Inhomogeneous Patterns Research Articles

On the Impact of a Dry Intrusion Driving Cloud-Regime Transitions in a Midlatitude Cold-Air Outbreak

Abstract Marine cold-air outbreaks (CAOs) occur in the postfrontal sector of midlatitude storms, usually accompanied by dry intrusions (DIs) shaping the free-tropospheric (FT) air aloft. Substantial rain initiates overcast to broken regime transitions in marine boundary layer (MBL) cloud decks that form where cold air first meets relatively high sea surface temperatures. An exemplary CAO in the northwest Atlantic shows earlier transitions (corresponding to reduced extents of overcast clouds) closer to the low pressure center. We hypothesize that gradients in the meteorological pattern imposed by the prevailing DI induced a variability in substantial rain onset and thereby transition. We compile satellite observations, reanalysis fields, and Lagrangian large-eddy simulations (LES) translating along MBL trajectories to show that postfrontal trajectories closer to the low pressure center are more favorable to rain formation (and thereby cloud transitions) because of 1) weaker FT subsidence rates, 2) greater FT humidity, 3) stronger MBL winds, and 4) a colder MBL with reduced lower-tropospheric stability. LES confirms the observed variability in transitions, with substantial rain appearing earlier where there is swifter reduction of cloud condensation nucleus (CCN) concentration and increase of liquid water path (LWP). Prior to substantial rain, CCN budgets indicate dominant loss terms from FT entrainment and hydrometeor collisions. LWP-enhancing cloud thickness increases more rapidly for weaker large-scale subsidence that enables faster MBL deepening. Mere MBL warming and moistening cannot explain cloud thickness increases. The generality of such a DI-imposed cloud transition pattern merits further investigation with more cases that may additionally be convoluted by onshore aerosol gradients. Significance Statement Cold-air outbreaks (CAOs) lead to marine boundary layer (MBL) clouds that commonly undergo rain-initiated overcast to broken cloud regime transitions that can drastically impact reflected solar radiation. We aim to better understand what mechanisms control these transitions. For a CAO event in the northwest Atlantic that shows earlier transitions closer to the low pressure center, we find the transition timing to be largely governed by the coinciding dry intrusion that imposes an inhomogeneous large-scale meteorological pattern onto the overlying free troposphere and thereby affects MBL rain formation. Our findings update conceptual understanding of extratropical cyclones and motivate analyzing observations and conducting simulations for more postfrontal cases through a Lagrangian perspective as done here for one case, to assess the generality of our findings.

Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.

Digital rock characterization and CO2 flow simulation of high-volatile bituminous coal: An application to carbon geosequestration

The permeability of CO2 sequestration is influenced by the characteristics of pore–fracture structures in coal, yet the flow simulation via the pore network model (PNM) and the controls of topology and morphology on permeability remain to be understood. First, the pore–fracture structure of high-volatile bituminous coal (HVBC) is characterized using micro-computed tomography, and the flow characteristics of single-phase CO2 in the connected pore–fracture network are simulated by the PNM. Second, the surface roughness of the connected pore–fracture is extracted by fractal characterization, and morphological algorithms are applied to accurately present the pore–fracture network structure. Finally, the implications of structural parameters (pore or throat diameter, coordination number, tortuosity, and sphericity) on CO2 transport are discussed, and the mechanism of pore–fracture structure response due to mineral dissolution in CO2 injection is analyzed. The results shows that the HVBC sample provides significant pore–fracture space (porosity of 10.87%) and flow path (connectivity of 66.50%) for hydrogen and carbon storage. CO2 flow simulation results demonstrate anisotropic flow, with higher CO2 permeability observed in the Z-axis direction (0.061 × 10−3 μm2) compared to the X- and Y-axis directions (0.044 × 10−3 μm2 and 0.059 × 10−3 μm2, respectively). Moreover, the fractures perpendicular to the coal bedding plane in the coal seam with a large tectonic dip strongly influence the flow of CO2 injection. Fractal analysis reveals a positive correlation between fractal dimension and porosity, indicating that structures with higher surface roughness are not convenient for CO2 transport. Significant pore angle characteristics (sphericity average of 0.58), high pore–throat connectivity (coordination number average of 4.31), and low capillary resistance (tortuosity average of 1.19) collectively affect the flow of CO2. Overall, the strongly anisotropic pore–fracture structure contributes to the inhomogeneous flow pattern in CO2 geosequestration. Changes in pore–fracture structure resulting from mineral dissolution during the early stage of CO2–coal matrix interaction in the HVBC reservoir can significantly enhance storage potential. This study contributes to the existing understanding of flow characteristics and provides insights for optimizing CO2 injection efficiency in carbon geosequestration.

Sequentially coupling LBNL-method and Modelica to model and operate adaptive facades with inhomogeneous printing patterns

In this work, two U- and g-value Modelica models of a three-layer membrane construction with inhomogeneous stripe pattern were set up. Thus, a simple ISO 52022 model is compared with a detailed model with Modelica integration of Klems-Matrices by LBNL method calculation. For the U-value, both models equally predict the heat transmission. For the g-value, the detailed model shows an strong angular behavior depending on the stripe pattern, the layer distances. Compared to a reference glazing, the application of an adaptive operating strategy results in a reduction of the total energy consumption by up to 27%. Depending on the operation strategy the heating energy increases between 33-100% and cooling energy decreases by 50-80%. This is mainly due to the lower g-value with the detailed model. The actuation energy required for this can be neglected. The resulting reductions in heating and cooling energy exceed the actuation energy by several orders of magnitude.

Proof-of-Principle of Absolute Dosimetry Using an Absorbed Dose Portable Calorimeter with Laser-Driven Proton Beams

Charged particle beams driven to ultra-high dose rates (UHDRs) have been shown to offer potential benefits for future clinical applications, particularly in the reduction of normal-tissue toxicity. Studies of the so-called FLASH effect have shown promise, generating huge interest in high dose rate radiation studies. With laser-driven proton beams, where the duration of the proton burst delivered to a sample can be as short as hundreds of picoseconds, the instantaneous dose rates are several orders of magnitude higher than those used for conventional radiotherapy. The dosimetry of these beam modalities is not trivial, with conventional active detectors, such as ionisation chambers, experiencing saturation effects making them unusable at the extremely high dose rates. Calorimeters, measuring the radiation-induced temperature rise in an absorber, offer an ideal candidate for the dosimetry of UHDR beams. However, their application in the measurement of laser-driven UHDR beams has so far not been trialled, and their effective suitability to work with the quasi-instantaneous and inhomogeneous dose deposition patterns and the harsh environment of a laser-plasma experiment has not been tested. The measurement of the absorbed dose of laser-driven proton beams was conducted in a first-of-its-kind investigation, employing the VULCAN-PW laser system of the Central Laser Facility (CLF) at the Rutherford Appleton Laboratory (RAL), using a small-body portable graphite calorimeter (SPGC) developed at the National Physical Laboratory (NPL) and radiochromic films. A small number of shots were recorded, with the corresponding absorbed dose measurements resulting from the induced temperature rise. The effect of the electromagnetic pulse (EMP) generated during laser–target interaction was assessed on the system, showing no significant effects on the derived signal-to-noise ratio. These proof-of-principle tests highlight the ability of calorimetry techniques to measure the absorbed dose for laser-driven proton beams.

Stability and spatially inhomogeneous patterns induced by nonlocal prey competition in a generalist predator–prey system

In this paper, we investigate the influence of the nonlocal prey competition on the spatio-temporal dynamics for a generalist predator–prey system. The condition of stability and bifurcations is clearly determined. Our results show that when the prey spreads quickly, the nonlocal intraspecific competition of the prey does not affect the dynamics, however, when the prey spreads slowly, it can affect the dynamics. Besides, no Hopf bifurcation occurs if the ratio of the growth rate of the predator to prey is larger, otherwise, system has Hopf bifurcation and Hopf Bogdanov–Takens bifurcation and so on. It is surprised that the system only with the nonlocal prey competition has more rich dynamics than the system with the nonlocal competitions in both the prey and the predator. The coexistence of bistable spatially inhomogeneous steady states is also found.

Spatiotemporal inhomogeneous pattern of a predator–prey model with delay and chemotaxis

Spatiotemporal inhomogeneous pattern of a predator–prey model with delay and chemotaxis

Cross diffusion induced spatially inhomogeneous Hopf bifurcation for a three species Lotka–Volterra food web model with cycle

In this article, we consider a three species Lotka–Volterra food web reaction–diffusion model with cycle, in which the intensity of the rate of preying on species 1 by species 2, the rate of preying on species 2 by species 3 and the rate of preying on species 3 by species 1 are in general asymmetrical. By suitably choosing cross diffusion coefficients as the bifurcation parameter, a spatially inhomogeneous Hopf bifurcation at a positive constant steady state is proved to occur for a sequence of critical values of the bifurcation parameter. In addition, we demonstrate that these spatially inhomogeneous bifurcating periodic solutions are stable when diffusion coefficients are located in suitable ranges. Our results show that cross diffusion plays a key role in the formation of spatially inhomogeneous periodic oscillatory patterns.

Implementation and evaluation of the AAPM TG 111 for radiation dosimetry in a state-of-the-art C-arm cone beam CT system

The aim of this study was to assess the dosimetric characteristics of a state-of-the-art C-arm cone beam computed tomography (CBCT) system using the methodology proposed by the American Association of Physicists in Medicine (AAPM) Task Group (TG) 111. The dose measurement methodology described in AAPM TG 111 for wide cone beam acquisitions without table translation was employed to estimate equilibrium beam length () and equilibrium dose () in various interventional task-specific protocols with different tube arc projection geometries. Dose profiles were derived from point dose measurements in the centre and peripheral locations of the ICRU/AAPM and standard polymethyl methacrylate (PMMA) body phantom. Dose measurements were performed in phantom and free-in-air using a solid-state point detector. Monte Carlo (MC) based simulation dosimetry was performed to quantify the inhomogeneous dose patterns imparted in the phantoms. Estimated and on the ICRU/AAPM phantom was up to 49.4 cm and 6.17 mGy/100 mAs, respectively. Corresponding values determined on the PMMA phantom were 139 cm and 8.8 mGy/100 mAs, respectively. Free-in-air dose measurement ranged from 1.43 mGy/100 mAs to 5.93 mGy/100 mAs. Per cent difference in and between MC simulation and solid-state point detector measurement methods in the ICRU/AAPM phantom were within 16% and 18%, respectively. Manufacturers can use the presented methodology to characterize the dosimetric properties of C-arm CBCT systems. Clinical medical physicists may follow this methodology to verify corresponding data provided by the manufacturer and check for C-arm CBCT system performance dosimetric consistency.

Testing the representativity of Palaeolithic site distribution: The role of sampling bias in the european upper and Final Palaeolithic record

Archaeological sites are not distributed evenly throughout the landscape. For the Palaeolithic record, signals derived from the inhomogeneous spatial patterns are used to infer spatial decision-making processes or ecological preferences of our ancestors. However, to date it is still largely unclear how sampling biases affect the large-scale distribution of sites and whether the observable spatial patterns are actually representative of the distribution of humans in the palaeo-landscape. To answer this question, this study assesses the spatial distribution of 4200 Upper and Final Palaeolithic occupations from two different perspectives, i.e., past settlement choice and likelihood of discovery. On the one hand, site distribution is thus examined for settlement-relevant factors such as topography, geology and sedimentology. On the other, discovery-relevant biases, such as recent land cover and building activity are analysed. The comprehensive spatial and statistical assessments show that the actual distribution of sites seems to be most strongly influenced by sampling biases. The assessed environmental variables representing the settlement factors show a far lower statistical association to the distribution of sites. They do, however, still support several common archaeological assumptions. For all approaches using site distribution as input, such as predictive modelling, the results of this study suggests that the sampling bias must be addressed. To this end, we suggest including environmental variables addressing discovery-relevant factors to quantify the potential biases. For further studies on the sampling bias of Upper and Final Palaeolithic sites, we recommend building on this pilot study by adding more occupations to the dataset and more environmental variables to the settlement and discovery factors. Due to the current positive trend in openly available geo-datasets, we see great future potential in this.

Ex-situ quantification of impurity deposition depth on HL-2A divertor graphite tile by laser-induced breakdown spectroscopy

During tokamak discharges, the Plasma Wall Interaction (PWI) would lead to impurity deposition and fuel retention on the surface of the Plasma Facing Materials (PFMs). Laser-induced breakdown spectroscopy (LIBS) has emerged as a promising technique to facilitate in-situ, real-time, online characterization of the impurity deposition and fuel retention on the wall of tokamaks for PWI studies. The purpose of this investigation is to quantify the impurity deposition layer on the graphite tile removed from the dome region of the HL-2A tokamak lower divertor by using the ex-situ LIBS approach. The investigations indicate that the primarily deposited impurity elements are Fe, Cr, Ni, Mn, Ca, Al, Cu, Si, C, which may originate from the stainless steel first wall, divertor, limiter or the siliconized wall conditioning due to the PWI process in HL-2A tokamak. This has been further supported by observing a significantly positive correlation between the Cr, Ni, Mn, Al and Fe elements by spectral cumulative intensity linear regression analysis. The 3D morphology of the laser-ablated craters is reconstructed using a confocal microscope, revealing the laser ablation rates for the deposition layer and the substrate graphite tile to be 348 nm/pulse and 220 nm/pulse, respectively, under the laser fluence of 10 J/cm2. Then the thickness of the deposition layer is determined by using the correlation coefficient method. Along the poloidal direction of HL-2A tokamak, the deposited impurity shows an inhomogeneous pattern, with the thickness of the deposition layer varying from 1.74 μm to 5.92 μm. Finally, the absolute depth distribution of each element is also quantitatively measured.

Turbulent Structure and Characterization of ‘11’-type Iron-based Superconductors by Magneto-optical Imaging

Magneto-optical imaging is employed to investigate the vortex penetration modes in ‘11’-type iron-based superconductors (IBSs) Fe(Te0.6Se0.4) and FeSe single crystals. In Fe(Te0.6Se0.4), vortices penetrate mostly homogeneously from all edges, forming an unstable turbulent interface with pre-existing anti-vortices, where ‘Meissner hole’ emerges as those have been reported in ‘122’-type IBSs. In FeSe, however, the penetration is restricted to numerous mesoscopic stripe-like regions. Further experiments revealed an inhomogeneous vortex propagation pattern, where vortices are most likely to be channeled along the twin boundaries.

Elastofibroma Dorsi: Case Series of a Rare Chest Wall Pseudotumor.

Elastofibroma dorsi (EFD) is a pseudotumor of the thoracic wall that can be difficult to diagnose due to its rarity. Prompt recognition can limit unnecessary workup and expedite treatment. This study retrospectively analyzed patients with a diagnosis of EFD, discussing clinical presentations and surgical outcomes. This is an IRB-approved single-center retrospective study of all patients with a diagnosis of elastofibroma at our institution between 2000 and 2022. Ten patients were identified to have a pathologic diagnosis of EFD since 2000, with half presenting in the last 5years. Our cohort had an average age of 56.8years and was 50% female. The average age of male subjects was younger than females, 49.6-64.0years, respectively (p = 0.10). Eighty percent (8/10) of patients had unilateral EFDs and symptoms lasted 27.1months on average prior to diagnosis. Surgical resection was performed on 66.67% (8/12) of masses, with 87.5% (7/8) of patients who underwent surgery reporting complete resolution of their symptoms and none reporting recurrence. Although EFD is a rare pseudotumor, its incidence may be increasing. As such, surgeons should be aware of the typical clinical presentation; specifically, a slow growing, predominantly unilateral, painful, subscapular mass with an inhomogeneous pattern on imaging. Originally thought to predominantly affect elderly women, our study shows that younger men may be at risk as well. If patients present with EFD, complete surgical resection should be performed to achieve favorable outcomes and resolution of symptoms.

Spatiotemporal Patterns of a Host-Generalist Parasitoid Reaction–Diffusion Model

In this paper, we study a delayed host-generalist parasitoid diffusion model subject to homogeneous Dirichlet boundary conditions, where generalist parasitoids are introduced to control the invasion of the hosts. We construct an explicit expression of positive steady-state solution using the implicit function theorem and prove its linear stability. Moreover, by applying feedback time delay [Formula: see text] as the bifurcation parameter, spatially inhomogeneous Hopf bifurcation near the positive steady-state solution is proved when [Formula: see text] is varied through a sequence of critical values. This finding implies that feedback time delay can induce spatially inhomogeneous periodic oscillatory patterns. The direction of spatially inhomogeneous Hopf bifurcation is forward when parameter [Formula: see text] is sufficiently large. We present numerical simulations and solutions to further illustrate our main theoretical results. Numerical simulations show that the period and amplitude of the inhomogeneous periodic solution increase with increasing feedback time delay. Our theoretical analysis results only hold for parameter [Formula: see text] when it is sufficiently close to 1, whereas numerical simulations suggest that spatially inhomogeneous Hopf bifurcation still occurs when [Formula: see text] is larger than 1 but not sufficiently close to 1.

Spatiotemporal Variabilities of the Recent Indian Summer Monsoon Activities in the Tibetan Plateau: A Reanalysis of Outgoing Longwave Radiation Datasets

Abstract Unstable hydrological cycles and water resource instability over and around the Tibetan Plateau (TP) are topics of wide concern. The Indian summer monsoon (ISM) is one of the TP’s most important moisture sources; as such, its behavior is key to any changes in precipitation and water-related environments. However, there have been relatively few thorough investigations into ISM activities. Here we primarily explore ISM activities using outgoing longwave radiation (OLR) datasets in TP, and precipitation isotopes recorded at Lhasa, for the period 1975–2020. Our major findings are that 1) the ISM onset (retreat date) is between ∼31 May and 19 July (∼8 August–27 September), with ISM duration of ∼40–110 days; 2) significant spatial inhomogeneous patterns are evident in ISM activities, i.e., the western part of our study area experiences earlier ISM onset, delayed retreat, longer duration, and greater intensity and strength, and the inverse is true in the eastern sector of the study area; 3) the ISM activities that dominate the 1975–98 period determine their general patterns over the entire 1975–2020 period, taking into account evident discrepancies in subperiods; and 4) the negative relations between precipitation δ18O and ISM intensity/strength at Lhasa confirm the ISM activities defined using OLR. These results will improve our understanding of hydrological cycles in TP and provide insights into hydrological studies in the “Asian Water Tower” region. Significance Statement Over the recent decades, the Tibetan Plateau (TP) (Asian Water Tower) has undergone dramatic environmental changes, evinced by the instabilities of hydrological cycles. As one of TP’s most important moisture sources, the Indian summer monsoon (ISM) is key to changes in precipitation and water-related environments. To get thorough investigations into ISM activities, we primarily explore ISM activities using outgoing longwave radiation (OLR) datasets in TP and precipitation isotopes at Lhasa. Significant spatial inhomogeneous patterns are evident in ISM activities: the western part experiences earlier ISM onset, delayed retreat, longer duration, and stronger intensity and strength, and the inverse occurs in the eastern sector. These results will improve our understanding of hydrology, meteorology, ecology, and paleoclimate reconstructions in the Asian Water Tower region.

Optimization of residual stress in low-pressure casting of ZL205A alloys

ZL205A alloys are prone to generate serious residual stress due to the long solidification intervals and multi-phase composition. In this study, the low-pressure casting process for ZL205A alloy hemisphere shell casting was investigated and continuously optimized. In the initial process, the knockout time, pouring temperature, preheating temperature of the sand mould, dwelling pressure, and filling rate were 3 h, 710 °C, 30 °C, 65 kPa, and 0.33 kPa·s−1, respectively. Macroscopic properties and microstructural features were simulated using a combination of ProCAST and Thermal-Calc software. Additionally, a series of experimental procedures, including EBSD, SEM, EDS, and XRD tests, were conducted to investigate the formation, morphology, and distribution of the microstructure. Current findings demonstrate that during the solidification process, the maximum temperature difference exceeds 220 °C, the maximum undercooling reaches 49.56 °C, and the maximum effective stress peaks at 301.7 MPa. The residual stress ranges from 20 to 200 MPa. Furthermore, there is no significant texture and preferred grain orientation during nucleation and solidification, and the structure field exhibits an equiaxed crystal but inhomogeneous pattern. Moreover, the finer and more homogeneous the grains and the smaller the deviation in grain orientation, the lower the residual stress. Specifically, two analytical models are developed: one between the casting parameters and the residual stress, and another between the shrinkage defects and the casting parameters. The lowest residual stress is achieved when the knockout time, pouring temperature, preheating temperature of the sand mould, dwelling pressure, and filling rate are 6 h, 725 °C, 250 °C, 95 kPa, and 1.67 kPa·s−1 respectively.

Discrete element simulation of the hydrate-bearing sediments mechanical behaviors under typical hydrate dissociation patterns

The hydrate-bearing sediments (HBS) mechanical properties during hydrate dissociation are important to the safe, efficient and sustainable exploitation of natural gas hydrates (NGH). However, the inhomogeneous hydrate dissociation patterns inherent to HBS may make it difficult to accurately obtain its mechanical properties. In this study, a discrete element method (DEM) model was adopted to simulate the HBS mechanical behavior under various hydrate dissociation patterns. By investigating the simulation results and the corresponding internal mechanism, it is found that the stratified and radial inhomogeneous hydrate dissociation in HBS significantly affects its stress‒strain characteristics, and HBS under radial hydrate dissociation has a larger deviation. Moreover, it is suggested that when designing experiments to study the hydrate dissociation effect on the HBS mechanical strength, if the hydrate dissociation homogeneity cannot be guaranteed, a preference for a stratified hydrate dissociation pattern can lead to more desirable results. Finally, a method to judge the HBS hydrate dissociation pattern was also proposed. The results have a guiding significance for the experimental study of HBS mechanisms under hydrate dissociation and ultimately contribute to the realization of accurately predicting reservoir mechanical behavior during NGH exploitation.

Numerical investigation of flow and heat transfer of supercritical carbon dioxide in the vertical helically-coiled tube under half-side heating condition

ABSTRACT The supercritical boiler is one of the ways to enable sustainable energy development. Its revolution cannot be separated from the study of the characteristics of supercritical carbon dioxide in a spiral pipe. This research article provided an industrially compliant model of a water-cooled wall spiral pipe with one-side heating for heat transfer. The simulation was set for various parameters including P = 30.42 MPa, Tin = 578–643 K, q = 105–180 kW/m2, G = 1784–2348 kg/m2s. The article discussed in detail factors such as buoyancy and secondary flow for these cases. The results showed that in the range of high parameters, mass fluxes, heat fluxes, and inlet temperature all had a substantial influence on the temperature and velocity fields, with the mass flux showing a non-monotonic trend on the HTC and the heat flux having a more subtle influence on the HTC. The inhomogeneous heating pattern affected the buoyancy and secondary flow motion, changing the temperature field in the tube, and enhancing the velocity field at the bend and on the heating side. A new empirical correlation for supercritical CO2 with non-uniform heating was proposed.

Ultrasound Patterns and Disease Progression in Medullary Sponge Kidney in Adults.

Our paper presents the ultrasound (US) patterns of a rare kidney disease-medullary sponge kidney (MSK)-that have not been described before in comparison with other causes of medullary hyperechogenicity and correlates them with the severity of the disease and prognosis. This is a clinical observational study of all US examinations in the Nephrology Department over a period of 6 years. The abdominal US focused on the kidneys was recorded. US characteristics of the medulla and cortex were analyzed. We found 10 patients with characteristic daisy flower (DF) kidneys. Positive diagnosis in association with other renal risk factors, prognosis, and evolution were evaluated. Two patterns of medullary hyperechogenicity were found and were correlated with disease severity and kidney function. The first pattern is a homogenous echogenicity of the medulla described as a "daisy-like" appearance. The second pattern: calcifications associated with medullar echogenicity, stone production, nephrocalcinosis, and impaired kidney function: "atypical daisy-like." Medullary hyperechogenicity can have more US patterns. In MSK, if the medullary echogenicity is homogenous the evolution is benign, whereas the second, inhomogeneous pattern, has a variable clinical presentation with nephrocalcinosis and the outcome is more severe, leading to chronic kidney disease and impairing the quality of life.

Multimodal distribution of transient time of predator extinction in a three-species food chain.

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.