Spatiotemporal Stability Research Articles

Spatio-Temporal Stability of Left Atrial Electroanatomical Characteristics in Longstanding Persistent Atrial Fibrillation: Novel Insights Using the Ensite HD Grid Catheter

Spatio-Temporal Stability of Left Atrial Electroanatomical Characteristics in Longstanding Persistent Atrial Fibrillation: Novel Insights Using the Ensite HD Grid Catheter

Absolute and convective instabilities in combined Couette-Poiseuille flow past a neo-Hookean solid

Temporal and spatio-temporal stability analyses are carried out to characterize the occurrence of convective and absolute instabilities in combined Couette-Poiseuille flow of a Newtonian fluid past a deformable, neo-Hookean solid layer in the creeping-flow limit. Plane Couette flow of a Newtonian fluid past a neo-Hookean solid becomes temporally unstable in the inertia-less limit when the parameter Γ = V η/(GR) exceeds a critical value. Here, V is the velocity of the top plate, η is the fluid viscosity, G is the shear modulus of the solid layer, and R is the fluid layer thickness. The Kupfer-Bers method is employed to demarcate regions of absolute and convective instabilities in the Γ-H parameter space, where H is the ratio of solid to fluid thickness in the system. For certain ranges of the thickness ratio H, we find that the flow could be absolutely unstable, and the critical Γ required for absolute instability is very close to that for temporal instability, thus making the flow absolutely unstable at the onset of temporal instability. In some cases, there is a gap in the parameter Γ between the temporal and absolute instability boundaries. The present study thus shows that absolute instabilities are possible, even at very low Reynolds numbers in flow past deformable solid surfaces. The presence of absolute instabilities could potentially be exploited in the enhancement of mixing at low Reynolds numbers in flow through channels with deformable solid walls.

Causation, lawhood and determinism in electoral systems research: why ‘Duverger’s law’ deserves to be called a law

In the 1950s, Maurice Duverger formulated several propositions connecting electoral systems and the number of political parties partaking in the election. For example, he put forward that a simple-majority single-ballot system favours the two-party system. This claim has been referred to as Duverger’s law. Throughout the years, there has been a lot of debate about whether this claim (and other generalisations in the social sciences) deserves to be called a ‘law’. In this paper, we defend the view that Duverger’s law does deserve to be called a law. To argue for this, we present an account of lawhood based on the work of the philosopher Sandra Mitchell. In this account, the criterion for lawhood is spatio-temporal stability (and not, for example, determinism). We argue that spatio-temporal stability is the reason that many of the laws of physics are considered laws. We then show that Duverger’s law is spatio-temporal in the same way that many of the laws of physics are. Correspondingly, we conclude that Duverger’s law deserves to be called a law, as much as many of the laws of physics deserve this title. We finish with a reflection on the difference between determinism and lawhood, and argue that they should be separated conceptually.

Spatiotemporal stability and sensitivity analysis of a holling type-II prey predator system with Allee effect

In this article, an analytical investigation is carried out on two species prey predator model having Holling type II interaction with Allee effect. We analysed the local and global behaviour of the interior equilibrium point.The theoretical aspects such as the investigation of the existence and stability of the equilibriums as well as the oscillatory and sensitivity behaviours of the corresponding diffusive system have been pursued. Also, analysed the effect of white noise and diffusion analysis of the proposed system. Finally, all the analytical results are interpreted ecologically and compared with the numerical results generated by MATLAB.

Stability of a radially stretching disk beneath a uniformly rotating fluid

The steady radial stretching of a disk beneath a rigidly rotating flow with constant angular velocity is considered. The steady base flow is determined numerically for both a stretching and a shrinking disk. The convective instability properties of the flow are examined using temporal stability analysis of the governing Rayleigh equation, and typically for small to moderate radial wave numbers, the range of azimuthal wave numbers β , over which the flow is unstable increases for both a stretched and a shrinking disk, compared to the unstretched case. The inviscid absolute instability properties of the resulting base flows are also examined using spatiotemporal stability analysis. For suitably large stretching rates, the flow is absolutely unstable in only a small range of positive β . For small stretching rates there exists a second region of absolute instability for a range of negative β values. In this region the “effective” two-dimensional base flow, comprised of a linear combination of the radial and azimuthal velocity profiles that enter the Rayleigh equation calculation, has a critical point (unlike for β > 0 ) that can dominate the absolute instability growth rate contribution compared to the shear layer component. A similar behavior is found to occur for a radially shrinking disk, except these profiles have a strong shear layer structure and hence are more unstable than the stretching disk profiles. We thus find for a suitably large shrinking rate the absolute instability contribution from the critical point becomes subdominant to the shear layer contribution.

Spatiotemporal model for assessing the stability of urban human convergence and divergence patterns

ABSTRACTUnderstanding the stability of urban flows is critical for urban transportation, urban planning and public health. However, few studies have measured the stability of aggregate human convergence or divergence patterns. We propose a spatiotemporal model for assessing the stability of human convergence and divergence patterns. A mobile phone location data set obtained from Shenzhen, China, was used to assess the stability of daily human convergence and divergence patterns at three different spatial scales, i.e. points (cell phone towers), lines (bus lines) and areas (traffic analysis zones [TAZs]). Our analysis results demonstrated that the proposed model can identify points and bus lines with time-dependent variations in stability, which is useful for delineating TAZs for transportation planning, or adjusting bus timetables and routes to meet the needs of bus riders. Comparisons of the results obtained from the proposed model and the widely used entropy measure indicated that the proposed model is suitable for assessing the differences in stability for various types of spatial analysis units, e.g. cell phone towers. Therefore, the proposed model is a useful alternative approach of measuring spatiotemporal stability of aggregate human convergence and divergence patterns, which can be derived from the space–time trajectories of moving objects.

Land surface model performance using cosmic-ray and point-scale soil moisture measurements for calibration

Abstract. At very high resolution scale (i.e. grid cells of 1 km2), land surface model parameters can be calibrated with eddy-covariance flux data and point-scale soil moisture data. However, measurement scales of eddy-covariance and point-scale data differ substantially. In our study, we investigated the impact of reducing the scale mismatch between surface energy flux and soil moisture observations by replacing point-scale soil moisture data with observations derived from Cosmic-Ray Neutron Sensors (CRNSs) made at larger spatial scales. Five soil and evapotranspiration parameters of the Joint UK Land Environment Simulator (JULES) were calibrated against point-scale and Cosmic-Ray Neutron Sensor soil moisture data separately. We calibrated the model for 12 sites in the USA representing a range of climatic, soil, and vegetation conditions. The improvement in latent heat flux estimation for the two calibration solutions was assessed by comparison to eddy-covariance flux data and to JULES simulations with default parameter values. Calibrations against the two soil moisture products alone did show an advantage for the cosmic-ray technique. However, further analyses of two-objective calibrations with soil moisture and latent heat flux showed no substantial differences between both calibration strategies. This was mainly caused by the limited effect of calibrating soil parameters on soil moisture dynamics and surface energy fluxes. Other factors that played a role were limited spatial variability in surface fluxes implied by soil moisture spatio-temporal stability, and data quality issues.

Changes in Tumor Biology During Chemoradiation of Cervix Cancer Assessed by Multiparametric MRI and Hypoxia PET

PurposeImaging biomarkers assessed with magnetic resonance imaging (MRI) and/or positron emission tomography (PET) enable non-invasive tumor characterization in cervix cancer patients. We investigated the spatio-temporal stability of hypoxia, perfusion, and the cell density of tumors over time by repetitive imaging prior to, during, and after radio-chemotherapy.ProceduresThirteen patients were included in this prospective study. The imaging protocol included the following: [18F]fluoromisonidazole ([18F]FMISO)-PET/x-ray computed tomography (CT) and multiparametric (mp)-MRI at four time-points (TP): baseline (BL); and weeks 2 (TP1), 5 (TP2), and 19 after treatment start (follow-up FU). Complete datasets for six patients could be assessed for tumor volume, enhancement kinetics, diffusivity, and [18F]FMISO-avidity (P1–P6). In addition, two patients completed all PET/CT examinations (P7–P8) but not all MR scans; however, one of them had no hypoxia (P8). Descriptive statistics, correlations, and voxel-by-voxel analysis were performed. For various, independent reasons, five patients could not complete the study according to the protocol with all imaging sequences.ResultsMedian tumor ADCs (in ×10−3 mm2/s) were 0.99 ± 0.10 at BL, 1.20 ± 0.12 at TP1, 1.33 ± 0.14 at TP2, and 1.38 ± 0.21 at FU. The median TBRpeak (tumor-to-background) was 2.7 ± 0.8 at BL, 1.6 ± 0.2 at TP1, 1.8 ± 0.3 at TP2, and 1.7 ± 0.3 at FU. The voxel-by-voxel analysis of the [18F]FMISO uptake at BL and TP1 showed no correlation. Between TP2 and TP1 and FU and TP2, weak correlations were found for two patients.ConclusionsLongitudinal mp-MR and PET imaging enables the in vivo tumor characterization over time. While perfusion and cell density decreased, there was a non-uniform change of hypoxia observed during radiotherapy. To assess the potential impact with regard to more personalized treatment approaches, hypoxia imaging-based dose painting for cervix cancer requires further research.

Thermocapillary effect on the absolute and convective instabilities of film flows down a fibre

We consider the motion of a gravity-driven flow down a uniformly heated vertical fibre. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity at the interface. A spatio-temporal stability analysis is performed to investigate the effect of thermocapillarity (Marangoni effect) on the convective/absolute instability (CI/AI) characteristics of the problem. We also performed a numerical simulation of Eq. (30) on the nonlinear evolution of the film to connect the breakup behaviours with the CI/AI characteristics. Our numerical results showed that for various Marangoni number (Ma), breakup of the film mainly occurs in the AI regime. With the increase of Ma, the film has a tendency to break up into droplets due to the enhancement of the absolute instability.

Transition and turbulence in horizontal convection: linear stability analysis

The linear instability mechanisms of horizontal convection in a rectangular cavity forced by a horizontal buoyancy gradient along its surface are investigated using local and global stability analyses for a Prandtl number equal to unity. The results show that the stability of the base flow, a steady circulation characterized by a narrow descending plume and a broad upwelling region, depends on the Rayleigh number, $Ra$. For free-slip boundary conditions at a critical value of $Ra\approx 2\times 10^{7}$, the steady base flow becomes unstable to three-dimensional perturbations, characterized by counter-rotating vortices originating within the plume region. A Wentzel–Kramers–Brillouin (WKB) method applied along closed streamlines demonstrates that this instability is of a Rayleigh–Taylor type and can be used to accurately reconstruct the global instability mode. In the case of no-slip boundary conditions, the base flow also becomes unstable to a self-sustained two-dimensional instability whose critical Rayleigh number is $Ra\approx 1.7\times 10^{8}$. Beyond this critical $Ra$, two-dimensional equilibrium stationary states of the Navier–Stokes equations are computed using the selective frequency damping method. The two-dimensional onset of instability is shown to be characterized by a family of modes also originating within the plume. A local spatio-temporal stability analysis shows that the flow becomes absolutely unstable at the origin of the plume. Taken together, these results illustrate the mechanisms behind the onset of turbulence that has been observed in horizontal convection.

Global instability of low-density jets

The global stability of laminar axisymmetric low-density jets is investigated in the low Mach number approximation. The linear modal dynamics is found to be characterised by two features: a stable arc branch of eigenmodes and an isolated eigenmode. Both features are studied in detail, revealing that, whereas the former is highly sensitive to numerical domain size and its existence can be linked to spurious feedback from the outflow boundary, the latter is the physical eigenmode that is responsible for the appearance of self-sustained oscillations in low-density jets observed in experiments at low Mach numbers. In contrast to previous local spatio-temporal stability analyses, the present global analysis permits, for the first time, the determination of the critical conditions for the onset of global instability, as well the frequency of the associated oscillations, without additional hypotheses, yielding predictions in fair agreement with previous experimental observations. It is shown that under the conditions of those experiments, viscosity variation with composition, as well as buoyancy, only have a small effect on the onset of instability.

Towards a quantitative comparison between global and local stability analysis

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

Massive introgression drives species radiation at the range limit of Anopheles gambiae

Impacts of introgressive hybridisation may range from genomic erosion and species collapse to rapid adaptation and speciation but opportunities to study these dynamics are rare. We investigated the extent, causes and consequences of a hybrid zone between Anopheles coluzzii and Anopheles gambiae in Guinea-Bissau, where high hybridisation rates appear to be stable at least since the 1990s. Anopheles gambiae was genetically partitioned into inland and coastal subpopulations, separated by a central region dominated by A. coluzzii. Surprisingly, whole genome sequencing revealed that the coastal region harbours a hybrid form characterised by an A. gambiae-like sex chromosome and massive introgression of A. coluzzii autosomal alleles. Local selection on chromosomal inversions may play a role in this process, suggesting potential for spatiotemporal stability of the coastal hybrid form and providing resilience against introgression of medically-important loci and traits, found to be more prevalent in inland A. gambiae.

Bipolar Electrodeposition: A Pathway for Direct-Write Patterning of Metals without Electrical Connections to the Substrate

Recent advances in additive manufacturing technologies have been primarily driven by the availability of simple, integrated software/hardware platforms capable of rendering computer aided design files into fabricated objects. These easy-to-use systems facilitate a wider range of users, allowing highly technological hardware (such as 3D-printing) to be used both by hobbyists and trained technicians [1]. Despite these advances in 3D-printing, a similar shift to fully software-reconfigurable electrodeposition-based prototyping has yet to emerge. The commercial electrodeposition patterning standard, through-mask plating, requires a mask and several deposition and etch steps to fully develop the pattern. More sophisticated electrochemical fabrication technology, such as EFAB or MICA, also need a series of deposition, planarization, and chemical etch steps to build 3D objects layer-by-layer. The reliance on masks and chemical etching limits the reconfigurability of these technologies. However, direct-write electrodeposition methods can bridge the advantages of electrodeposition-based fabrication to user friendly software reconfigurable additive manufacturing techniques. Microelectrodes and microjet nozzles have demonstrated local electrodeposition dictated by the geometry of the electrode or nozzle for direct-write patterning of materials [2-3]. Impinging jet electroplating was further expanded by our research group by implementing full software control of electrodeposition and mass transport conditions with a system called Electrochemical Printing (EcP) [4]. More recently, our lab modified the EcP system to operate in a bipolar manner, enabling direct-write electrodeposition and patterning without direct electrical connections to the substrate [5]. This configuration, which we call a scanning bipolar cell (SBC), is potentially advantageous for direct electrodeposition on surfaces that are difficult to connect to and allows for further automation of the software/hardware. Bipolar electrochemistry involves spatially segregated, equal and opposite oxidation and reduction reactions on a single substrate. In the SBC (shown schematically in Figure 1), reduction of metal ions to metal occurs beneath the microjet nozzle and oxidation of an electron-donating species in solution takes place across the far-field area of the conductive substrate. The constraint of connecting to the substrate in standard electroplating techniques is eliminated through more intricate electrolyte design. In this presentation, we outline the design guidelines for bipolar electrodeposition of metals across a wide range of nobilities (Ni, Cu, Ag, and Au), and discuss how the kinetic reversibility affects the spatiotemporal stability of the electrodeposited patterns. Selecting a suitable electron-donating oxidation chemistry for a given reduction chemistry depends on the reversibility and thermodynamics of the reduction redox couple. Nickel deposition is mostly irreversible, and therefore an electron-donator such as ascorbic acid oxidation to dehydroascorbic acid with an equilibrium potential more positive than that of nickel is used. This bipolar pair is thermodynamically uphill and the reactions are driven by additional current supplied by the SBC. For reversible deposition chemistries, such as silver reduction, previously patterned material can be electrochemically erased during subsequent patterning, since silver etching can act as the equal and opposite oxidation chemistry. This challenge is overcome by designing pseudo-stable baths, similar to electroless formulations, which protect the metal from oxidation. For silver reduction, Fe2+ oxidation to Fe3+ is used as the far-field oxidation chemistry. The electrolyte is designed so the equilibrium potential for Fe2+/Fe3+ is marginally less than that of Ag+/Ag(s) (about 20mV), creating a system where Fe2+ oxidation is preferential to silver etching. Electrodeposition manufacturing processes are unique for their ability to control vertical material resolution at the nanometer scale. Incorporating micropipettes and nanopipettes through direct-write electroplating with EcP or the SBC adds control of lateral resolution ideal for additive manufacturing and patterning. The highest value commercial application for metal patterning in this domain is in integrated circuit and printed circuit board manufacturing. Bipolar electrodeposition with the SBC offers a solution for automated direct-write patterning by eliminating the need to electrically connect to the multifaceted substrates in these industries. Further research in this area will explore scale-down of the SBC nozzles to sub-micron dimensions as well as the impact of substrate surface area on the spatiotemporal behavior of bipolar electrodeposition.

Spatiotemporal Stability Patterns of Brook Trout Abundance and Implications for Stream Research and Monitoring

AbstractHigh spatial and temporal variation in many stream resident trout populations complicates basic sampling questions. We used 4 years of census data from 3 km of stream to examine (1) spatial and temporal stability in Brook Trout Salvelinus fontinalis populations and the implications for representative reaches, (2) stream lengths necessary to estimate abundance and biomass, and (3) comparative performance of site selection methods. Sections of highest relative abundance and biomass were consistently high across years and had significantly lower coefficients of variation. Greater pool area and depth were associated with higher temporal stability, which suggests that sections with the best habitats can serve as effective representative reaches for trend monitoring. However, extrapolating from reference reaches grossly overestimated the census size. Randomizing site sections generally required less stream to estimate population size at a desired precision, but the required stream lengths were sensitive to the census size; less stream was required in years of higher abundances. Regardless of the year, sampling at least 10% of the available stream length was required under most scenarios, with some requiring substantially more. Our results highlight trade‐offs between the information needs versus the effort required and the importance of tailoring sampling strategy to the question.Received August 3, 2016; accepted December 2, 2016 Published online March 3, 2017

Nonlocal elasticity tensors in dislocation and disclination cores

Nonlocal elastic constitutive laws are introduced for crystals containing defects such as dislocations and disclinations. In addition to pointwise elastic moduli tensors adequately reflecting the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. The convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.

Ultraefficient reduced model for countercurrent two-layer flows

A reduced two-phase model suitable for industrial uptake is introduced to predict the onset of flow reversal in falling films under countercurrent flow. Analysis of spatiotemporal stability and wave topology shows that vortex distribution plays a crucial role in the incipience of flow reversal.

Spatiotemporal stability of management zones in a table grapes vineyard in Greece

Research on precision viticulture on table grapes is relative new compared to wine grapes. The aim of this study was to assess the spatiotemporal stability of yield and quality components in a vineyard of table grapes. The study was conducted in a commercial vineyard (1.4 ha) of table grapes for two successive cultivation years 2015 and 2016. Yield and quality parameters were assessed using destructive and non-destructive methods. The preliminary results revealed that spatiotemporal stability of management zones is affected by weather conditions and is different for each crop parameter, while NDVI presented good performance for delineating management zones.

Dynamic gait stability of treadmill versus overground walking in young adults

Treadmill has been broadly used in laboratory and rehabilitation settings for the purpose of facilitating human locomotion analysis and gait training. The objective of this study was to determine whether dynamic gait stability differs or resembles between the two walking conditions (overground vs. treadmill) among young adults. Fifty-four healthy young adults (age: 23.9±4.7years) participated in this study. Each participant completed five trials of overground walking followed by five trials of treadmill walking at a self-selected speed while their full body kinematics were gathered by a motion capture system. The spatiotemporal gait parameters and dynamic gait stability were compared between the two walking conditions. The results revealed that participants adopted a “cautious gait” on the treadmill compared with over ground in response to the possible inherent challenges to balance imposed by treadmill walking. The cautious gait, which was achieved by walking slower with a shorter step length, less backward leaning trunk, shortened single stance phase, prolonged double stance phase, and more flatfoot landing, ensures the comparable dynamic stability between the two walking conditions. This study could provide insightful information about dynamic gait stability control during treadmill ambulation in young adults.

Simple and double microemulsions via the capillary breakup of highly stretched liquid jets

We present an exhaustive experimental and theoretical study of the shapes of simple and compound jets formed when one (simple) or two (compound) immiscible liquids are injected into another liquid. The viscosity of the co-flowing external liquid is chosen to vary the characteristic Reynolds number of the outer stream, $Re_{o}$, over a wide range of values. Our slender-body theory in Gordillo et al. (J. Fluid Mech., vol. 738, 2014, pp. 335–357) is extended to predict the shapes of simple jets when $Re_{o}$ is such that $Re_{o}\gg 1$ and also to predict the shapes of compound jets in the case of $Re_{o}\lesssim O(1)$. The validity of our theoretical results, applicable to describe the dynamics of simple or compound jets within an outer carrier fluid in a wide variety of practical situations, is tested using a set-up where the liquids flow from a pressurized chamber towards an extraction tube, finding a very good agreement between the predicted and the observed shapes. Moreover, when $Re_{o}\lesssim O(1)$, and thanks to the fact that the liquid jets produced using our method are highly stretched in the downstream direction, we find that the values of the critical capillary number above which a steady stretched jet is produced, with the capillary number defined here using the outer stream velocity and viscosity, is well below the corresponding critical values characterizing other similar procedures, like flow focusing. This experimental result, which is supported by a spatio-temporal stability analysis in which the axial gradients of the unperturbed solution are retained in the dispersion relation, imply a substantial saving of energy and of the volume of outer liquid necessary to generate a steady capillary jet from which drops are regularly produced. Additionally, making use of continuity arguments and of the fact that drops are formed as a consequence of the growth of a capillary instability, we provide closed expressions for the drop diameters and their production frequencies when the capillary number is above the critical one, in very good agreement with experiments. The simple or double microemulsions generated by the capillary disintegration of the type of simple or compound highly stretched steady jets described here might find applications in biotechnology, pharmacy, cosmetics or materials science.