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During magnetospheric substorms, plasma from magnetic reconnection in the magnetotail is thought to reach the inner magnetosphere and form a partial ring current. We simulate this process using a fully kinetic 3D particle‐in‐cell (PIC) numerical code along with a global magnetohydrodynamics (MHD) model. The PIC simulation extends from the solar wind outside the bow shock to beyond the reconnection region in the tail, while the MHD code extends much further and is run for nominal solar wind parameters and a southward interplanetary magnetic field. By the end of the PIC calculation, ions and electrons from the tail reconnection reach the inner magnetosphere and form a partial ring current and diamagnetic current. The primary source of particles to the inner magnetosphere is bursty bulk flows (BBFs) that originate from a complex pattern of reconnection in the near‐Earth magnetotail at xGSM=−18RE ${x}_{\text{GSM}}=-18{R}_{\mathrm{E}}$ to −30RE ${-}30{R}_{\mathrm{E}}$. Most ion acceleration occurs in this region, gaining from 10 to 50 keV as they traverse the sites of active reconnection. Electrons jet away from the reconnection region much faster than the ions, setting up an ambipolar electric field allowing the ions to catch up after approximately 10 ion inertial lengths. The initial energy flux in the BBFs is mainly kinetic energy flux from the ions, but as they move earthward, the energy flux changes to enthalpy flux at the ring current. The power delivered from the tail reconnection in the simulation to the inner magnetosphere is >2×1011 ${ >} 2\times 1{0}^{11}$ W, which is consistent with observations. Plain Language Summary: During intervals of increased solar activity, the magnetic field in Earth's stretched night‐side tail undergoes intense reconfiguration that can energize particles. This process is called magnetic reconnection. Ions and electrons from reconnection can reach the inner magnetosphere. In this paper, we simulate this process using a novel model that includes Earth's global magnetic field configuration and self‐consistently models particle physics for both electrons and ions. We find that the particles are accelerated significantly near the sites of magnetic field reconfiguration with ions gaining 10 s of keV energy. As they propagate earthward, they end up contributing energetically to the formation of a ring current system partially encircling Earth. Key Points: Ions and electrons accelerated by 10–50 keV near the magnetotail reconnection can reach the inner magnetosphereA partial ring current is formed during the simulation, with highest energy flux between midnight and duskThe ion and electron energy fluxes are mostly kinetic in the reconnection region but change to enthalpy flux earthward [ABSTRACT FROM AUTHOR]

In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and L 1 -boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios. [ABSTRACT FROM AUTHOR]

This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in level 2 receive inputs from one specific neuron in level 1 and all neurons in level 3. The neurons in level 3 (all other neurons) receive inputs from all other neurons in levels 2 and 3. Furthermore, the right-hand side of pre-synaptic neurons is connected to the left-hand side of the post-synaptic neurons. The synchronization phenomenon is observed for neurons in level 3, even though the system is initiated with different functions. As far as we know, it is the first time that evidence of the synchronization phenomenon is provided for spatially extended Hodgkin–Huxley equations, which are periodically forced at three different sites and embedded in such a hierarchical network with space-dependent coupling interactions. [ABSTRACT FROM AUTHOR]

Spectral double power laws are common in solar high-energy phenomena such as flares and interplanetary energetic-electron events. However, the physical mechanism that produces the changes in power-law index within a single spectrum is unclear. We developed a fully analytical method of forming single power-law spectra from sequential acceleration of particles orbiting inside and hopping between simulated large-scale magnetic islands formed by flare reconnection. Here, we extend the analytical method to the formation of double power-law spectra by assuming sequential acceleration in two successive regions with different acceleration and particle-transport rates. The resulting spectral distribution is continuous and smooth, with a flattening at low energies, two power-law regions at mid-energies, and a steep rollover at high energies. The model provides analytical expressions for the spectral indices, all energy breaks, and normalization constants as functions of just three physical parameters of each acceleration region: (1) the energy gain in each accelerator, (2) the percentage of particles transferred between accelerators, and (3) the number of accelerators visited. One of the most salient predictions of our work is that the spectral index at high (low) energies is determined by the parameters of the first "seed" (second) acceleration region. By constructing the spectral distribution through an iterative analytical process, the evolution toward a double power law is easily characterized and explained. Our analytical model provides tools to interpret space- and ground-based observations from RHESSI, FOXSI, NuSTAR, Solar Orbiter/STIX, EOVSA, and future high-energy missions. [ABSTRACT FROM AUTHOR]

We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and we identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the "tendency of rate of profit to fall" in certain economic models. [ABSTRACT FROM AUTHOR]

In this paper, we study the one-parameter κ -generalized oscillator algebra κ (which includes the case of the standard Weyl–Heisenberg algebra). This algebra admits representations of finite-dimensional for negative values of the parameter κ. We construct the associated Perelomov like coherent states. We discuss their statistical properties. In particular, we derive the expressions of the Mandel parameter and Husimi function and we discuss the squeezing of the κ coherent states. [ABSTRACT FROM AUTHOR]

In this work, we introduce three families of quantum states associated with the Pegg-Barnett phase operators : i) Phase states defined as eigenstates of the Pegg-Barnett operator, ii) Coherent states obtained by a unitary displacement of the vacuum of the quantum harmonic oscillator and iii) The eigenstates of the phase annihilator operator obtained from the factorization of the Pegg-Barnett phase operator. We also discuss several statistical properties of the obtained quantum states by computing the Q-Mandel parameter, the second-order correlation function, and analyzing their squeezing properties. [ABSTRACT FROM AUTHOR]

Simple Summary: This article provides original numerical and mathematical insights about the FHR model and non-homogeneous FitzHugh–Nagumo reaction-diffusion systems. This article focuses on the qualitative analysis of complex dynamics arising in a few mathematical models in neuroscience context. We first discuss the dynamics arising in the three-dimensional FitzHugh–Rinzel (FHR) model and then illustrate those arising in a class of non-homogeneous FitzHugh–Nagumo (Nh-FHN) reaction-diffusion systems. FHR and Nh-FHN models can be used to generate relevant complex dynamics and wave-propagation phenomena in neuroscience context. Such complex dynamics include canards, mixed-mode oscillations (MMOs), Hopf-bifurcations and their spatially extended counterpart. Our article highlights original methods to characterize these complex dynamics and how they emerge in ordinary differential equations and spatially extended models. [ABSTRACT FROM AUTHOR]

Introduction: Endometriosis is a benign nevertheless a chronic condition which impacts greatly the quality of life through cyclic discomfort. We aim to report the case of umbilical endometriosis and a literature review of the different treatment modalities. Case Report: This was a case of a 43-year-old woman, with no history, who presented with a painful hemorrhagic umbilical swelling during the menstrual period associated with dysmenorrhea. Abdominal ultrasound revealed a subcutaneous umbilical mass of non-vascularized tissue nature confirmed on Doppler. Pelvic MRI which confirms the diagnosis of primary umbilical endometriosis. The patient underwent wide local excision of the endometriotic nodule with umbilical reconstruction. Histology confirmed the diagnosis of umbilical endometriosis. Resection margins were clear. Discussion: Extra-pelvic endometriosis sites are not common, especially the umbilicus. It usually occurs secondary to surgical scars, specifically after laparoscopy or open abdominal surgery. Surgical management is currently described as gold standard. Laparoscopic approach is recommended as it allows better visual inspection for secondary localization of endometriosis. Medical management corresponds to combined oral contraceptives (COCs) or progestins for management of endometriotic implants decreasing inflammatory effects, or Gonadotropin-releasing hormone for long-course treatment. Malignant transformation of the umbilical nodule has been described in literature with a reported risk of malignant transformation to be 3%. Conclusion: Current management of extragenital endometriosis suggest radical surgery with wide local excision. Due to the rarity, there is a paucity of data on umbilical endometriosis and mostly reported from case reports. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this article, an analytical approach is demonstrated to show the emerging traveling pulses for the local evolution of a set of diffusively coupled dynamical equations representing neuronal impulses. The derived dynamics governing the traveling pulses solution is described in a space-time reference frame with a two-dimensional excitable Hindmarsh-Rose (H-R) type oscillator. We deduce the conditions that allow us to describe explicitly the nature of propagating traveling pulses. We have constructed the detailed analytical results using semi-discrete approximation method with numerical simulations illuminating possible traveling pulses that include dispersion relations and group velocity equations. We show that the diffusive network can be expressed by the complex Ginzburg-Landau equation. The extended excitable medium with a homogeneous diffusive connection exhibits envelope solitons and multipulses. We observe how the series expansion parameter and coupling play key roles for the appearance of different traveling pulses. The transition phases and amplitude modulations are reported. The obtained results in the form of single solitary pulses and multipulses, reveal the possibility of collective behavior for information processing in excitable system. [ABSTRACT FROM AUTHOR]

In this paper, we consider a predator-prey model given by a reaction-diffusion system. This model encompasses the classic Holling I, Holling II, Holling III, and Holling IV functional responses. We investigate the stabilization problem of the considered system using multiplicative controls. By linearizing the system and using the maximum principle, we construct a multiplicative control that exponentially stabilizes the system towards its steady-state solutions. The proposed feedback control allows us to reach a large class of steady-state solutions. The global well-posedness is obtained via Banach fixed point. Applications and numerical simulations to Holling responses I, II, III, and IV are presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a delayed mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to the logistic growth function, incorporating viral lytic cycle. The tumour population cells are divided into uninfected and infected cell sub-populations and the virus spreading is supposed to be in a direct mode (i.e. from cell to cell). Depending on the time delay, we analyze the positivity and boundedness of solutions and the stability of tumour, infected and uninfected free equilibria (TFE, IFE, UFE) and uninfected–infected equilibrium (UIE) is established. We prove that, delay can lead to "Jeff's phenomenon" observed in a laboratory which causes oscillations in tumour size whose phase and period change over time. With nonlinear dependence of UIE equilibrium on time delay, we develop a more general algorithm determining the stability/instability of the oscillating periodic solutions bifurcating from the UIE equilibrium. Finally, we present numerical simulations illustrating our theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modeled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of propagating pulses. The symmetric or asymmetric nature of traveling pulses is characterized, and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions, and show how system parameters and coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves. [ABSTRACT FROM AUTHOR]

In this paper, the authors presented the effects of space voids and electrical conductivity on the flow of a pseudoplastic (Rabinowitsch) fluid analyzed in a curved two-dimensional plane geometry. The walls of the channel are considered to develop the peristaltic waves along its length. The problem is manipulated under the observations of long wavelength and low Reynolds number approximations. The motion is assumed to be steady by transforming it in a wave frame traveling with the speed of wave. Analytical hybrid perturbation techniques have been incorporated to handle the complicated coupled differential equations. It is found that the results are well in agreement with the existing literature as a special case, evocating the validity of the study. Expressions of velocity, pressure gradient, and stream function have been invoked graphically. It is concluded from the results that porous medium and magnetic field suggest opposite variations of velocity and trapping circulating contours are stretching with magnetic field and contracting with increasing voids. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number |$\mathcal {R}_0$| when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that |$\mathcal {R}_0 \approx 1.8377 $| in Cameroon, while |$\mathcal {R}_0 \approx 1.0379$| in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals |$\mathcal {R}_{0h}$| and from the SARS-CoV-2 in the environment |$\mathcal {R}_{0v}$| has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with |$\mathcal {R}_{0h}$| = 0.05721 and |$\mathcal {R}_{0v}$| = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with |$\mathcal {R}_{0h}$| = 0.63899 and |$\mathcal {R}_{0v}$| = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government. [ABSTRACT FROM AUTHOR]

The auroral wave-like structures called "omega bands" appear within the post-midnight sector auroral oval with shapes resembling the Greek letter omega, and are typically associated with the recovery phase of substorms. Prior work and MHD simulations suggest both high speed earthward flows and postmidnight flow shears are possible omega band source mechanisms. However, what produces omega bands is not well understood. It is most likely that the paucity of concurrent magnetospheric data has limited our ability to understand fully the mechanism responsible for the generation of the omega bands. We have identified about 263 auroral omegas in seven different THEMIS all sky cameras (ASCs) over a 10 year period. A fraction appear to form from north-south streamers, but some appear to form from east-west auroral arcs. Fifty-one of the 263 O also have conjugate or near conjugate THEMIS and GOES spacecraft data. There is evidence in about 80% of these events that high speed earthward flows have occurred prior to or at about the same time as the auroral omega observation. This evidence consists of high speed earthward flows, magnetic field dipolarizations, particle injections into the inner magnetosphere, and auroral streamers. 11 events also show plasma flow data azimuthally along the inner magnetosphere, but for six of these events the Vy component is inconsistent with the auroral omega direction of motion. Of the remaining five events, four have Vy flow shear events but also show evidence of magnetic field dipolarizations, particle injections into the inner magnetosphere, and auroral streamers. Our observations suggest high speed earthward flows are more likely to be the source of auroral omega bands. [ABSTRACT FROM AUTHOR]

The significance of the present investigation is to explore the impacts of the Hall current and variable traits of thermal conductivity and the mass diffusion instead of the constant on a three-dimensional (3D) Darcy–Forchheimer–Casson nanofluid flow past a deformable rotating disk extendable in the radial direction. However, the motion of the flow is induced owing to the rotation and deformation of the disk. The process of heat transfer is inspected in the presence of the Cattaneo–Christov heat and mass fluxes, thermal radiation, and the activation energy amalgamated with chemical reaction added to witness the effect on the mass transfer. The novelty of the model is enhanced with the additional effects of momentum slip and convective boundary conditions. On utilizing the Von Karmann similarity variable, the formulated problem is transformed into ordinary differential equations. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The upshot of sundry parameters versus involved profiles is deliberated graphically. It is perceived that on escalating the Brownian motion and temperature-dependent thermal conductivity, the temperature field escalates. The velocity field in radial and azimuthal direction decays for up surging the Casson fluid and magnetic parameters. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider networks of reaction–diffusion systems of Hodgkin–Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as the existence of invariant regions and of the attractor. Then, we illustrate some relevant numerical examples and exhibit bifurcation phenomena and propagation of bursting oscillations through one and two coupled non-homogeneous systems. [ABSTRACT FROM AUTHOR]

This article considers the dispersion of hybrid and mono nanoparticles in a fluid with viscosity (Williamson) dependent on shear rate, over a heated surface moving with nonuniform velocity and exposed to a magnetic field in the presence of an applied current. Extensive modeling leads to complex coupled mathematical models that are solved numerically via the finite element method (FEM). Convergent simulations are run to investigate the role of parameters on the dynamics of flow fields. The magnetic field intensity plays a role in controlling the magnetohydrodynamic boundary layer thickness (BLT) and thermal radiation controls the thickness of thermal boundary layers (TBL). However, the magnetic field intensity is responsible for an increase in BLT. In contrast to this, thermal radiation plays a role in controlling the thickness of the TBL. The impact of shear rate dependent viscosity on velocity is remarkable for both fluids. The motion of both of the fluids slows down when viscosity varies as a function of shear rate. Viscosity depending on the shear rate has a significant impact on wall shear stress. It is observed from simulations that wall shear increases when the parameters appearing in the model for shear rate dependent viscosity are increased. However, this increase in wall shear stress associated with a hybrid nanofluid is greater than the increase in wall shear stress associated with a mono nanofluid. [ABSTRACT FROM AUTHOR]

Human mobility has been significantly influencing public health since time immemorial. A susceptible-infected-deceased epidemic reaction diffusion network model using asymptotic transmission rate is proposed to portray the spatial spread of the epidemic among two cities due to population dispersion. Qualitative behaviour including global attractor and persistence property are obtained. We also study asymptotic behaviour of the whole network with the help of asymptotic behaviour at individual cities. The epidemic model shows up two equilibria, (i) the disease-free, and (ii) unique endemic equilibria. An expression that can be used to calculate the basic reproduction number for heterogeneous environment, for the entire network is obtained. We use graph theory to analyze the global stability of our diffusive two-city model. We also performed bifurcation analysis and discovered that endemic equilibrium changes stability via Hopf bifurcations. A significant reduction in the number of infectives were observed when proper migration rate is maintained between the cities. Numerical results are provided to illuminate and clarify theoretical findings. Simulation experiments for two-dimensional spatial models show that infectious populations will increase if contact heterogeneity is increased, but it will decline if infective populations perform more local random movement. We observe that infection risk may be understated if the parameters used to estimate the basic reproduction number remains unchanged through space or time. [ABSTRACT FROM AUTHOR]

We propose a new compartmental mathematical model describing the transmission and the spreading of COVID-19 epidemic with a special focus on the non-total immunity. The model (called SIARD) is given by a system of differential equations which model the interactions between five populations "susceptible", "reported infectious", "unreported infectious", "recovered with/without non total immunity" and "death". Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case. [ABSTRACT FROM AUTHOR]

The nematode Caenorhabditis elegans (C. elegans) is a well-known model organism in neuroscience. The relative simplicity of its nervous system, made up of few hundred neurons, shares some essential features with more sophisticated nervous systems, including the human one. If we are able to fully characterize the nervous system of this organism, we will be one step closer to understanding the mechanisms underlying the behavior of living things. Following a recently conducted electrophysiological survey on different C. elegans neurons, this paper aims at modeling the three non-spiking RIM, AIY and AFD neurons (arbitrarily named with three upper case letters by convention). To date, they represent the three possible forms of non-spiking neuronal responses of the C. elegans. To achieve this objective, we propose a conductance-based neuron model adapted to the electrophysiological features of each neuron. These features are based on current biological research and a series of in-silico experiments which use differential evolution to fit the model to experimental data. From the obtained results, we formulate a series of biological hypotheses regarding currents involved in the neuron dynamics. These models reproduce experimental data with a high degree of accuracy while being biologically consistent with state-of-the-art research. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of dissipative evolution problems, determined by complex networks of reaction-diffusion systems, is investigated with an original approach. We establish a novel estimation of the fractal dimension of exponential attractors for a wide class of continuous dynamical systems, clarifying the effect of the topology of the network on the large time dynamics of the generated semi-flow. We explore various remarkable topologies (chains, cycles, star and complete graphs) and discover that the size of the network does not necessarily enlarge the dimension of attractors. Additionally, we prove a synchronization theorem in the case of symmetric topologies. We apply our method to a complex network of competing species systems modeling an heterogeneous biological ecosystem and propose a series of numerical simulations which underpin our theoretical statements. [ABSTRACT FROM AUTHOR]

To evaluate the rooting ability and growth performance in semihardwood cuttings of Argania spinosa under nonmist greenhouse conditions, our experimentation was conducted with three cutting diameters (0.10.3, 0.30.6 and 0.60.9 cm), four leaf retention treatments (leafless, 2, 4 and 8 leaves) and three different rooting substrates (fine sand, peat moss, a 1:1 mixture of fine sand/peat moss). Significant effects of cuttings diameter, leaf retention and rooting substrate on sprouting, rooting and survival ability from A. spinosa semihardwood cuttings were observed. Among all diameters tested, a diameter of (0.30.6 cm) showed maximum rooting and survival capacity, while cuttings with a diameter of 0.60.9 cm resulted in the greatest sprouting ability. Successful vegetative propagation was restricted to leafy stem cuttings. Moreover, it was observed that the highest rooting ability was reached in cuttings planted in finesand substrate. However, the highest sprouting ratio (85.0%) and survival rate (92.5%) were achieved in a mixture of sand and peat moss. Thus, argan trees vegetative propagation could be most effectively achieved using semihardwood cuttings with a 0.4 cm diameter and 4 leaves, planted in a fine sand substrate during the root initiation period and grown in a mixture of fine sand and peat moss for hardening. [ABSTRACT FROM AUTHOR]

A system of nonlinear differential equations is proposed to assess the effects of prevalence-dependent disease contact rate, pathogen’s shedding rates, and treatment rate on the dynamics of schistosomiasis in a general setting. The decomposition techniques by Vidyasagar and the theory of monotone systems are the main ingredients to deal completely with the global asymptotic analysis of the system. Precisely, a threshold quantity for the analysis is derived and the existence of a unique endemic equilibrium is shown. Irrespective of the initial conditions, we prove that the solutions converge either to the disease-free equilibrium or to the endemic equilibrium, depending on whether the derived threshold quantity is less or greater than one. We assess the role of an integrated control strategy driven by human behavior changes through the incorporation of prevalence-dependent increasing the prophylactic treatment and decreasing the contact rate functions, as well as the mechanical water sanitation and the biological elimination of snails. Because schistosomiasis is endemic, the aim is to mitigate the endemic level of the disease. In this regard, we show both theoretically and numerically that: the reduction of contact rate through avoidance of contaminated water, the enhancement of prophylactic treatment, the water sanitation, and the removal of snails can reduce the endemic level and, to an ideal extent, drive schistosomiasis to elimination. [ABSTRACT FROM AUTHOR]

The generalized windmill graphs are good models for many real-world networks. In this paper, we obtain analytic expressions for the eigenvalues of the adjacency matrices and of the Laplacian matrices of the generalized windmill graphs. Using this information, we study some structural and dynamical properties of these graphs. To the end, we investigate the metro networks of four France cities and propose our suggestions for the planning of public transport networks. [ABSTRACT FROM AUTHOR]

The exact controllability can be mapped to the problem of maximum algebraic multiplicity of all eigenvalues. In this paper, we focus on the exact controllability of deterministic complex networks. First, we explore the eigenvalues of two famous networks, i.e. the comb-of-comb network and the Farey graph. Due to their special structure, we find that the eigenvalues of each network are mutually distinct, showing that these two networks are optimal networks with respect to exact controllability. Second, we study how to optimize the exact controllability of a deterministic network. Based on the spectral graph theory, we find that reducing the order of duplicate sets or co-duplicate sets which are two special vertex subsets can decrease greatly the exact controllability. This result provides an answer to an open problem of Li et al. [X. F. Li, Z. M. Lu and H. Li, Int. J. Mod. Phys. C 26, 1550028 (2015)]. Finally, we discuss the relation between the topological structure and the multiplicity of two special eigenvalues and the computational complexity of our method. [ABSTRACT FROM AUTHOR]

Aedes aegypti (Ae. aegypti: mosquito) is a known vector of several viruses including yellow fever, dengue, chikungunya and zika. In the current paper, we present a delayed mathematical model describing the dynamics of Ae. aegypti. Our model is governed by a system of three delay differential equations modeling the interactions between three compartments of the Ae. aegypti life cycle (females, eggs and pupae). By using time delay as a parameter of bifurcation, we prove stability/switch stability of the possible equilibrium points and the existence of bifurcating branch of small amplitude periodic solutions when time delay crosses some critical value. We establish an algorithm determining the direction of bifurcation and stability of bifurcating periodic solutions. In the end, some numerical simulations are carried out to support theoretical results.. [ABSTRACT FROM AUTHOR]

We investigate an interval of moderate magnetic activity from 0-8 UT on 14 March 2008 by using a global magnetohydrodynamics (MHD) simulation with high spatial and temporal resolution. Observations show several distinct substorms during this interval. One of these with onset at 04:44 UT occurs at 04:42 UT in the simulation. The simulation shows reconnection is continuously present at multiple sites. During the growth phase, the number of X-lines decreases as their total length increase and their locations approach the Earth. The X-lines create multiple fast flow channels with dipolarization fronts. The total length and area of these channels increase during the growth phase as they penetrate closer to the Earth carrying more magnetic flux. The 04:42 UT onset in the simulation was preceded by the growth of an X-line that eventually extended 55 RE from 12 RE premidnight to 50 on the dawn side. It produced a narrow flow channel parallel to the X-line that eventually penetrated inside 10 RE rapidly depositing magnetic flux as the expansion phase developed. Despite this good agreement in expansion phase onset time, ground and satellite observations suggest a quiet growth phase with a sudden onset of reconnection. It may be possible to explain the difference between observations and simulations if all growth phase activity in the simulation maps to the ionosphere at very high latitudes. An auroral streamer at onset maps in the simulation very close to Earth. A recovery phase streamer maps to the middle tail. [ABSTRACT FROM AUTHOR]

The significance of the local skin friction as well as the heat transfer rate on the motion of water H 2 O and ethylene glycol C 2 H 6 O 2 conveying metallic and metallic oxide nanoparticles (e.g., Al, Cu, Zn, Al203, CuO and ZnO) along a vertical thin needle is needed to improve the performance of chemical reactors, heat exchangers, pharmaceutical equipment and hybrid-powered engines. This led to the investigation of mixed convection flow and heat transfer of some nanofluids, in which the thermal conductivity and viscosity vary nonlinearly with the volume fraction. For simplifying the present investigation, appropriate variables were introduced successfully in the mathematical formulation to convert the governing nonlinear partial differential equations to coupled ordinary differential equations (ODEs). Moreover, the resulting ODEs were solved numerically via a robust differential quadrature algorithm. Furthermore, a comparative study with the existing literature is found to be in an excellent agreement. The enhancement of heat transfer in nanofluids is ascertained by increasing the convection ratio. Generally, the maximum improvement in the local skin friction was perceived for the flows of zinc–water-based nanofluids (Zn – H 2 O ) with the upsurge in the volume fraction of the nanoparticles Zn . On the contrary, the highest enhancement in the heat transfer rate was revealed for the flows of copper–ethylene glycol-based nanofluids (Cu – C 2 H 6 O 2 ) with the increase in the weight percent of the Cu nanomaterial loading. [ABSTRACT FROM AUTHOR]

We investigate the relation of fast flows at the inner edge of the plasma sheet to the onset of auroral expansion. Recent work suggests that nearly all expansions are an instability triggered by an auroral streamer from far out in the magnetotail. We investigate an 8‐hr interval of activity on 14 March 2008 using ground magnetometer and all‐sky camera data to determine the onset times of six substorm expansions. We compare these times with Time History of Events and Macroscale Interactions during Substorms observations of plasma flow and magnetic field. We show that every expansion followed the arrival of a fast flow and dipolarization event at the inner edge of the plasma sheet. To relate the aurora to flows, we develop procedures for removing fixed lights, the moving Moon and its reflection, and contamination due to scattered moonlight. We scan movies of enhanced images for auroral streamers. Three onsets were tentatively associated with streamers. For two, the apparent source was very close to the growth phase arc mapping close to Earth. For one, an onset occurred in the recovery phase of an earlier substorm after a double oval had formed. For this one, the end of an N‐S streamer stopped about 2° north of the breakup arc. For the remaining three expansions, no streamers were associated with the onsets. Most substorms exhibit N‐S streamers in the recovery phase. These usually cannot be associated with fast flows. Either fast flows in the growth phase do not produce streamers or they make streamers that require significant image enhancement. Plain Language Summary: Auroral streamers are narrow bands of auroral luminosity that originate near the poleward edge of the auroral oval. They generally propagate from north to south often with a large azimuthal component. Researchers think that these streamers impact the outer magnetosphere triggering an instability that appears as a localized expansion of aurora towards the poles. This paper describes the processing of ground auroral images to identify the existence of streamers. We compare their occurrence with ground magnetometer data signaling the onset of auroral expansion and with spacecraft data showing high‐speed flows transporting magnetic flux to the inner edge of the plasma sheet. We find that all six expansions were associated with the arrival of fast flows transporting magnetic flux towards Earth. Only three of these could be associated with a streamer. Two were primarily E‐W from a source close to Earth. The third was a classic N‐S streamer that occurred in the recovery phase of an earlier substorm. At this time, aurora was present in two bands at the edges of the auroral oval. There was no obvious connection of the equatorward end of this streamer to the activated arc. We find that the fast flows causing substorm expansion either do not produce visible aurora or are so weak that special processing of the camera images is required to see the streamers. Key Points: All six auroral expansions in the study interval were preceded by the arrival of a bursty bulk flow at inner edge of plasma sheetOnly three of the fast flows were definitely associated with auroral streamersOnly one expansion occurred when classic streamers originating at the poleward edge of the auroral oval were present [ABSTRACT FROM AUTHOR]

In this work, the heat transfer within MEMS devices materialised by a cavity is envisaged. The problem is studied using the Grad's 13-moments and the Navier–Stokes and Fourier field of equations (NSF), with first order of slip and jump boundary conditions, compared to the direct simulation Monte Carlo (DSMC) results. A Maxwelllian gas is assumed to be confined in a cavity at the environmental temperature. The cavity is taken to have a hot chip, an adiabatic one while the two others are taken to the environmental temperature. The 13-moments solutions are in accordance with DSMC predicting, besides the classical hot to cold vortices, two additional counter-rotating ones exchanging energy with the two cold walls, which are not predicted by the continuum-based model. The Knudsen number growth, gas rarefaction degree, affects the vortices by pushing the classical ones towards the centre and hot plate, while strengthening the others. [ABSTRACT FROM AUTHOR]

This paper takes the reaction–diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By means of analyzing the eigenvalue spectrum, we show that the persistent positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via Hopf bifurcation when time delay crosses some critical value. Using normal form and center manifold theory, we investigate the stability of the bifurcating branches of periodic solutions and the direction of the Hopf bifurcation. Numerical simulations are carried out to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this work, the design and analysis of new Level Shifter with Gate Driver for Li-Ion battery charger is proposed for high speed and low area in 180nm CMOS technology. The new proposed level shifter is used to raise the voltage level and significantly reduces transfer delay 1.3ns (transfer delay of conventional level shifter) to 0.15ns with the same input signal. Also, the level shifter with gate driver achieves a propagation delay of less than 0.25ns and the total area is only 0.05mm². The proposed level shifter with gate driver was designed, simulated and layouted in Cadence using TSMC 180nm CMOS technology. [ABSTRACT FROM AUTHOR]

Argania spinosa (L.) is an endemic tree species of southwestern Morocco; it plays a very important socioeconomic and environmental role. However, the vegetative propagation of the argan tree by traditional cuttings is limited by the difficulty of rooting and survival during transplantation in the field. Considering these facts, this study intended to investigate the rooting ability and growth performance of argan tree cuttings, collected from four élite trees rated ASOC1, ASOC2, ASOC3 and ASOC4, and treated with four concentrations (0, 1000, 3000 and 5000 mgL1) of IBA, NAA and IAA. The results revealed cuttings of ASOC2 and ASOC3 genotypes were relatively less responsive than ASOC1 and ASOC4, this genotype effect was more pronounced in auxin treated cuttings. Treatment of cuttings by IBA was more effective than treatments by either NAA or IAA. Among all the media tested, 3000 mgL1 of IBA with ASOC1 resulted in higher sprouting (81.75%), rooting (60.75%) and survival rates (96.25%). However, with the increase of IBA concentration levels (>3000 mgL1), adventitious roots and sprouts performances decreased in all the genotypes. Argania spinosa could be successfully propagated by cuttings from selected élite trees. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the asymptotic behaviour of a complex network of reaction–diffusion systems for a geographical model, which was proposed recently, in order to better understand behavioural reactions of individuals facing a catastrophic event. After stating sufficient conditions for the problem to admit a positively invariant region, we establish energy estimates and prove the existence of a family of exponential attractors. We explore the influence of the size of the network on the nature of those attractors, in correspondence with the geographical background. Numerical simulations illustrate our theoretical results and show the various possible dynamics of the problem. [ABSTRACT FROM AUTHOR]

We focus on the long-time behaviour of complex networks of reaction–diffusion (RD) systems. In a previous work, we have proved the existence of the global attractor and the |$L^{\infty }$| -bound for these networks. Here, we discuss the synchronization phenomenon and establish the existence of a coupling strength threshold value that ensures this synchronization. Then, we apply these results to some particular networks with different structures (i.e. different topologies) and perform numerical simulations. We found out theoretical and numerical heuristic laws for the minimal coupling strength needed for synchronization with respect to the number of nodes and the network topology. We also discuss the link between spatial heterogeneity and synchronization. Our main conclusion is that some of widespread heuristic laws known for synchronization of ordinary differential equations remain valid for networks of RD systems, i.e. networks in which each node has its own spatial heterogeneity. [ABSTRACT FROM AUTHOR]