On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states

Halite as a Methane Sequestration Host: A Possible Explanation for Periodic Methane Release on Mars, and a Surface-accessible Source of Ancient Martian Carbon

We present the hypothesis that halite may play a role in methane sequestration on the martian surface. In terrestrial examples, halite deposits sequester large volumes of methane and chloromethane. Also, examples of chloromethane-bearing, approximately 4.5 Ga old halite from the Monahans meteorite show that this system is very stable unless the halite is damaged. On Mars, methane may be generated from carbonaceous material trapped in ancient halite deposits and sequestered. The methane may be released by damaging its halite host; either by aqueous alteration, aeolian abrasion, heating, or impact shock. Such a scenario may help to explain the appearance of short-lived releases of methane on the martian surface. The methane may be of either biogenic or abiogenic origin. If this scenario plays a significant role on Mars, then martian halite deposits may contain samples of organic compounds dating to the ancient desiccation of the planet, accessible at the surface for future sample return missions

On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

Nonlinear Schroedinger equation with two symmetric point interactions in one dimension

We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric potential double well represented by two delta interactions. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Czech version of the Outcome Rating Scale : Selected psychometric properties

Objectives. The Outcome Rating Scale (ORS) is an ultra-brief self-report scale designed to measure change during psychotherapy. The goal of this study was to test (a) the factor structure of the ORS, (b) the measurement invariance between a clinical and a non-clinical sample, between pre-therapy and post-therapy assessment (within the clinical sample), and between online and paper-and-pencil forms of administration (within the non-clinical sample), (c) concurrent validity with other outcome measures, and (d) sensitivity to therapeutic change. Sample and settings. N = 256 patients, N = 210 non-clinical respondents, and N = 89 students participated in the study. Patients responded to the ORS before and after psychotherapy. Statistical analysis. The factor structure and measurement invariance were tested using confirmatory factor analysis. Concurrent validity and test-retest reliability were assessed using correlational analysis. Sensitivity to change was assessed using the Reliable Change Index and pre-post effect size. Results. The unidimensional structure was supported. The best-fitting model was a partially tau-equivalent model with the first and the fourth items’ loadings fixed to the same value. While only metric invariance was demonstrated between the clinical and non-clinical samples, the ORS demonstrated scalar invariance between pre- and post-therapy assessment and strict invariance between the paper-and-pencil and online forms of administration. Internal consistency, as well as concurrent validity, were satisfactory. The sensitivity to the therapeutic change was adequate. Furthermore, internal consistency and sensitivity to change were increased if the score was computed as a weighted sum of items. Study limitation. The samples were not representative

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences

1D-confined crystallization routes for tungsten phosphides

Topological materials confined in one-dimension (1D) can transform computing technologies, such as 1D topological semimetals for nanoscale interconnects and 1D topological superconductors for fault-tolerant quantum computing. As such, understanding crystallization of 1D-confined topological materials is critical. Here, we demonstrate 1D-confined crystallization routes during template-assisted nanowire synthesis where we observe diameter-dependent phase selectivity for topological metal tungsten phosphides. A phase bifurcation occurs to produce tungsten monophosphide and tungsten diphosphide at the cross-over nanowire diameter of ~ 35 nm. Four-dimensional scanning transmission electron microscopy was used to identify the two phases and to map crystallographic orientations of grains at a few nm resolution. The 1D-confined phase selectivity is attributed to the minimization of the total surface energy, which depends on the nanowire diameter and chemical potentials of precursors. Theoretical calculations were carried out to construct the diameter-dependent phase diagram, which agrees with experimental observations. Our find-ings suggest a new crystallization route to stabilize topological materials confined in 1D.Comment: 5 figure

Morphology, Morphometry and Distribution of Isolated Landforms in Southern Chryse Planitia, Mars

The margin of Chryse Planitia, Mars, contains >10⁵ kilometer‐scale mesas, buttes, and plateaus (“mounds”), many of which are found in and around Oxia Planum, the ExoMars 2022 Rover landing site. Despite this, their origins and evolution are unknown. We have analyzed the morphologies and morphometries of 14,386 individual mounds to: (1) classify them based on their geomorphology; (2) constrain when they formed based on their stratigraphic and spatial relationships; and (3) develop hypotheses for their geological history. The mounds are classified as compound mounds, mesas, clustered mounds, and hills. Mound heights show that their elevations above the plains tend to a maximum height of 500 m. We interpret this as the thickness of a previously continuous layer that extended several hundred kilometers from the southern highlands into Chryse Planitia. Stratigraphy constrains the deposition of this layer to the Early‐Middle Noachian, correlatable to the phyllosilicate‐bearing strata of Mawrth Vallis, with similar layering also observable in some mounds, suggesting a genetic relationship. The mounds sometimes occur in circular arrangements, interpreted as an association with buried impact structures. We propose that the mounds formed through differential erosion after the premound layer was indurated by mineralization from groundwater in areas superposing underlying crustal weaknesses, for example, at buried crater margins. The subsequent differential erosion of this layer preferentially removed areas unaffected by this induration in the Late Noachian‐Early Hesperian leaving the mound population seen at present. These features present accessible three‐dimensional exposures of ancient layered rocks, and so are exciting targets for future study

Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. II: The Second Year (2009-2010)

As an extension of the project in Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 61 SU UMa-type dwarf novae mainly observed during the 2009-2010 season. The newly obtained data confirmed the basic findings reported in Kato et al. (2009): the presence of stages A-C, as well as the predominance of positive period derivatives during stage B in systems with superhump periods shorter than 0.07 d. There was a systematic difference in period derivatives for systems with superhump periods longer than 0.075 d between this study and Kato et al. (2009). We suggest that this difference is possibly caused by the relative lack of frequently outbursting SU UMa-type dwarf novae in this period regime in the present study. We recorded a strong beat phenomenon during the 2009 superoutburst of IY UMa. The close correlation between the beat period and superhump period suggests that the changing angular velocity of the apsidal motion of the elliptical disk is responsible for the variation of superhump periods. We also described three new WZ Sge-type objects with established early superhumps and one with likely early superhumps. We also suggest that two systems, VX For and EL UMa, are WZ Sge-type dwarf novae with multiple rebrightenings. The O-C variation in OT J213806.6+261957 suggests that the frequent absence of rebrightenings in very short-Porb objects can be a result of sustained superoutburst plateau at the epoch when usual SU UMa-type dwarf novae return to quiescence preceding a rebrightening. We also present a formulation for a variety of Bayesian extension to traditional period analyses.Comment: 63 pages, 77 figures, 1 appendix, Accepted for publication in PASJ, data correctio