ESCAP Region Research Articles

ESCAPE PROCESSES IN EMBRYOS OF DICYEMIDS (PHYLUM DICYEMIDA).

Dicyemid mesozoans usually consist of 10 to 40 cells. They are characterized by 2 distinct embryos, vermiform and infusoriform, that develop within the axial cell of the adult. The means of escape of each embryo from the parent body was studied in Dicyema japonicum and Dicyema misakiense, parasites of Octopus sinensis. There were no differences in means of escape between species or embryo type, apparently due to morphological constraints whereby the parents (nematogen or rhombogen) share a similar body organization. Escapes were effected through the gap between adjacent peripheral cells of the adult, rupturing the axial cell membrane and the membrane that envelopes the embryo. After the embryo escaped, the path was closed by the enveloping membrane left behind by the embryo. Vermiform embryos can escape from any region of the body, although more embryos were observed to escape from anterior regions than from posterior regions. Infusoriform embryos escaped from both anterior and posterior regions in the axial cell, with more embryos observed to escape from the posterior regions. The different escape regions for the 2 types of embryo are presumably related to the adult body plan lacking a genital opening, so each different type of embryo has its appropriate site of escape.

Local Electron Density Depletions in the Martian Upper Ionosphere Obtained From MARSIS: Comparison With ASPERA‐3, and MAVEN, and the Connection With Crustal Magnetic Fields

AbstractSteep electron density depletions in the Martian ionosphere are important, especially because they could be regions of significant plasma escape. Local electron density profiles of the Martian ionosphere obtained from the radar sounder onboard the Mars Express spacecraft often show large fluctuations. In some cases, these fluctuations are observed as deep depletions in the electron density. Investigation over the past 12 years of Mars Advanced Radar for Subsurface and Ionospheric Sounding data have revealed over 200 cases of density depletions where the lowest density is less than one fifth of the density in the surrounding regions. These density dips occur both on the dayside and the nightside, with an abundance between solar zenith angles of 50–70° and 100–120°. They occur at all altitudes in the ionosphere. Many of the depletions occur in the southern hemisphere where the crustal magnetic field is stronger and there are more regions where the crustal magnetic field is mostly vertical. In more than half of the cases, the depletion in the local electron density corresponds to a decrease in the electron flux measured with the Analyzer of Space Plasmas and Energetic Atoms electron spectrometer. Several different mechanisms could be responsible for the formation of the depletions, including regions of localized electric fields or magnetic fields creating areas of increased field pressure, escape of the plasma along magnetic field lines depleting density locally, and the density decrease around the photoelectron boundary followed by an increase in the plasma density due to plasma clouds.

Small Region, Big Impact: Highly Anisotropic Lyman-continuum Escape from a Compact Starburst Region with Extreme Physical Properties

Extreme, young stellar populations are considered to be the primary contributor to cosmic reionization. How the Lyman continuum (LyC) escapes these galaxies remains highly elusive, and it is challenging to observe this process in actual LyC emitters without resolving the relevant physical scales. We investigate the Sunburst Arc, a strongly lensed LyC emitter at z = 2.37 that reveals an exceptionally small-scale (tens of parsecs) region of high LyC escape. The small (<100 pc) LyC-leaking region has extreme properties: a very blue UV slope (β = −2.9 ± 0.1), a high ionization state ([O iii] λ5007/[O ii] λ3727 = 11 ± 3 and [O iii] λ5007/Hβ = 6.8 ± 0.4), strong oxygen emission (EW([O iii]) = 1095 ± 40 Å), and a high Lyα escape fraction (0.3 ± 0.03), none of which are found in nonleaking regions of the galaxy. The leaking region’s UV slope is consistent with approximately “pure” stellar light that is minimally contaminated by the surrounding nebular continuum emission or extinguished by dust. These results suggest a highly anisotropic LyC escape process such that LyC is produced and escapes from a small, extreme starburst region where the stellar feedback from an ionizing star cluster creates one or more “pencil-beam” channels in the surrounding gas through which LyC can directly escape. Such anisotropic escape processes imply that random sight-line effects drive the significant scatters between measurements of galaxy properties and LyC escape fraction, and that strong lensing is a critical tool for resolving the processes that regulate the ionizing budget of galaxies for reionization.

Resonant escape induced by a finite time harmonic excitation.

The purpose of this paper is twofold. First, we obtain the critical forcing needed for a resonant escape in finite time in the presence of damping. Second, we adapt the isolated resonance approximation (AIR) method to find the escaping time and analyze the escape in finite time. Approximations of the escape time on both the phase and the parameter planes were obtained. In particular, a peculiar fractal-like boundary of the finite-time escape region was revealed. This discovery helps to better understand the limitations of AIR and explains the sensitivity of the numerical experiments to the integration time.

Numerical studies of hydrogen buoyant flow in storage aquifers

Understanding buoyancy-driven flow is essential for ensuring the safety, reliability, and efficiency of underground hydrogen storage in saline aquifers. In this study, we develop a three-dimensional (3D) numerical model of an aquifer for hydrogen storage, with an isothermal system at 323.15 K, to investigate the behavior of hydrogen buoyant flow. We perform a series of sensitivity simulations to examine the influence of storage formation heterogeneity, including Dykstra-Parsons coefficient, autocorrelation length, and permeability anisotropy, as well as fluid-rock interaction parameters, such as capillary pressure and relative permeability, on storage efficiency. We evaluate the efficiency of geologic storage containment by quantifying a defined metric “escape ratio,” which is the mass fraction of hydrogen in a presumed escape region over the total mass of hydrogen. Our results indicate that hydrogen escape ratios and migration characteristics are primarily influenced by formation heterogeneities. The escape ratio decreases as Dykstra-Parsons coefficient increases and permeability anisotropy ratio decreases. The specific hydrogen escape path is controlled by spatial structures (i.e., autocorrelation length). Inclusion of capillary heterogeneity results in a decrease in the escape ratio, and the escape region exhibits a smoother appearance in the absence of capillary heterogeneity trapping as compared to when it is modeled. As for fluid-rock interactions, the hydrogen escape ratio is highly susceptible to the exponent of Brooks-Corey relative permeability function. Nevertheless, the magnitude of the escape ratio variation is predominantly determined by formation heterogeneity.

Encounter-based approach to the escape problem.

We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to deal with a more general setting, in which the reactive region is surrounded by a reflecting boundary with an escape region. We derive a spectral expansion for the full propagator and investigate the behavior and probabilistic interpretations of the associated probability flux density. In particular, we obtain the joint probability density of the escape time and the number of encounters with the reactive region before escape, and the probability density of the first-crossing time of a prescribed number of encounters. We briefly discuss generalizations of the conventional Poissonian-type surface reaction mechanism described by Robin boundary condition and potential applications of this formalism in chemistry and biophysics.

NMPC-Based Cooperative Strategy to Lure Two Attackers Into Collision by Two Targets

This letter presents a cooperative target defense strategy using nonlinear model-predictive control (NMPC) framework for a two–target two–attacker (2T2A) problem. Each attacker needs to capture a designated target individually. The objective of the two targets is to cooperate such that they lure the two attackers into a collision. We assume that the targets do not have perfect knowledge of the attacker states, and hence they estimate the attacker states using EKF. The NMPC scheme computes closed-loop optimal control commands for the targets while satisfying state and control constraints. Theoretical analysis is carried out to determine escape regions that will lead to the targets’ survival or capture. Numerical simulations are carried out to evaluate the performance of the proposed NMPC-based strategy for different scenarios validating the theoretical results.

Narrow escape problem in two-shell spherical domains.

Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and microtubules, respectively. Recently it was reported that the mean first passage time (MFPT) for transport to a specific area on the cell membrane is minimal for an optimal actin cortex width. In this paper, we ask whether this optimization in a two-compartment domain can also be achieved by passive Brownian particles. We consider a Brownian motion with different diffusion constants in the two shells and a potential barrier between the two, and we investigate the narrow escape problem by calculating the MFPT for Brownian particles to reach a small window on the external boundary. In two and three dimensions, we derive asymptotic expressions for the MFPT in the thin cortex and small escape region limits confirmed by numerical calculations of the MFPT using the finite-element method and stochastic simulations. From this analytical and numeric analysis, we finally extract the dependence of the MFPT on the ratio of diffusion constants, the potential barrier height, and the width of the outer shell. The first two are monotonous, whereas the last one may have a minimum for a sufficiently attractive cortex, for which we propose an analytical expression of the potential barrier height matching very well the numerical predictions.

Photon emission from circular equatorial Kerr orbiters

We consider monochromatic and isotropic photon emission from circular equatorial Kerr orbiters. We derive analytic expressions for the photon escape probability and the redshift-dependent total flux collected on the celestial sphere as a function of emission radius and black hole parameters. These calculations crucially involve the critical curve delineating the region of photon escape from that of photon capture in each emitter's sky. This curve generalizes to finite orbital radius the usual Kerr critical curve and displays interesting features in the limit of high spin, which we investigate by developing a perturbative expansion about extremality. Although the innermost stable circular orbit appears to approach the event horizon for very rapidly spinning black holes, we find in this regime that the photon escape probability tends to $5/12+1/(\sqrt{5}\pi)\arctan\sqrt{5/3}\approx54.65\%$. We also obtain a simple formula for the flux distribution received on the celestial sphere, which is nonzero. This confirms that the near-horizon geometry of a high-spin black hole is in principle observable. These results require us to introduce a novel type of near-horizon double-scaling limit. We explain the dip observed in the total flux at infinity as an imprint of the black hole: the black hole "bite".

Influence of the gravitational radius on asymptotic behavior of the relativistic Sitnikov problem.

The Sitnikov problem is a classical problem broadly studied in physics which can represent an illustrative example of chaotic scattering. The relativistic version of this problem can be attacked by using the post-Newtonian formalism. Previous work focused on the role of the gravitational radius λ on the phase space portrait. Here we add two relevant issues on the influence of the gravitational radius in the context of chaotic scattering phenomena. First, we uncover a metamorphosis of the KAM islands for which the escape regions change insofar as λ increases. Second, there are two inflection points in the unpredictability of the final state of the system when λ≃0.02 and λ≃0.028. We analyze these inflection points in a quantitative manner by using the basin entropy. This work can be useful for a better understanding of the Sitnikov problem in the context of relativistic chaotic scattering. In addition, the described techniques can be applied to similar real systems, such as binary stellar systems, among others.

Diffusion and escape times in the open-leaky standard map.

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum coordinate vary freely and restrict only angle with periodic boundary condition. We also define a pair of artificial holes placed symmetrically along the momentum axis where the particles might leave the system. As a consequence of the leaks the diffusion can be analyzed making use of only the ensemble of survived particles. We present how the diffusion coefficient depends on the size and position of the escape regions. Since the accelerator modes and, thus, the diffusion are strongly related to the system's control parameter, we also investigate effects of the perturbation strength. Numerical simulations show that the short-time escape statistics do not follow the well-known exponential decay especially for large values of perturbation parameters. The analysis of the escape direction also supports this picture as a significant amount of particles skip the leaks and leave the system just after a longtime excursion in the remote zones of the phase space.

Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system

We provide rigorous computer-assisted proofs of the existence of different dynamical objects, like stable families of periodic orbits, bifurcations and stable invariant tori around them, in the paradigmatic Henon–Heiles system. There are in the literature a large number of articles with numerical simulations on this system, and other open Hamiltonians, but only a few give a rigorous guarantee of simulations. In this article, we present the necessary link between the numerical simulations and the mathematical structure of the system, since it is relevant to provide evidence of the existence of some of the different objects detected numerically to evaluate the quality of the numerical results. Remarkably, we present a proof of the existence of stable regions in the non-hyperbolic and hyperbolic regimes classically established for the Henon–Heiles system. In particular, we prove the important results of the existence of bounded stable regular regions located within the escape region, far from the regime of the KAM islands, which are called “safe regions”.

Escape, bound and capture geodesics in local static coordinates in Schwarzschild spacetime

The classical geodesics of timelike particles in Schwarzschild spacetime is analyzed according to the particle starting radius $r$, velocity $v$ and angle $\alpha$ against the radial outward direction in the reference system of an local static observer. The region of escape, bound and capture orbits in the parameter space of $(r,~v,~\alpha)$ are solved using the three cases of the effective potential. It is found that generally for radius smaller than $4M$ or velocity larger than $c/\sqrt{2}$ there will be no bound orbits. While for fixed radius larger than $4M$ (or velocity smaller than $c/\sqrt{2}$), as velocity (or radius) increase from zero (or $2M$), the particle is always captured until a critical value $v_{\mathrm{crit1}}$ (or $r_{\mathrm{crit1}}$) when the bound orbit start to appear around $\alpha=\pi/2$ between a double-napped cone structure. As the velocity (or radius) increases to another critical value $v_{\mathrm{crit2}}$ (or $r_{\mathrm{crit2}}$) then the bound directions and escape directions in the outward cone become escape directions, leaving only the inward cone separating the capture and bound directions. The angle of this cone will increase to its asymptotic value as velocity (or radius) increases to its asymptotic value. The implication of these results in shadow of black holes formed by massive particles, in black hole accretion and in spacecraft navigation is briefly discussed.

Reduced Atmospheric Ion Escape Above Martian Crustal Magnetic Fields

AbstractMartian crustal fields were considered as too weak to have a distinctive effect on global escape rates of Martian heavy ions. However, new observations by the Mars Atmosphere and Volatile Evolution mission reveal a more precise result and show a notably lower atmospheric ion escape region above the area of the strongest crustal fields. A comparison between the fluxes of high and low energy O+ ions suggests that the strongest crustal fields may trap low energy ions and reduce the solar wind pick‐up efficiency while high energy ions form a flux depletion above the crustal field. Statistical results indicate a maximum reduction of the global escape flux by nearly 35% when the strongest crustal field region is oriented sunward. This is the first time that the protective effect of the crustal fields on heavy planetary ions has been observed and it might indicate a more effective protection of atmospheres by stronger magnetic fields like at Earth.

The narrow escape problem in a circular domain with radial piecewise constant diffusivity

The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the consequence of the existence of two compartments with different diffusion constant for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusion constants in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary. For the annulus geometry we find that the MFPT can be minimized for a specific value of the width of the outer shell. In contrast for the two-shell geometry we show that the MFPT depends monotonously on all model parameters, in particular on the outer shell width. Moreover we find that the distance between the starting point and the narrow escape region which maximizes the MFPT depends discontinuously on the ratio between inner and outer diffusivity.

Lévy noise induced escape in the Morris–Lecar model

The phenomenon of an excitable system producing a pulse under external or internal stimulation may be interpreted as a stochastic escape problem. This work addresses this issue by examining the Morris–Lecar neural model driven by symmetric α-stable Lévy motion (non-Gaussian noise) as well as Brownian motion (Gaussian noise). Two deterministic quantities: the first escape probability and the mean first exit time, are adopted to analyze the state transition from the resting state to the excited state and the stability of this stochastic model. Additionally, a recent geometric concept, the stochastic basin of attraction is used to explore the basin stability of the escape region. Our main results include: (i) the larger Lévy motion index with smaller jump magnitude and the relatively small noise intensity are conducive for the Morris–Lecar model to produce pulses; (ii) a smaller noise intensity and a larger Lévy motion index make the mean first exit time longer, which means the stability of the resting state can be enhanced in this case; (iii) the effect of ion channel noise is more pronounced on the stochastic Morris–Lecar model than the current noise. This work provides some numerical simulations about the impact of non-Gaussian, heavy-tailed, burst-like fluctuations on excitable systems such as the Morris–Lecar system.

Role of trap recharge time on the statistics of captured particles.

We consider n particles diffusing freely in a domain. The boundary contains absorbing escape regions, where the particles can escape, and traps, where the particles can be captured. Modeled after biological examples such as receptors in the synaptic cleft and ambush predators waiting for prey, these traps, or capture regions, must recharge between captures. We are interested in characterizing the time courses of the number of particles remaining in the domain, the number of cumulative captures, and the number of available capture regions. We find that under certain conditions, the number of cumulative captures increases linearly in time with a slope and duration determined explicitly by the recharge rate of the capture regions. This recharge rate also determines the mean and variance of the clearance time, defined as the time it takes for all particles to leave the domain. Further, we find that while a finite recharge rate will always result in a lower number of captured particles when compared to instantaneous recharging, it can either increase or decrease the amount of variability. Lastly, we extend the model to partially absorbing traps in order to investigate the dynamics of receptor activation within an idealized synaptic cleft. We find that the width of the domain controls the amount of time that these receptors are activated, while the number of receptors controls the amplitude of activation. Our mathematical results are derived from considering this system in several ways: as a full spatial diffusion process with recharging traps, as a continuous-time Markov process on a discrete state space, and as a system of ordinary differential equations in a mean-field approximation.

Compositional distributions and evolutionary processes for the near-Earth object population: Results from the MIT-Hawaii Near-Earth Object Spectroscopic Survey (MITHNEOS)

Advancing technology in near-infrared instrumentation and dedicated planetary telescope facilities have enabled nearly two decades of reconnoitering the spectral properties for near-Earth objects (NEOs). We report measured spectral properties for more than 1000 NEOs, representing >5% of the currently discovered population. Thermal flux detected below 2.5 µm allows us to make albedo estimates for nearly 50 objects, including two comets. Additional spectral data are reported for more than 350 Mars-crossing asteroids. Most of these measurements were achieved through a collaboration between researchers at the Massachusetts Institute of Technology and the University of Hawaii, with full cooperation of the NASA Infrared Telescope Facility (IRTF) on Mauna Kea. We call this project the MIT-Hawaii Near-Earth Object Spectroscopic Survey (MITHNEOS; myth-neos). While MITHNEOS has continuously released all spectral data for immediate use by the scientific community, our objectives for this paper are to: (1) detail the methods and limits of the survey data, (2) formally present a compilation of results including their taxonomic classification within a single internally consistent framework, (3) perform a preliminary analysis on the overall population characteristics with a concentration toward deducing key physical processes and identifying their source region for escaping the main belt. Augmenting our newly published measurements are the previously published results from the broad NEO community, including many results graciously shared by colleagues prior to formal publication. With this collective data set, we find the near-Earth population matches the diversity of the main-belt, with all main-belt taxonomic classes represented in our sample. Potentially hazardous asteroids (PHAs) as well as the subset of mission accessible asteroids (ΔV ≤ 7 km/s) both appear to be a representative mix of the overall NEO population, consistent with strong dynamical mixing for the population that interacts most closely with Earth. Mars crossers, however, are less diverse and appear to more closely match the inner belt population from where they have more recently diffused. The fractional distributions of major taxonomic classes (60% S, 20% C, 20% other) appear remarkably constant over two orders of magnitude in size (10 km to 100 m), which is eight orders of magnitude in mass, though we note unaccounted bias effects enter into our statistics below about 500 m. Given the range of surface ages, including possible refreshment by planetary encounters, we are able to identify a very specific space weathering vector tracing the transition from Q- to Sq- to S-types that follows the natural dispersion for asteroid spectra mapped into principal component space. We also are able to interpret a shock darkening vector that may account for some objects having featureless spectra. Space weathering effects for C-types are complex; these results are described separately by Lantz, Binzel, DeMeo. (2018, Icarus 302, 10–17). Independent correlation of dynamical models with taxonomic classes map the escape zones for NEOs to main-belt regions consistent with well established heliocentric compositional gradients. We push beyond taxonomy to interpret our visible plus near-infrared spectra in terms of the olivine and pyroxene mineralogy consistent with the H, L, and LL classes of ordinary chondrites meteorites. Correlating meteorite interpretations with dynamical escape region models shows a preference for LL chondrites to arrive from the ν6 resonance and H chondrites to have a preferential signature from the mid-belt region (3:1 resonance). L chondrites show some preference toward the outer belt, but not at a significant level. We define a Space Weathering Parameter as a continuous variable and find evidence for step-wise changes in space weathering properties across different planet crossing zones in the inner solar system. Overall we hypothesize the relative roles of planetary encounters, YORP spin-up, and thermal cycling across the inner solar system.

Lévy noise-induced escape in an excitable system**This work was partly supported by the NSF grant 1620449, and NSFC grants 11531006, 11371367 and 11271290.

This paper considers the dynamics of escape in the stochastic FitzHugh–Nagumo (FHN) neuronal model driven by symmetric α-stable Lévy noise. External or internal stimulation may make the excitable system produce a pulse or not, which can be interpreted as an escape problem. A new method to analyse the state transition from the rest state to the excitatory state is presented. This approach consists of two deterministic indices: the first escape probability (FEP) and the mean first exit time (MFET). We find that higher FEP in the rest state (equilibrium) promotes such a transition and MFET reflects the stability of the rest state directly with the selected escape region. The developed two dimensional numerical simulation method to calculate FEP and MFET can not only avoid a dimension reduction, but is also applicable for the cases with large noise. In addition, FEP provides us with a new perspective to understand the seperatrix of the stochastic FHN model. It can be seen that smaller jumps of the Lévy motion and relatively small noise intensity are conducive to the production of spikes. In order to characterize the effect of noise on the selected escape region in which the equilibrium lies, the area of higher FEP and MFET in the escape region are calculated. Meanwhile, Brownian motion as a special case is also taken into account for comparison.

The escape problem for mortal walkers.

We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a first-order kinetics (i.e., exponentially distributed lifetimes), we study the effect of the associated death rate onto the survival probability, the exit probability, and the mean first passage time. We derive the upper and lower bounds and some approximations for these quantities. We reveal three asymptotic regimes of small, intermediate, and large death rates. General estimates and asymptotics are compared to several explicit solutions for simple domains and to numerical simulations. These results allow one to account for stochastic photobleaching of fluorescent tracers in bio-imaging, degradation of mRNA molecules in genetic translation mechanisms, or high mortality rates of spermatozoa in the fertilization process. Our findings provide a mathematical ground for optimizing storage containers and materials to reduce the risk of leakage of dangerous chemicals or nuclear wastes.