Simple Description Research Articles

Clustering of buoyant tracer in quasi-geostrophic coherent structures

We have investigated the dynamics of floating tracer in an idealised turbulent quasi-geostrophic ocean by advecting Lagrangian particles in a high-resolution velocity field enhanced by the potential flow associated with vortex stretching. At first order in the Rossby number expansion, this component of the ageostrophic circulation can be derived through a diagnostic equation in terms of the geostrophic velocities. Borrowing methods from the theory of Lagrangian coherent structures, we identify coherent material loops around strong vortex cores using the Lagrangian averaged vorticity deviation (LAVD). Building on studies of clustering in kinematic, stochastic velocity fields, we utilise methods from statistical topography to show that the coherent vortices dominate the distribution of extreme values of the concentration field. We find that the presence of clusters and voids in a coherent vortex depends on more than just the sense of rotation, but also on the full evolution of the vorticity over its lifecycle. We identify the mechanism behind the cluster formation that respects the symmetries of the quasi-geostrophic equations but can be expected to hold robustly in more complicated regimes, due to the simple physical description. The association of cluster formation with vortex stretching implies that LAVD is a particularly relevant metric for floating tracer dynamics. The detection of intense clustering also has implications for reaction rates between ocean-borne flotsam, meaning that our results are relevant to understanding the general risk of floating microplastics and marine biological populations.

Nonlinear Rayleigh–Taylor instability in an accelerated soap film

Rupture and fragmentation of thin liquid films are of great importance in manufacturing, agriculture, disease transmission, and other fields. An individual rupture event typically results from the nonlinear growth of small perturbations excited by the classical Rayleigh–Taylor mechanism and opposed by surface tension on the film interfaces. We study an initially uniform liquid film accelerated in the direction perpendicular to its interfaces, constructing a new reduced description of the flow in the limit of large surface tension consisting of three coupled (nonlinear) partial differential equations. This system is linearly unstable to disturbances of small wavenumber; we derive a simplified asymptotic description to gain analytical understanding of the nonlinear development until rupture. An initial phase of exponential film thinning leads to the accumulation of liquid in a central bulge. At a well-defined time, a localised pinch-off mechanism, driven by a mismatch in the interfacial curvature at the edge of the bulge, results in a self-similar thinning that breaks the film in finite time. Across a wide parameter range, the resultant droplet formed from the central bulge contains a significant fraction of the initial film volume.

On the flow behaviour of unconfined dual porosity aquifers with sloping base

The flow in an unconfined double-porosity aquifer with a sloping base is investigated and equations are developed for its description. In order to obtain a relatively simple description of the problem, similar assumptions as in Moutsopoulos (2021) have been adopted; the pressure in the unsaturated zone, especially in the fractures’ network, is considered to be atmospheric, and the Dupuit-Forchheimer approximation is invoked, reducing the dimensionality by eliminating the vertical direction. The derived equations have been linearized and solved analytically for a problem involving interaction between an inclined aquifer and an adjacent surface water body similar to the one examined by Akylas and Koussis (2007). The analytical solution has been checked against results obtained with state-of-the-art numerical codes. The agreement between the two approaches is excellent. The solution tools were used to gain insight in the influence of the aquifer's base inclination on the flow quantities.

Multiple-quantum magic-angle spinning NMR spectra in the static limit: The I = 3/2 case.

A simplified theoretical description of multiple-quantum excitation and mixing for nuclear magnetic resonance of half-integer quadrupolar nuclei is presented. The approach recasts the multiple-quantum nutation behavior in terms of reduced excitation and mixing curves through a scaling of the first-order offset frequency by the quadrupolar coupling constant. The two-dimensional correlation of the static first-order anisotropic line shape to the second-order anisotropic magic-angle-spinning (MAS) line shape is utilized to transform the three-dimensional integral over the three Euler angles into a single integral over the dimensionless first-order offset parameter. These transformations lead to a highly efficient algorithm for simulating the multiple-quantum (MQ)-MAS spectrum for arbitrary excitation and mixing radio frequency (RF) field strengths, pulse durations, and MAS rates within the static limit approximation, which is defined in terms of the rotation period, pulse duration, RF field strength, and quadrupolar coupling parameters. This algorithm enables a more accurate determination of the relative site populations and quadrupolar coupling parameters in a least-squares analysis of MQ-MAS spectra. Furthermore, this article examines practical considerations for eliminating experimental artifacts and employing affine transformations to improve least-squares analyses of MQ-MAS spectra. The optimum ratio of RF field strength to the quadrupolar coupling constant and the corresponding pulse durations that maximize sensitivity within experimental constraints are also examined.

Reinforcement Learning for Data-driven Workflows in Radio Interferometry. I. Principal Demonstration in Calibration

Radio interferometry is an observational technique used to study astrophysical phenomena. Data gathered by an interferometer require substantial processing before astronomers can extract scientific information from them. Data processing consists of a sequence of calibration and analysis procedures where choices must be made about the sequence of procedures as well as the specific configuration of the procedure itself. These choices are typically based on a combination of measurable data characteristics, an understanding of the instrument itself, an appreciation of the trade-offs between compute cost and accuracy, and a learned understanding of what is considered best practice. A metric of absolute correctness is not always available and validity is often subject to human judgment. The underlying principles and software configurations to discern a reasonable workflow for a given data set is the subject of training workshops for students and scientists. Our goal is to use objective metrics that quantify best practice, and numerically map out the decision space with respect to our metrics. With these objective metrics we demonstrate an automated, data-driven, decision system that is capable of sequencing the optimal action(s) for processing interferometric data. This paper introduces a simplified description of the principles behind interferometry and the procedures required for data processing. We highlight the issues with current automation approaches and propose our ideas for solving these bottlenecks. A prototype is demonstrated and the results are discussed.

Shadclips: When Parameter-Efficient Fine-Tuning with Multimodal Meets Shadow Removal

Segment Anything Model (SAM), an advanced universal image segmentation model trained on an expansive visual dataset, has set a new benchmark in image segmentation and computer vision. However, it faced challenges when it came to distinguishing between shadows and their backgrounds. To address this, we proposed ShadClips, which consists of SAM-optimizer and SONet. It has dramatically enhanced SAM’s ability to segment shadow images, differentiating between the background and both soft and hard shadows adeptly. Due to its dependence on pixel point inputs, the SAM-Optimizer interface could do better. This method presents challenges, especially when dealing with long, extended shadows. To make the user experience more intuitive and effective, we incorporated the capabilities of CLIPs. Therefore, simple text descriptions like “A photo of a shadow” can be used to guide the SAM-Optimizer, allowing it to select the most relevant shadow mask from SAM’s comprehensive category list. Meanwhile, we introduce SONet to shadow removal. A large number of experiments on ISTD/SRD prove that the proposed method is effective and satisfactory. The source code of the ShadClips can be accessed from https://github.com/zhangbaijin/SAM-helps-Shadow .

School Mathematics in Colonial India

This article analyzes a popular arithmetic textbook, Arithmetic: For the Use of Schools and Colleges, authored by Jadav Chandra Chakravarti, to examine the contents and pedagogies in the text for how mathematics was taught and learned from the end of the nineteenth century through the first half of the twentieth century in colonial India. The study findings provide us with a glimpse of the teaching and learning of mathematics in colonial India and help us to better understand current school mathematics and its curriculum evolution and development in the subcontinent. Even though Chakravarti’s textbook is mainly based on rule-method pedagogy, it has simple descriptions of rules and procedures, and a gradual progression from simple to complex in exercises and topics, which was unique at the time. The textbook maintains coherence in its style and presentation of the contents, and engages students and teachers by reflecting social life and cultural traditions in colonial India, which perhaps contributes to a long period of popularity of this book in the Indian subcontinent. The textbook has its legacy in modern education in the Indian subcontinent. Still, in the subcontinent, textbooks are one of the main sources of mathematics teaching and learning, as well as test preparation for high-stakes exams.

Shock cooling emission from explosions of massive stars – III. Blue supergiants

ABSTRACT Light emission in the first hours and days following core-collapse supernovae is dominated by the escape of photons from the expanding shock-heated envelope. In preceding papers, we provided a simple analytic description of the time-dependent luminosity, L, and colour temperature, $T_{\rm col}$, as well as of the small (${\simeq} 10 {{\, \rm per\, cent}}$) deviations of the spectrum from a blackbody at low frequencies, $h\nu \lt 3T_{\rm col}$, and of ‘line dampening’ at $h\nu \gt 3T_{\rm col}$, for explosions of red supergiants (RSGs) with convective polytropic envelopes (without significant circumstellar medium). Here, we extend our work to provide similar analytic formulae for explosions of blue supergiants with radiative polytropic envelopes. The analytic formulae are calibrated against a large set of spherically symmetric multigroup (frequency-dependent) calculations for a wide range of progenitor parameters (mass, radius, and core/envelope mass ratios) and explosion energies. In these calculations, we use the opacity tables we constructed (and made publicly available), which include the contributions of bound–bound and bound–free transitions. The analytic formulae reproduce the numeric L and $T_{\rm col}$ to within 10 and 5 per cent accuracy, and the spectral energy distribution to within ${\sim} 20\!-\!40 {{\, \rm per\, cent}}$. The accuracy is similar to that achieved for RSG explosions.

The Impacts of Thermospheric Circulation and Exospheric Transport on the Coupled System

AbstractThe boundary between the thermosphere and exosphere is often given the simplified description of being a separation between highly collisional continuum mechanics and a collisionless domain. The realistic smooth transition through this space has historically presented a challenge to model as the assumptions used to simplify the Boltzmann equation in fluid models are invalidated at higher altitudes. A lack of rigorous modeling of the region limits the ability to understand the dynamics of light atmospheric species. This manuscript describes the dynamics present in a two‐way coupled fluid‐particle atmospheric model extending from the mesosphere through the exosphere with a smooth transition between fluid and particle domains. This model is used to examine the coupled nature of the thermosphere and exosphere using the fluid simulation TIME‐GCM and the direct simulation Monte Carlo simulation Monaco. The coupled model allows for examination of the thermosphere circulation and exosphere transport mechanisms, as well as their impacts on the distribution of hydrogen. In this analysis, upper transport regions in the exosphere are revealed and distinguished from lower transport regions during June solstice. Furthermore, coupling allows TIME‐GCM to account for effects of lateral exospheric transport of hydrogen, altering its upper boundary condition and consequentially the spatial distribution of hydrogen throughout the thermosphere. Finally, it is asserted that a self‐consistent hydrogen exobase distribution is necessary to constrain other analytical extrapolation techniques used to predict the vertical hydrogen profile in the exosphere. Plasma interactions are excluded from this study to isolate neutral dynamics.

Bifurcations in the Kuramoto model with external forcing and higher-order interactions.

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, and cardiac cells) or artificial (like metronomes, power grids, and Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here, we investigate this model by combining two common features that have been observed in many systems: External periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf, and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability.

On Solutions of Some Functional Equations of Radical Type

Many authors have studied various functional equations of forms patterned on the equation expressed as ga2+b2=g(a)+g(b), which can be considered, e.g., for real functions. Such equations are usually referred to as radical functional equations or of the radical type. Authors mainly study the so-called Ulam stability of such equations, i.e., they investigate how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. Quite often, information about the solutions of these equations is also provided, but unfortunately, sometimes, such information is given in a misleading or incomplete way. It seems, therefore, that there is a need for a publication containing simple descriptions of such solutions (with appropriate examples), which would help in easy correction of such information and avoidance of similar problems for future authors. This is the main motivation for this expository paper. We present a general approach to the topic and consider two general forms of such equations. Moreover, the results presented in this paper show significant symmetry between the solutions of numerous functional equations and the solutions of equations of the radical type that correspond to them. To make this publication accessible to a wider audience, we omit various related information, avoid advanced generalizations, and present several simple examples.

Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission

We consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory. This allows us to solve for the acoustic wake trailing the perturber and the resulting dynamical friction, in the limit where the self-gravity of the response can be ignored. In a steady state and for subsonic velocities v p < c s , the dynamical friction torque Fφ∝vp3 is suppressed for perturbers orbiting in an isothermal sphere relative to the infinite, homogeneous medium expectation F φ ∝ v p . For highly supersonic motions, both expectations agree and are consistent with a local approximation to the gravitational torque. At fixed resolution (a given Coulomb logarithm), the response of the system is maximal for Mach numbers near the constant circular velocity of the singular isothermal profile. This resonance maximizes the gravitational-wave (GW) emission produced by the trailing acoustic wake. For an inspiral around a massive black hole of mass 106 M ⊙ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of a black hole binary at subnanohertz frequencies when the small black hole enters the Bondi sphere of the massive one. The exact magnitude of this effect depends on departures from hydrostatic equilibrium and on the viscosity present in any realistic astrophysical fluid, which are not included in our simplified description.

Analysis of Glucose Responsive Glucagon Therapeutics using Computational Models of the Glucoregulatory System.

Glucose-responsive glucagon (GRG) therapeutics are a promising technology for reducing the risk of severe hypoglycemia as a complication of diabetes mellitus. Herein, the performance of candidate GRGs in the literature by modeling the kinetics of activation and connecting them as input into physiological glucoregulatory models is evaluated and projected the two distinct GRG designs, experimental results reported in Wu etal. (GRG-I) and Webber etal. (GRG-II) is considered. Both are evaluated using a multi-compartmental glucoregulatory model (IMPACT) and used to compare in-vivo experimental data of therapeutic performance in rats and mice. For GRG-I and GRG-II, the total integrated glucose material balances are overestimated by 41.5% ± 14% and underestimated by 24.8% ± 16% compared to in-vivo time-course data, respectively. These large differences to the relatively simple computational descriptions of glucagon dynamics in the model, which underscores the urgent need for improved glucagon models is attributed. Additionally, therapeutic insulin and glucagon infusion pumps are modeled for type 1 diabetes mellitus (T1DM) human subjects to extend the results to additional datasets. These observations suggest that both the representative physiological and non-physiological models considered in this work require additional refinement to successfully describe clinical data that involve simultaneous, coupled insulin, glucose, and glucagon dynamics.

Physical Models for the Astrophysical Population of Black Holes: Application to the Bump in the Mass Distribution of Gravitational-wave Sources

Gravitational-wave observations of binary black holes have revealed unexpected structure in the black hole mass distribution. Previous studies employ physically motivated phenomenological models and infer the parameters that control the features of the mass distribution that are allowed in their model, associating the constraints on those parameters with their physical motivations a posteriori. In this work, we take an alternative approach in which we introduce a model parameterizing the underlying stellar and core-collapse physics and obtaining the remnant black hole distribution as a derived by-product. In doing so, we constrain the stellar physics necessary to explain the astrophysical distribution of black hole properties under a given model. We apply this to the mapping between initial mass and remnant black hole mass, accounting for mass-dependent mass loss using a simple parameterized description. Allowing the parameters of the initial mass–remnant mass relationship to evolve with redshift permits correlated and physically reasonable changes to features in the mass function. We find that the current data are consistent with no redshift evolution in the core–remnant mass relationship, but place only weak constraints on the change of these parameters. This procedure can be applied to modeling any physical process underlying the astrophysical distribution. We illustrate this by applying our model to the pulsational pair instability supernova (PPISN) process, previously proposed as an explanation for the observed excess of black holes at ∼35 M ⊙. Placing constraints on the reaction rates necessary to explain the PPISN parameters, we concur with previous results in the literature that the peak observed at ∼35 M ⊙ is unlikely to be a signature from the PPISN process as presently understood.

Mетод визначення зміни просторового положення об'єкта орбітального сервісу з невідомою формою

This paper presents a method for determining the pose of an on-orbit service object (target) with an unknown surface shape based on processing target surface point clouds. It is assumed that a point cloud is obtained using a sensor in the form of a lidar-based system onboard the service spacecraft. The algorithm of the method operates with a simplified description of the cloud; it uses only the coordinates of the cloud points without identifying any surface features. The idea of the method is as follows. From all cloud points obtained at a certain time instant, select points that are close to a certain degree to a given set of planes arranged in space in a certain way. From the point cloud corresponding to the next time instant, select points that are close to the same set of planes, but moved in space in a known way. By convention, let the arrangement of the projections of the selected cloud points onto the given planes be called a pattern of the intersection of the point clouds with the planes. By varying the displacement of the set of planes, maximize the coincidence of the intersection patterns of the first and second clouds of points. The degree of coincidence of the intersection patterns is characterized by a specified objective function whose arguments are target pose parameters. The target displacement parameters are found as the arguments of the objective function that maximize it. A variant of the objective function is proposed. A test example of the application of the proposed method is considered. A global optimization method known as the direct search method was used to find the arguments of the objective function. Test calculations were performed, and they confirmed the workability of the algorithm and determined its scope of applicability. The computational burden was not considered: the goal was to verify the workability of the method in principle. The advantage of the proposed method is its ability to determine a change in the pose of an object with an unknown surface shape. The proposed method may be considered as a source of observation data for a filtering procedure when estimating the parameters of the relative motion of a target with an unknown surface shape.

Egg-shaped sections of fluid structures around black holes

Astrophysical fluids subjected to the strong gravity of black holes can form rotating toroidal-like structures known as thick accretion discs. In order to facilitate the study of such structures, we introduce approximate empirical formulae for a relatively simple analytical description of their poloidal cross-sections that are usually described only numerically. Our comparisons of the approximate and exact descriptions of the cross-sections of the structures rotating around Schwarzschild and Kerr central black holes, together with the determination of the associated total masses of these structure, indicate a high degree of accuracy for these introduced formulae.

Realizing multiband states with ultracold dipolar quantum simulators

The manipulation of dipolar interactions within ultracold molecular ensembles represents a pivotal advancement in experimental physics, aiming at the emulation of quantum phenomena unattainable through mere contact interactions. Our study uncovers regimes of multiband occupation which allow to probe more realistic, complex long-range interacting lattice models with ultracold dipolar simulators. By mapping out experimentally relevant ranges of potential depths, interaction strengths, particle fillings, and geometric configurations, we calculate the agreement between the state prepared in the quantum simulator and a target lattice state. We do so by separately calculating numerically exact many-body wave functions in the continuous space and single- or multiband lattice representations, and building their many-body state overlaps. Our findings reveal that for shallow lattices and stronger interactions above half filling, multiband population increases, resulting in fundamentally different ground states than the ones observed in simple lowest-band descriptions, e.g., striped vs checkerboard states. A wide range of probed parameter regimes in its turn provides a systematic and quantitative blueprint for realizing multiband states with two-dimensional quantum simulators employing ultracold dipolar molecules. Published by the American Physical Society 2024

Pseudotransitions in a dilute Ising chain.

This study provides a comprehensive analysis of the ground state and thermodynamic properties of a spin-pseudospin chain representing a model of a one-dimensional dilute magnet with two types of nonmagnetic charged impurities. For this purpose, a method utilizing the transfer-matrix properties is employed. Despite the wide variety of intriguing frustrated phase states, we show that the model showcases pseudotransitions solely between simple charge and magnetic quasiorders. These pseudotransitions are characterized by distinct features in the thermodynamic and magnetic quantities, resembling first- and second-order phase transitions. In addition to pseudotransitions for the "pure" system, similar to those observed in other one-dimensional spin models, this study also reveals the presence of "second-order" pseudotransitions for the dilute case. We show that the nature of these discovered pseudotransitions is associated with the phase separation in the chain into regions of (anti)ferromagnetic and charge-ordered phases. The ability to compare the results of an exact transfer-matrix calculation with a simple phenomenological description within the framework of Maxwell construction contributes to a deeper understanding of both the physical mechanisms underlying this phenomenon and the analytical methods used.

A global–land snow scheme (GLASS) v1.0 for the GFDL Earth System Model: formulation and evaluation at instrumented sites

Abstract. Snowpacks modulate water storage over extended land regions and at the same time play a central role in the surface albedo feedback, impacting the climate system energy balance. Despite the complexity of snow processes and their importance for both land hydrology and global climate, several state-of-the-art land surface models and Earth System Models still employ relatively simple descriptions of the snowpack dynamics. In this study we present a newly-developed snow scheme tailored to the Geophysical Fluid Dynamics Laboratory (GFDL) land model version 4.1. This new snowpack model, named GLASS (Global LAnd–Snow Scheme), includes a refined and dynamical vertical-layering snow structure that allows us to track the temporal evolution of snow grain properties in each snow layer, while at the same time limiting the model computational expense, as is necessary for a model suited to global-scale climate simulations. In GLASS, the evolution of snow grain size and shape is explicitly resolved, with implications for predicted bulk snow properties, as they directly impact snow depth, snow thermal conductivity, and optical properties. Here we describe the physical processes in GLASS and their implementation, as well as the interactions with other surface processes and the land–atmosphere coupling in the GFDL Earth System Model. The performance of GLASS is tested over 10 experimental sites, where in situ observations allow for a comprehensive model evaluation. We find that when compared to the current GFDL snow model, GLASS improves predictions of seasonal snow water equivalent, primarily as a consequence of improved snow albedo. The simulated soil temperature under the snowpack also improves by about 1.5 K on average across the sites, while a negative bias of about 1 K in snow surface temperature is observed.

Crack patterns in masonry structures using phase field method

This work aims to study the crack pattern in masonry-like structures by a simplified description of the mediumusing a variational damage model. In literature, when modeling fractures in masonry structures, capturingboth fracture types, cracks in units, and cracks at the interface simultaneously, usually requires a complicated scheme. The phase-field method has been widely used recently because of its robustness in capturing variousfracture types. In this work, we consider the mortar and the interface (between the mortar and units) as a thickinterface layer with pseudo-material properties. We conduct numerical tests on a bending beam and a tensilewall using strategies of material properties with a phase field model. As it is not distinguished the crack in themortar and the brick-mortar interface, it is shown in this work that both types of fracture, in the thick interfacelayer and the unit, can be captured just using the phase field method and the simplified micro model.