Local carbon reserves are insufficient for phloem terpene induction during drought in Pinus edulis in response to bark beetle-associated fungi.

Stomatal closure during drought inhibits carbon uptake and may reduce a tree's defensive capacity. Limited carbon availability during drought may increase a tree's mortality risk, particularly if drought constrains trees' capacity to rapidly produce defenses during biotic attack. We parameterized a new model of conifer defense using physiological data on carbon reserves and chemical defenses before and after a simulated bark beetle attack in mature Pinus edulis under experimental drought. Attack was simulated using inoculations with a consistent bluestain fungus (Ophiostoma sp.) of Ips confusus, the main bark beetle colonizing this tree, to induce a defensive response. Trees with more carbon reserves produced more defenses but measured phloem carbon reserves only accounted for c. 23% of the induced defensive response. Our model predicted universal mortality if local reserves alone supported defense production, suggesting substantial remobilization and transport of stored resin or carbon reserves to the inoculation site. Our results show that de novo terpene synthesis represents only a fraction of the total measured phloem terpenes in P. edulis following fungal inoculation. Without direct attribution of phloem terpene concentrations to available carbon, many studies may be overestimating the scale and importance of de novo terpene synthesis in a tree's induced defense response.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness.

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavcic and Wang's (Miklavcic and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking.

Homochirality, the phenomenon by which one of two virtually identical (non-superimposable mirror images) compounds is favored over the other in the chemistry of life, has been regarded as a requisite for the emergence of all living things on earth. Spontaneous mirror symmetry breaking has been proposed to produce the imbalance. Under this framework, Frank presented, in his foundational article "On spontaneous asymmetric synthesis", a simple chemical reaction network that displays spontaneous symmetry breaking for a specific set of reaction rates. Research has since focused on finding more complex and plausible models, each one with its advantages and disadvantages. Nevertheless, finding reaction rate values that make a model exhibit spontaneous symmetry breaking is a complex task, even for specially crafted models. LInear STability ANALysis of CHEmical Mechanism, Listanalchem, is a method and software for the search for appropriate reaction rates. It includes four different algorithms inspired by the analysis of Frank's network. Two classical algorithms are also included in Listanalchem: the Trace-Determinant plane and the Stoichiometric Network Analysis by Bruce Clarke. Listanalchem reads a chemical reaction network from plain text and runs one or more of the available algorithms according to the user selection. Listanalchem is tested and verified by studying classical, modified, and recent models proposed to explain the origin of biological homochirality.•Listanalchem allows a fast and reliable search for instability behavior in chemical mechanisms that pretend to explain spontaneous mirror symmetry breaking.•Listanalchem contains several model examples, including the most cited in the related literature.•Listanalchem is a tool that tests models that pretend to explain the origin of biological homochirality, helps find errors, and aids in designing new models.

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors.

The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard's theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions ζ and ϵ leads to an increase in the number of people living with diabetes mellitus.

Thermoelectric instabilities in a circular Couette flow.

The stability of a non-isothermal circular Couette flow is analyzed when subjected to a dielectrophoretic force field. Outward and inward heating configurations are considered when the inner cylinder is rotating and the outer cylinder is at rest. In addition, an alternating voltage is applied between the two cylinders to induce a radial electric buoyancy that acts on the dielectric fluid. The linear stability analysis provides the threshold for the first transition to instability, as well as the corresponding wavenumber and frequency of the modes. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

spliceJAC: transition genes and state-specific gene regulation from single-cell transcriptome data.

Extracting dynamical information from single-cell transcriptomics is a novel task with the promise to advance our understanding of cell state transition and interactions between genes. Yet, theory-oriented, bottom-up approaches that consider differences among cell states are largely lacking. Here, we present spliceJAC, a method to quantify the multivariate mRNA splicing from single-cell RNA sequencing (scRNA-seq). spliceJAC utilizes the unspliced and spliced mRNA count matrices to constructs cell state-specific gene-gene regulatory interactions and applies stability analysis to predict putative driver genes critical to the transitions between cell states. By applying spliceJAC to biological systems including pancreas endothelium development and epithelial-mesenchymal transition (EMT) in A549 lung cancer cells, we predict genes that serve specific signaling roles in different cell states, recover important differentially expressed genes in agreement with pre-existing analysis, and predict new transition genes that are either exclusive or shared between different cell state transitions.

Delay effects on the stability of large ecosystems.

The common intuition among the ecologists of the midtwentieth century was that large ecosystems should be more stable than those with a smaller number of species. This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May's bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species' interactions may appear after a time lag rather than instantaneously. The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space. We find a critical delay curve that separates the region of stability from that of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalize Wigner's as well as Girko's laws. Interestingly, we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric.

The Elbert range of magnetostrophic convection. I. Linear theory.

In magnetostrophic rotating magnetoconvection, a fluid layer heated from below and cooled from above is equidominantly influenced by the Lorentz and the Coriolis forces. Strong rotation and magnetism each act separately to suppress thermal convective instability. However, when they act in concert and are near in strength, convective onset occurs at less extreme Rayleigh numbers ( R a , thermal forcing) in the form of a stationary, large-scale, inertia-less, inviscid magnetostrophic mode. Estimates suggest that planetary interiors are in magnetostrophic balance, fostering the idea that magnetostrophic flow optimizes dynamo generation. However, it is unclear if such a mono-modal theory is realistic in turbulent geophysical settings. Donna Elbert first discovered that there is a range of Ekman ( E k , rotation) and Chandrasekhar ( C h , magnetism) numbers, in which stationary large-scale magnetostrophic and small-scale geostrophic modes coexist. We extend her work by differentiating five regimes of linear stationary rotating magnetoconvection and by deriving asymptotic solutions for the critical wavenumbers and Rayleigh numbers. Coexistence is permitted if E k < 16 / ( 27 π ) 2 and C h ≥ 27 π 2 . The most geophysically relevant regime, the Elbert range, is bounded by the Elsasser numbers 4 3 ( 4 4 π 2 E k ) 1 / 3 ≤ Λ ≤ 1 2 ( 3 4 π 2 E k ) - 1 / 3 . Laboratory and Earth's core predictions both exhibit stationary, oscillatory, and wall-attached multi-modality within the Elbert range.

Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions.

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain.

Controlling the Connected Vehicle with Bi-Directional Information: Improved Car-Following Models and Stability Analysis.

Connected vehicle (CV) technologies are changing the form of traditional traffic models. In the CV driving environment, abundant and accurate information is available to vehicles, promoting the development of control strategies and models. Under these circumstances, this paper proposes a bidirectional vehicles information structure (BDVIS) by making use of the acceleration information of one preceding vehicle and one following vehicle to improve the car-following models. Then, we deduced the derived multiple vehicles information structure (DMVIS), including historical movement information of multiple vehicles, without the acceleration information. Next, the paper embeds the four kinds of basic car-following models into the framework to investigate the stability condition of two structures under the small perturbation of traffic flow and explored traffic response properties with different proportions of forward-looking or backward-looking terms. Under the open boundary condition, simulations on a single lane are conducted to validate the theoretical analysis. The results indicated that BDVIS and the DMVIS perform better than the original car-following model in improving the traffic flow stability, but that they have their own advantages for differently positioned vehicles in the platoon. Moreover, increasing the proportions of the preceding and following vehicles presents a benefit to stability, but if traffic is stable, an increase in any of the parameters would extend the influence time, which reveals that neither ß1 or ß2 is the biggest the best for the traffic.

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods.

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid-fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. We discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

A new integrable model of long wave-short wave interaction and linear stability spectra.

We consider the propagation of short waves which generate waves of much longer (infinite) wavelength. Model equations of such long wave-short wave (LS) resonant interaction, including integrable ones, are well known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new LS integrable model which generalizes those first proposed by Yajima and Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearized LS model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.

Impact of collision models on the physical properties and the stability of lattice Boltzmann methods.

The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference temperature.

With growing interest in the simulation of compressible flows using the lattice Boltzmann (LB) method, a number of different approaches have been developed. These methods can be classified as pertaining to one of two major categories: (i) solvers relying on high-order stencils recovering the Navier-Stokes-Fourier equations, and (ii) approaches relying on classical first-neighbour stencils for the compressible Navier-Stokes equations coupled to an additional (LB-based or classical) solver for the energy balance equation. In most cases, the latter relies on a thermal Hermite expansion of the continuous equilibrium distribution function (EDF) to allow for compressibility. Even though recovering the correct equation of state at the Euler level, it has been observed that deviations of local flow temperature from the reference can result in instabilities and/or over-dissipation. The aim of the present study is to evaluate the stability domain of different EDFs, different collision models, with and without the correction terms for the third-order moments. The study is first based on a linear von Neumann analysis. The correction term for the space- and time-discretized equations is derived via a Chapman-Enskog analysis and further corroborated through spectral dispersion-dissipation curves. Finally, a number of numerical simulations are performed to illustrate the proposed theoretical study. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis.

BACKGROUND AND OBJECTIVE: The hydrodynamic stability of nanofluids of one phase is investigated in this paper based on linear stability theory. The overall thrust here is that the linear stability features of nanofluids can be estimated from their corresponding working fluid, at least in special circumstances. METHODS: The approach uses the adjusting parameter to make assertions about stability. This is possible by certain correlations between the resulting eigenvalues. RESULTS: It is shown that as the nanoparticles are added, the mean flow of nanofluids is slightly modified and the resulting eigen space of nano disturbances is built on the corresponding pure flow eigen space of perturbations. Several fluid dynamics problems are revisited to verify the usefulness of the obtained correlations. CONCLUSION: The presented approach in this work serves us to understand the stabilizing/destabilizing effects of nanofluids as compared to the standard base fluids in terms of stability of viscous/inviscid and temporal/spatial senses. To illustrate, the critical Reynolds number in a traditional boundary layer flow is shown to be pushed to higher values with the dispersed nanoparticles in a working fluid, clearly implying the delay in transition from laminar to turbulent state.

On Thermodynamic and Kinetic Mechanisms for Stabilizing Surface Solid Solutions.

Many processes for energy storage rely on transformations between phases with strong separation tendencies. In these systems, performance limitations can arise from undesirable chemical and mechanical factors associated with the phase separation behavior. Solid solutions represent a desirable alternative, provided the conditions for their formation are known. Here, we invoke linear stability theory and diffuse-interface mesoscopic simulations to demonstrate that solid solutions can be stabilized near surface layers of phase-separating systems. Two factors are found to drive surface solid-solution formation: surface relaxation of solution self-strain energy and anisotropy of diffusion mobility. Using a strongly phase-separating LiXFePO4 particle as a model system, we show that the relaxation of the solution self-strain energy competes against the relaxation of the coherency strain energy to stabilize surface solid solutions. Our theoretical understanding also suggests that highly anisotropic diffusion mobility can provide an alternative kinetic route to achieve the same aim, with stabilizing behavior strongly dependent on the specific alignment of the surface orientation. Our findings provide fundamental guidance for manipulating solid-solution behavior in nanoscale structures, in which surface effects become especially significant. Beyond energy storage materials, our findings have important implications for understanding solid-solution formation in other phase-separating systems from metal alloys to ceramics.

Analysis of a Mathematical Model for the Glutamate/Glutamine Cycle in the Brain.

Our aim in this article is to study the well-posedness and properties of a system with delay which is related with brain glutamate and glutamine kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions. We also give numerical simulations and compare their order of magnitude with experimental data.

A chemotaxis-based explanation of spheroid formation in 3D cultures of breast cancer cells.

Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro cultures of breast cancer cells exhibiting patterns. Understanding their formation is of particular interest in the context of cancer since metastases have been shown to be created by cells moving in clusters. In this paper, we propose that the main mechanism which leads to the emergence of patterns is chemotaxis, i.e., oriented movement of cells towards high concentration zones of a signal emitted by the cells themselves. Studying a Keller-Segel PDE system to model chemotactical auto-organization of cells, we prove that it admits Turing unstable solutions under a time-dependent condition. This result is illustrated by two-dimensional simulations of the model showing spheroidal patterns. They are qualitatively compared to the biological results and their variability is discussed both theoretically and numerically.

Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment.

In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka-Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal increases the fitness of species in a spatially heterogeneous environment. The results are obtained through an eigenvalue analysis of the semi-trivial steady state solutions for the linearized operator derived from the model with nonuniform random diffusion on IGPrey and IGPredator, respectively. Finally, a simulation and its biological interpretations are presented based on our results.

Stability of a Dumbbell Micro-Swimmer.

A squirmer model achieves propulsion by generating surface squirming velocities. This model has been used to analyze the movement of micro-swimmers, such as microorganisms and Janus particles. Although squirmer motion has been widely investigated, motions of two connected squirmers, i.e., a dumbbell squirmer, remain to be clarified. The stable assembly of multiple micro-swimmers could be a key technology for future micromachine applications. Therefore, in this study, we investigated the swimming behavior and stability of a dumbbell squirmer. We first examined far-field stability through linear stability analysis, and found that stable forward swimming could not be achieved by a dumbbell squirmer in the far field without the addition of external torque. We then investigated the swimming speed of a dumbbell squirmer connected by a short rigid rod using a boundary element method. Finally, we investigated the swimming stability of a dumbbell squirmer connected by a spring. Our results demonstrated that stable side-by-side swimming can be achieved by pullers. When the aft squirmer was a strong pusher, fore and aft swimming were stable and swimming speed increased significantly. The findings of this study will be useful for the future design of assembled micro-swimmers.