PeWEC, a similar float design is used in the HRWEC to facilitate comparison with available data. The dynamics and power capture are obtained using a frequency domain model, and the power capture is maximized for damping-only control for regular waves. It is shown that this new concept exhibits a broadband response compared to the PeWEC concept, which is linked to an additional mode created by the internal water body motion. As a result, this new concept expected to be suitable candidate for applications in broadband wave climatic conditions.

Strongly nonlinear phenomena are attributes of suspension system dynamics of vehicles operated at high dynamic loads and high speeds. The causes of these phenomena are backlasches and dry friction in the mechanisms, detachments of the wheel from the roadway, impacts on the bumper elements, etc. It is well known that modelling of strong nonlinear phenomena can be based on a piecewise linear approach. To simplify the mathematical description of such phenomena, Żardecki developed special luz(…) and tar(…) projections. These piecewise-linear projections have a surprisingly simple mathematical apparatus that enables analytical operations (eg. reductions) for differential and algebraic equations and inclusions with non-smooth nonlinearities, and simplifies numerical simulations. The application of this method to model and simulation studies of the dynamics of the car steering system (including freeplay and stick-slip processes) have been reported in several authorial articles. This article presents examples related to suspension system dynamics.

Many studies have demonstrated that mitotic cells can round up against external impediments. However, how the stiffness of external confinement affects the dynamics of rounding force/pressure and cell volume remains largely unknown. Here, we develop a theoretical framework to study the rounding of adherent cells confined between a substrate and a cantilever. We show that the rounding force and pressure increase exclusively with the effective confinement on the cell, which is related to the cantilever stiffness and the separation between cantilever and substrate. Remarkably, an increase of cantilever stiffness from 0.001 to 1 N/m can lead to a 100-fold change in rounding force. This model also predicts an active role of confinement stiffness in regulating the dynamics of cell volume and hydrostatic pressure. We find that the dynamic changes of cellular volume and hydrostatic pressure after osmotic shocks are opposite if the cantilever is soft, whereas the dynamic changes of cellular volume and pressure are the same if the cantilever is stiff. Taken together, this work demonstrates that confinement stiffness appears as a critical regulator in regulating the dynamics of rounding force and pressure. Our findings also indicate that the difference in cantilever stiffness need to be considered when comparing the measured rounding force and pressure from various experiments.

In this paper, we study a diffusive competition model with seasonal succession and different free boundaries. Two free boundaries represent the expanding front of species u and v, respectively, and the time periodicity accounts for the effect of two different seasons. We first prove the existence and uniqueness of global solutions. Under the weak competition assumption, we then study the long-time behaviors and sharp criteria for spreading and vanishing. Moreover, sharper estimates of asymptotic speeds of ( g , h ) and asymptotic spreading speeds of ( u , v ) are also given.

Microtubules are dynamic cytoskeletal filaments composed of αβ-tubulin heterodimers. Historically, the dynamics of single tubulin interactions at the growing microtubule tip have been inferred from steady-state growth kinetics. However, recent advances in the production of recombinant tubulin and in high-resolution optical and cryo-electron microscopies have opened new windows into understanding the impacts of specific intermolecular interactions during growth. The microtubule lattice is held together by lateral and longitudinal tubulin-tubulin interactions, and these interactions are in turn regulated by the GTP hydrolysis state of the tubulin heterodimer. Furthermore, tubulin can exist in either an extended or a compacted state in the lattice. Growing evidence has led to the suggestion that binding of microtubule-associated proteins (MAPs) or motors can induce changes in tubulin conformation and that this information can be communicated through the microtubule lattice. Progress in understanding how dynamic tubulin-tubulin interactions control dynamic instability has benefitted from visualizing structures of growing microtubule plus ends and through stochastic biochemical models constrained by experimental data. Here, we review recent insights into the molecular basis of microtubule growth and discuss how MAPs and regulatory proteins alter tubulin-tubulin interactions to exert their effects on microtubule growth and stability.

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

The mechanism of nanoparticle transport inside carbon nanotubes is taken into account to investigate the dynamics of single-walled carbon nanotubes carrying a nanoparticle. The motion of the nanoparticle is on helical tracks, which is induced by temperature difference in the nanotube, with main characteristics such as axial, and angular velocities and pitch angle. The helical motion is modeled based on constrained and unconstrained simulations. In the case of the former, the axial velocity is constant, however, in the latter simulation, the axial velocity is time-variant and stop-and-go events with simultaneous changes in the rotation direction are considered as random uncertainty in the system. Once the helical motion is clarified, the dynamic behavior of the nanotube acted upon by a moving nanoparticle is investigated for simply supported boundary conditions and stability analysis is performed to obtain the critical velocities as well as critical temperature differences based on Floquet theorem. For the case of the system with random uncertainty, the statistical properties as well as confidence and prediction intervals of the dynamic response are also studied by Monte-Carlo simulation. The results highlight the importance of the helical motion mechanism of the moving nanoparticle and the random uncertainty in the system.