Effects Of Spatial Gradients Research Articles

Adaptation of species as response to climate change: Predator-prey mathematical model

Most of the species currently threatened with extinction seem to be under the pressure of unsuitable environmental conditions; e.g., climate change, scarce food resource, habitat fragmentation. One should expect species to have forms of resilience against such extinction. The point here is to examine the effect of spatial gradients on species survival against increasing temperature arising from climate change. Therefore, we start with the question of whether, when faced with extinction stemming from climate change, a spatial gradient and a beachhead have the power to prevent extinction. This problem is addressed theoretically using a coupled reaction diffusion equation for a predator-prey system in which the prey experiences an Allee effect. It is demonstrated that there exists a relationship between the slope of the gradient and the beachhead at which the predator-prey system can stably survive. The tendency of the system can be defined by a function where the system includes the threshold point for extinction, that separates the areas of extinction and survival. The findings reveal that spatial gradient can be used as a precaution, when the species faces to extinction, for species to create new habitat and sustain its persistence. Therefore, in this paper, it is shown that, in theory, the recovery of species from unsuitable environmental conditions can be achieved. This can be possible by taking into account the spatial gradient to slow down the forthcoming ecological extinction, and thus extend the system a while as an adaptation mechanism.

Effects of spatial gradients in thermophysical properties on the topology of turbulence in heated channel flow of supercritical fluids

The current literature suggests that large spatial gradients of thermophysical properties, which occur in the vicinity of the pseudo-critical thermodynamic state, may result in significant variations in forced-convection heat transfer rates. Specifically, these property gradients induce inertia- and buoyancy-driven phenomena that may enhance or deteriorate the turbulence-dominated heat convection process. Through direct numerical simulations, the present study investigates the role of coherent flow structures in channel geometries for non-buoyant and buoyant flows of supercritical water, with buoyant configurations involving wall-normal oriented gravitational acceleration and downstream-oriented gravitational acceleration. This sequence of simulations enables the evaluation of the relative contributions of inertial and buoyancy phenomena to heat transfer variations. In these simulations, the state of the working fluid is in the vicinity of the pseudo-critical point. The uniform wall heat flux and the channel mass flux are specified such that the heat to mass flux ratio is 3 kJ/kg, with an inflow Reynolds number of 12 000 based on the channel hydraulic diameter, the area-averaged inflow velocity, and fluid properties evaluated at the bulk temperature and pressure of the inflow plane. In the absence of buoyancy forces, notable reductions in the density and viscosity in close proximity of the heated wall are observed to promote generation of small-scale vortices, with resultant breakdown into smaller scales as they interact with preexisting larger near-wall vortices. This interaction results in a reduction in the overall thermal mixing at particular wall-normal regions of the channel. Under the influence of wall-normal gravitational acceleration, the wall-normal density gradients are noted to enhance ejection motions due to baroclinic vorticity generation on the lower wall, thus providing additional wall-normal thermal mixing. Along the upper wall, the same mechanism generates streamwise vorticity of the opposing sense of rotation in the close vicinity to the respective legs of the hairpin vortices causing a net reduction in thermal mixing. Finally, in the case of downstream-oriented gravitational acceleration, baroclinic vorticity generation as per spanwise density gradients causes additional wall-normal thermal mixing by promoting larger-scale ejection and sweep motions.

A spatial model of fluid recycling in the airways of the lung

The genetic disease cystic fibrosis (CF) is a mutation in the cystic fibrosis transmembrane conductance regulator (CFTR) gene, and results in viscous mucus and impaired mucociliary clearance leading to chronic recurring pulmonary infections. Although extensive experimental research has been conducted over the last few decades, CF lung pathophysiology remains controversial. There are two competing explanations for the observed depletion of periciliary liquid (PCL) in CF lungs. The low volume hypothesis assumes fluid hyperabsorption through surface epithelia due to an over-active epithelial Na+ channel (ENaC), and the low secretion hypothesis assumes inspissated mucins secreted from glands due to lack of serous fluid secreted from gland acini.We present a spatial mathematical model that reflects in vivo fluid recycling via submucosal gland (SMG) secretion, and absorption through surface epithelia. We then test the model in CF conditions by increasing ENaC open probability and decreasing SMG flux while simultaneously reducing CFTR open probability. Increasing ENaC activity only results in increased fluid absorption across surface epithelia, as seen in in vitro experiments. However, combining potential CF mechanisms results in markedly less fluid absorbed while providing the largest reduction in PCL volume, suggesting that a compromise in gland fluid secretion dominates over increased ENaC activity to decrease the amount of fluid transported transcellularly in CF lungs in vivo. Model results also indicate that a spatial model is necessary for an accurate calculation of total fluid transport, as the effects of spatial gradients can be severe, particularly in close proximity to the SMGs.

TYPE I PLANET MIGRATION IN A MAGNETIZED DISK. I. EFFECT OF LARGE-SCALE VERTICAL AND AZIMUTHAL FIELD COMPONENTS

We study the effects of a large-scale, ordered magnetic field in protoplanetary disks on Type I planet migration using a combination of numerical simulations in 2D and 3D and a linear perturbation analysis. Steady-state models of such disks require the inclusion of magnetic diffusivity. To make progress using ideal MHD, we focus on simplified field configurations, involving purely vertical ($B_z$) and azimuthal ($B_\varphi$) field components and a combination of the two. For each of the models we calculate the locations of the relevant resonances and of the turning points, which delineate the propagation regions of the MHD waves that transport angular momentum from the planet to the disk. We use both numerical and semianalytic methods to evaluate the cumulative back torque acting on the planet, and explore the effect of spatial gradients in the disk's physical variables on the results. We conclude that, under realistic (3D) circumstances, a large-scale magnetic field can slow down the inward migration that characterizes the underlying unmagnetized disk --- by up to a factor of $\sim 2$ when the magnetic pressure approaches the thermal pressure --- but it cannot reverse it. A previous inference that a pure-$B_\phi$ field whose amplitude decreases fast enough with radius leads to outward migration applies only in 2D. In fact, we find that, in 3D, a pure-$B_\phi$ disk undergoes a rapid transition to turbulence on account of a magnetorotational instability that is triggered by the planet-induced appearance of a weak $B_z$ component.

Buoyant-MHD Flows in HCLL Blankets Caused by Spatially Varying Thermal Loads

In the helium-cooled lead lithium (HCLL) blanket concept convective phenomena caused by nonuniform thermal conditions due to bulk neutron volumetric heating can occur. Buoyancy can become very important and modify the velocity distribution and related heat transfer performance of the blanket. A numerical study has been performed to investigate liquid metal flows driven by buoyant forces in a breeder unit (BU) of a HCLL test blanket module (TBM) under the influence of intense uniform magnetic fields. According to the last design review, two internal cooling plates subdivide the fluid domain into three slender flow regions, which are thermally and electrically coupled through common walls. First, a uniform volumetric heat source is considered to identify the basic convective patterns that establish in the liquid metal. Results are then compared with those obtained by applying a realistic radial distribution of the power density as obtained from a neutronic analysis. This paper summarizes the main effects of spatial gradients of a neutron thermal load on velocity and temperature distribution in magnetohydrodynamic flows in a BU of a HCLL TBM.

Effect of spatial gradient in fluid shear stress on morphological changes in endothelial cells in response to flow

Arterial bifurcations are common sites for development of cerebral aneurysms. Although this localization of aneurysms suggests that high shear stress (SS) and high spatial SS gradient (SSG) occurring at the bifurcations may be crucial factors for endothelial dysfunction involved in aneurysm formation, the details of the relationship between the hemodynamic environment and endothelial cell (EC) responses remain unclear. In the present study, we sought morphological responses of ECs under high-SS and high-SSG conditions using a T-shaped flow chamber. Confluent ECs were exposed to SS of 2–10 Pa with SSG of up to 34 Pa/mm for 24 and 72 h. ECs exposed to SS without spatial gradient elongated and oriented to the direction of flow at 72 h through different processes depending on the magnitude of SS. In contrast, cells did not exhibit preferred orientation and elongation under the combination of SS and SSG. Unlike cells aligned to the flow by exposure to only SS, development of actin stress fibers was not observed in ECs exposed to SS with SSG. These results indicate that SSG suppresses morphological changes of ECs in response to flow.

Dynamics of thin liquid films on surfaces with a time-periodic wettability

The dynamics of thin liquid films on surfaces whose wettability changes in a time-periodic manner are examined in this work. A nonlinear evolution equation based on the lubrication approximation is used to describe the film height, and attractions due to van der Waals forces are incorporated. Film wettability is varied through an imposed sinusoidal modulation of the Hamaker constant. A linear stability analysis predicts that if the mean Hamaker constant is negative, disturbances at the film surface will eventually decay regardless of the amplitude and frequency of the oscillation. However, numerical solution of the evolution equation shows that the film can rupture at a given frequency if the amplitude is sufficiently large. The associated characteristic wavelength can be predicted from results for constant-wettability surfaces if an appropriate effective Hamaker constant is used. For positive mean Hamaker constants, film rupture can be accelerated, delayed, or prevented depending on how the Hamaker constant changes early in the oscillation cycle. The effects of spatial gradients in wettability are also considered, and it is found that oscillation can delay but not prevent rupture. Inclusion of short-range repulsive forces leads to the formation of droplet-like structures separated by ultra-thin films, but this can be prevented by sufficiently large and slow oscillations of the Hamaker constant. The results of this work may find use in applications that make use of surfaces whose wettability can be controlled by external stimuli.

Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in two dimensions: A study using deposition-evaporation kinetics

Deposition and evaporation of infinitely thin hard rods (needles) is studied in two dimensions using Monte Carlo simulations. The ratio of deposition to evaporation rates controls the equilibrium density of rods, and increasing it leads to an entropy-driven transition to a nematic phase in which both static and dynamical orientational correlation functions decay as power laws, with exponents varying continuously with deposition-evaporation rate ratio. Our results for the onset of the power-law phase agree with those for a conserved number of rods. At a coarse-grained level, the dynamics of the nonconserved angle field is described by the Edwards-Wilkinson equation. Predicted relations between the exponents of the quadrupolar and octupolar correlation functions are borne out by our numerical results. We explore the effects of spatial inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based arguments, and a study of the additional terms introduced in the free energy. The primary effect is that needles tend to align along the local spatial gradient of the ratio. A uniform gradient thus induces a uniformly aligned state, as does a gradient which varies randomly in magnitude and sign, but acts only in one direction. Random variations of deposition-evaporation rates in both directions induce frustration, resulting in a state with glassy characteristics.

Effects of Wind-induced Spatial Variation in Water Temperature and Zooplankton Concentration on the Growth of Young-of-the-year Smallmouth Bass, Micropterus dolomieu

Young-of-the-year (YOY) smallmouth bass, Micropterus dolomieu, spend their first summer in littoral areas near their nests. Evidence indicates that nests of smallmouth bass in Lake Opeongo, Ontario, Canada are more abundant in downwind locations than in upwind areas. We hypothesize that wind-induced lower water temperatures and food availability in upwind nesting areas lead to lower growth rates of YOY bass in upwind than in downwind nesting areas. We show that water temperatures were 0.6–1.3 °C higher in downwind than upwind littoral areas during the period from mid-June to mid-July, when the YOY bass were on or near their nests. Although quite variable, zooplankton concentrations were also higher at downwind sites. In addition, bioenergetic simulations based on time series of field-measured temperatures predicted higher growth rates of YOY bass in the downwind sites. Growth rates based on sequential sampling of bass fry from their nests did not, however, differ statistically between upwind and downwind sites, although fry consistently weighed more downwind than upwind in the basin with the longer fetch possibly due to earlier spring warming. Our hypothesis is thus only partially supported and we call for further research on effects of spatial gradients on smallmouth bass life history.

Multiterm solution of the reactive space–time-dependent Boltzmann equation

The effect of spatial gradients, whether associated with surfaces or otherwise, on charged particle phase-space distribution functions and transport properties is a long-standing problem in the kinetic theory of gases. This article first discusses the necessary ingredients for an accurate kinetic theory analysis of the space–time behavior of electrons in gases and compares the different approaches currently in use. We then focus upon the electrons in a radio-frequency discharge away from the walls, where gradients are weak, and point out that the fundamental kinetic theory of even the boundary-free problem still warrants more careful attention than has been given to it in much of the contemporary literature. We highlighted the importance of careful analysis by presenting results for the first comprehensive “multiterm” solution of Boltzmann’s equation furnishing the complete set of hydrodynamic transport coefficients for electrons in an ac field undergoing ionization and attachment.

On the influences of nonlinear bottom friction on the topographic rectification of tidal currents

Abstract The influences of nonlinear bottom friction on the along-isobath mean current associated with the topographic rectification of tidal currents are examined in the limit of depth-independence (no vertical structure in the horizontal currents), weak friction and weak nonlinearity. These influences are discussed in terms of the effects of spatial gradients and temporal variations in the effective friction coefficient relating bottom stress to velocity. For typical parameter values, spatial gradients in the coefficient enhance the mean current and temporal variations reduce it. The first influence is the source of Loder's (1980) suggestion that the mean current is enhanced by nonlinear friction. The second influence accounts for the mean current reduction upon the inclusion of nonlinear friction in the example considered by Huthnance (1981). However, it is shown that each of these influences can have the opposite effect for extreme parameter values. Additionally, the inclusion of mean current contribu...

Spectral Line Emission from a Transient Nonuniform Plasma

Some effects of spatial gradients and transient behavior on spectral line radiation from impurities in a low-energy θ-pinch plasma are discussed for a case where local thermodynamic equilibrium could not be assumed. The plasma was produced and preheated by a fast capacitor bank discharge, a controlled trapped magnetic field was generated by a slower discharge through the same coil, and magnetic compression was achieved by a fast rising reverse magnetic field. Measured carbon impurity line intensities were compared to predictions on the basis of magnetohydrodynamic calculations coupled with spectroscopic theory. Large errors are incurred in electron temperatures from relative intensities of lines from successive stages of ionization if the radial variation of ionization and excitation is ignored.