Unbounded Sets Research Articles

A Geomorphic Examination of the Calabrian Forearc Translation

AbstractThe evolution of subduction forearcs as archived in the tectonic and geomorphic record serves to constrain geodynamic models of many convergent plate margins. This paper presents geomorphic stream channel metrics and river longitudinal profile modeling to assess geodynamic models describing the late Cenozoic horizontal translation of a Mediterranean forearc. The northern flank of Sicily is drained by roughly parallel north‐flowing streams arranged across the hypothesized west‐to‐east migration path of the Calabrian forearc high. These streams present a snapshot of current geomorphic processes driven by spatiotemporal variations in crustal deformation, including river incision and landscape steepness. A stream power rule‐based numerical modeling of the fluvial response time and knickpoint migration provides an independent prediction for the history of rock uplift associated with the translating forearc over the past ∼4 Myr. The results serve as a test for two, crustal wave versus transform‐fault, end‐member geodynamic models for the Calabrian forearc evolution, suggesting that our modeling supports the former. The river profile modeling shows that northern Sicily rivers experienced two pulses of time‐transgressive rock uplift that progressively sweeps west to east. This analysis suggests the most rapid contemporary rock uplift rates are focused in NE‐Sicily, where the forearc is currently located and where Pleistocene marine terraces indicate the highest rock uplift rates. These results are consistent with the west‐to‐east passage of a forearc high embedded in the subduction wedge, followed by a dynamic wave of rock uplift in its wake similar to what has been proposed for slab windows in other plate boundary settings.

A Novel Concept of Uncertainty Optimization Based Multi-Granular Rough Set and Its Application

Data is generating at an exponential pace with the advancement in information technology. Such data highly contain uncertain and vague information. The rough set approximation is a way to find information in the data-set under uncertainty and to classify objects of the dataset. This work presents a mathematical approach to evaluate the data-sets uncertainties and their application to data reduction. In this work, we have extended the multi-granulation variable precision rough set in the context of uncertainty optimization. We develop an uncertainty optimization-based multi-granular rough set (UOMGRS) to minimize the uncertainties in the data set more effectively. Using UOMGRS, we find the most informative attribute in the feature space. It is desirable to minimize the rough set boundary region using the attribute having the highest approximation quality. Thus we group the attributes whose relative quality of approximation is the maximum to maximize the positive region and to minimize the uncertain region. We compare the UOMGRS with the single granulation rough set (SGRS) and the multi-granular rough set (MGRS). By our proposed method, we require only an average of 62% attributes for approximation whereas, SGRS and MGRS need an average of at least 72% of attributes in the data set for approximation of the concepts in the data-set. Our proposed method requires less amount of data for the classification of objects in the dataset. The method helps minimize the uncertainties in the dataset in a more efficient way.

Combinatorics of criniferous entire maps with escaping critical values

A transcendental entire function is called criniferous if every point in its escaping set can eventually be connected to infinity by a curve of escaping points. Many transcendental entire functions with bounded singular set have this property, and this class has recently attracted much attention in complex dynamics. In the presence of escaping critical values, these curves break or split at critical points. In this paper, we develop combinatorial tools that allow us to provide a complete description of the escaping set of any criniferous function without asymptotic values on its Julia set. In particular, our description precisely reflects the splitting phenomenon. This combinatorial structure provides the foundation for further study of this class of functions. For example, we use these results in another paper to give the first full description of the topological dynamics of a class of transcendental entire maps with unbounded postsingular set.

LES and URANS study on turbulent flow through 3 × 3 rod bundle with spacer grid and mixing vanes using spectral element method

In this paper, the turbulent flow in rod bundles with spacer grid and mixing vanes in nuclear reactor core was studied using spectral element method with large eddy simulation (LES) and unsteady RANS (URANS) method. Combining with the radial periodical boundary conditions, the turbulent mixing phenomena in central subchannels were investigated, especially focusing on the flow field after the spacer grid and mixing vanes. Other than setting up long bare rod bundle to establish the fully developed turbulent flow, only a 2-cm-long bare rod bundle was extruded upstream the spacer grid and mixing vanes, while the fully developed laminar velocity profile was applied on the inlet surface for velocity boundary settings. The results indicate that both of the models could predict time-averaged velocity at 0.5Dh, 1Dh, 4Dh downstream mixing vanes properly, while the URANS model underestimate the root-mean-square (RMS) value of fluctuating velocity due to the inlet treatment effect. Furthermore, turbulent kinetic energy contour with transverse velocity vector was combined to investigate the behaviors of vortices formed by split-type mixing vanes, revealing the behavior of vortices for preliminary dynamic and mechanic analysis in design process of fuel assembly.

Structure of sets of solutions of parametrised semi-linear elliptic systems on spheres

In this paper we study a parametrised non-cooperative symmetric semi-linear elliptic system on a sphere. Assuming that there exist critical orbits of the potential, we study the structure of the sets of solutions of the system. In particular, using the equivariant Rabinowitz alternative we formulate sufficient conditions for a bifurcation of unbounded sets of solutions.

Magnetohydrodynamics Buoyancy-Driven Unsteady Couette Flow with Fluctuating Viscosity

Magnetohydrodynamics plays a significant role in new development and future perspectives of clean energy power generation systems and flow control technology in the aeronautics, astronautics, plasma, and electrical conducting flow in the electric machinery. This paper examines the inherent irreversibility in an unsteady hydromagnetic Couette flow of a conducting variable viscosity fluid between two vertical parallel plates with thermal buoyancy and heat transfer characteristics. Necessary regulating model equations are obtained and then converted using dimensionless variables to form a set of nonlinear initial boundary valued problem. Employing a semi-discretization finite difference method known as the method of lines, the model is addressed numerically. The velocity and the temperature results obtained are used further to compute the entropy generation rate, the Bejan number, skin friction and Nusselt number. Some effects of the embedded parameters on the above-mentioned results are investigated and displayed by graphs. Our results revealed that entropy generation rate is enhanced with an upsurge in thermal buoyancy but a rise in magnetic field lessened it.

No explicit memory for individual trial display configurations in a visual search task.

Previous evidence demonstrated that individuals can recall a target's location in a search display even if location information is completely task-irrelevant. This finding raises the question: does this ability to automatically encode a single item's location into a reportable memory trace extend to other aspects of spatial information as well? We tested this question using a paradigm designed to elicit attribute amnesia (Chen & Wyble, Psychological Science, 26(2) 203-210, 2015a). Participants were initially asked to report the location of a target letter among digits with stimuli arranged to form one of two or four spatial configurations varying randomly across trials. After completing numerous trials that matched their expectations, participants were surprised with a series of unexpected questions probing their memory for various aspects of the display they had just viewed. Participants had a profound inability to report which spatial configuration they had just perceived when the target's location was not unique to a specific configuration (i.e., orthogonal). Despite being unable to report the most recent configuration, answer choices on the surprise trial were focused around previously seen configurations, rather than novel configurations. Thus, there were clear memories of the set of configurations that had been viewed during the experiment but not of the specific configuration from the most recent trial. This finding helps to set boundary conditions on previous findings regarding the automatic encoding of location information into memory.

An advanced uncertainty measure using fuzzy soft sets: Application to decision-making problems

In this paper, uncertainty has been measured in the form of fuzziness which arises due to imprecise boundaries of fuzzy sets. Uncertainty caused due to human's cognition can be decreased by the use of fuzzy soft sets. There are different approaches to deal with the measurement of uncertainty. The method we proposed uses fuzzified evidence theory to calculate total degree of fuzziness of the parameters. It consists of mainly four parts. The first part is to measure uncertainties of parameters using fuzzy soft sets and then to modulate the uncertainties calculated. Afterward, the appropriate basic probability assignments with respect to each parameter are produced. In the last, we use Dempster's rule of combination to fuse independent parameters into integrated one. To validate the proposed method, we perform an experiment and compare our outputs with grey relational analysis method. Also, a medical diagnosis application in reference to COVID-19 has been given to show the effectiveness of advanced method by comparing with other method.

On Markov Moment Problem and Related Results

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an Lν1 space, where ν is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

Mortality, morbidity and economic growth.

The question of whether and how changes to population health impact on economic growth has been actively studied in the literature, albeit with mixed results. We contribute to this debate by reassessing–and extending–[1], one of the most influential studies. We include a larger set of countries (135) and cover a more recent period (1990–2014). We also account for morbidity in addition to mortality and adopt the strategy of providing bounding sets for the effects of interest rather than point estimates. We find that reducing mortality and disability adjusted life years (DALYs), a measure which combines morbidity and mortality, promotes per capita GDP growth. The magnitude of the effect is moderate, but non negligible, and it is similar for mortality and DALYs.

Grid Partition Variable Step Alpha Shapes Algorithm

On the basis of Alpha Shapes boundary extraction algorithm for discrete point set, a grid partition variable step Alpha Shapes algorithm is proposed to deal with the shortcomings of the original Alpha Shapes algorithm in the processing of nonuniform distributed point set and multiconcave point set. Firstly, the grid partition and row-column index table are established for the point set, and the point set of boundary grid partition is quickly extracted. Then, the average distance of the k -nearest neighbors of the point is calculated as the value of α . For the point set of boundary grid partition extracted in the previous step, Alpha Shapes algorithm is used to quickly construct the point set boundary. The proposed algorithm is verified by experiments of simulated point set and measured point set, and it has high execution efficiency. Compared with similar algorithms, the larger the number of point sets is, the more obvious the execution efficiency is.

Quantitative Evaluation and Optimization of Feeding-Back Previous Cycles Information for Computational Fluid Dynamics Periodic Convergence

Abstract Unsteady simulations represent an expensive subset of computational fluid dynamics (CFD) simulations in terms of computational resources. Among the unsteady simulations, the time-periodic cases are of special interest in many applications such as turbomachinery. The special characteristics of these cases allow specific methodologies to improve its periodic convergence behavior, neglecting the physical transient to achieve it. The scope of this paper is focused on these unsteady periodic simulations. In this context, departing from a plain Dual Time-Step methodology, where the standard generic procedure is to converge every physical time-step from the solution of the previous one, the effect of feeding-back the previous period information to restart the convergence of the equivalent time-steps in the new period is assessed in this paper. With that aim, options to alleviate the possible penalties of the procedure are presented, and the parameter set election and boundary conditions optimized to define a complete methodology. Finally, a benchmarking of the defined methodology is performed against the standard plain Dual Time-Step technique and the much more efficient Harmonic Balance methodology. For that comparison, a basic two-dimensional (2D) case and a more realistic 3D compressor, both with harmonic torsion vibration, as well as two rotor–stator configurations, are computed and presented here. The results show that a comparable efficiency to the Harmonic Balance technique is achieved with lower memory requirements, meaning that the performance of the plain Dual Time-Step methodology is greatly improved just by changing small parts of its formulation.

Reciprocal burden: Adults with drug-resistant epilepsy reflect upon informal caregiver support

PurposeTo explore how a sample of people with uncontrolled seizures describe their experiences of receiving informal supportive care. MethodsUsing constructivist grounded theory, in-person, semi-structured interviews were conducted in 35 adults with drug-resistant epilepsy. These 20 (57%) women and 15 (43%) men were aged 18–68 years (mean= 35.6 years), with a range of verbal comprehension scores. The majority, 28 (80%) lived in nuclear family settings. ResultsUnpredictable seizures disrupted personal autonomy and generated unique challenges for everyday life. While supportive care was deemed necessary to survival, subjective reflections around the implications of care-receiving and caregiving, were ultimately experienced as mutually burdensome. Four dynamic and interactive dimensions revealed a mirrored, interactive perspective of what it meant to be a care-recipient: assuming responsibility; protecting and supervising; acknowledging reliance and setting boundaries. Care-recipience was not one-sided, but included actively hiding personal struggles as a way to shield the caregiver from the emotional and physical demands of caregiving. Relationship dynamics between caregivers and care-recipients played a major role in treatment decision-making. A clinically useful Theory of Reciprocal Burden resulted from our study. ConclusionsThis study adds an explanatory dimension to the concept of illness burden from the perspective of care-recipients. Relationship dynamics play a key role in patient-centered epilepsy care, with clinical implications for guiding supportive caregiving, fostering independence and promoting self-management strategies.

On a conjecture of Montgomery and Soundararajan

We establish lower bounds for all weighted even moments of primes up to X in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold unconditionally for an unbounded set of values of X, and hold for all X under the Riemann Hypothesis. We also deduce new unconditional $$\Omega $$ -results for the classical prime counting function.

Model Comparisons of Flow and Chemical Kinetic Mechanisms for Methane–Air Combustion for Engineering Applications

The reasonably accurate numerical simulation of methane–air combustion is important for engineering purposes. In the present work, the validations of sub-models were carried out on a laboratory-scale turbulent jet flame, Sandia Flame D, in comparison with experimental data. The eddy dissipation concept (EDC), which assumes that the molecular mixing and subsequent combustion occur in the fine structures, was used for the turbulence–chemistry interaction. The standard k-ε model (SKE) with the standard or the changed model constant C1ε, the realizable k-ε model (RKE), the shear-stress transport k-ω model (SST), and the Reynolds stress model (RSM) were compared with the detailed chemical kinetic mechanism of GRI-Mech 3.0. Different reaction treatments for the methane–air combustion were also validated with the available experimental data from the literature. In general, there were good agreements between predictions and measurements, which gave a good indication of the adequacy and accuracy of the method and its further applications for industry-scale turbulent combustion simulations. The differences between predictions and measured data might have come from the simplifications of the boundary settings, the turbulence model, the turbulence–reaction interaction, and the radiation heat transfer model. For engineering predictions of methane–air combustion, the mixture fraction probability density function (PDF) model for the partially premixed combustion with RSM is recommended due to its relatively low simulation expenses, acceptable accuracy predictions, and quantitatively good agreement with the experiments.

The effect of rotation on the free vibrations in a non-homogeneous orthotropic magneto-elastic hollow sphere

This article examines the free vibrations of spherical orthotropic within an elastic medium according to the one-dimensional (1D) elastic model. According to the linear elasticity model, rotation, magnetic field, and inhomogeneity effects on wave propagation in the orthotropic material are analyzed. The 1D magneto-elastodynamics equation is resolved concerning radial displacement. We consider three boundaries: free, fixed, and mixed orthotropic materials. Concerning harmonic vibrations, the eigenvalues of the natural frequency of the radial vibrations concerning various boundary settings are determined. For each case, the numerical results are provided, illustrated in graphs, and compared with those without rotation, magnetic field, and non-homogeneity. An increase in the rotation and non-homogeneity parameters is observed, similar to the findings of the classical sphere theory. The findings show that rotation, magnetic field, and non-homogeneity have a strong impact on wave propagation in orthotropic material. Increasing the rotation, magnetic field, and inhomogeneity parameters make the findings closer to the findings of the classical sphere model. Moreover, the present article applies to the design and optimal use of nanoplates and microplates. The findings show that the impacts of the magnetic field, rotation, and inhomogeneity parameter are very pronounced.

The structure of the singular set in the thin obstacle problem for degenerate parabolic equations

We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight |y|^a for a in (-1,1). Such problem arises as the local extension of the obstacle problem for the fractional heat operator (partial _t - Delta _x)^s for s in (0,1). Our main result establishes the complete structure and regularity of the singular set of the free boundary. To achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity formulas which generalize those for the case of the heat equation (a=0).

A Note on On-Line Ramsey Numbers of Stars and Paths

An on-line Ramsey game is a game between two players, Builder and Painter, on an initially empty graph with unbounded set of vertices. In each round, Builder selects two vertices and joins them with an edge while Painter colours the edge immediately with either red or blue. Builder’s aim is to force either a red copy of a fixed graph G or a blue copy of a fixed graph H. The game ends with Builder’s victory when Builder manages to force either a red G or a blue H. The minimum number of rounds for Builder to win the game, regardless of Painter’s strategy, is the on-line Ramsey number $${\tilde{r}}(G,H)$$ . This note focuses on the case when G and H are stars and paths. In particular, we will prove the upper bound of $${\tilde{r}}(S_3,P_{l+1})\le 5l/3+2$$ . We will also present an alternative proof for the upper bound of $${\tilde{r}}(S_2 = P_3, P_{l+1}) = \lceil 5l/4\rceil $$ .

Three dimensional modelling of aluminum foam through computed tomography scan technique

PurposeThis study aims to generate different three-dimensional (3D) foam models using computer tomography (CT) scan and solid continuum techniques. The generated foam models were used to study deformation mechanism and the elastic-plastic behaviour with the existing experimental foam behaviour.Design/methodology/approachCT scan model was generated by combing 2D images of foam in MIMICS software. Afterwards, it was imported in ABAQUS/CAE software. However, solid continuum model was generated in ABAQUS/CAE software by using crushable foam properties. Then, the generated foam models were sets boundary conditions for a compression test.FindingsCT scans capture the actual morphology of foam sample which may directly an image based finite element foam model. The sectional views of both the models were used to observe deformation mechanism on compression. The real compressive behaviour of foam was visualised in CT-Scan foam model. It was observed that CT-scan model was the more accurate modelling method than crushable foam model.Originality/valueThe internal structure of foam is very complex and difficult to analyse. Therefore, CT-scanning may be the accurate method for capturing the macro-level detailing of foam structure. A CT-scan foam model can be used for multiple times for mechanical analysis using a simulation software, which may reduce the manufacturing and the experimental cost and time.

Exclusion of quadruple collisions in minimizers of the planar equal-mass N-body problem

It has been shown by Chen that if all masses are in the same proper vector subspace of Rd(d≥2) on one of the free boundaries, local minimizers connecting the two free boundaries have no collision on that boundary. However, not much is known for other types of boundary configurations.In this paper, we consider minimizers connecting two free boundaries and study possible quadruple collisions under the following four symmetric configurations: isosceles trapezoid configuration, rectangular configuration, double isosceles configuration and diamond configuration. Whenever the boundary configuration of four bodies coincides with one of the four symmetric configurations, we show that these four bodies are free of quadruple collision on that boundary set. New ideas and detailed analysis are introduced in order to construct deformed paths in some of the cases and estimate their action values. As its applications, we show the existence of several sets of periodic orbits in the planar four-body and five-body problems.