Natural Boundary Research Articles

Configurational forces and ALE formulation for geometrically exact, sliding shells in non-material domains

The paper presents a novel Arbitrary Lagrangian–Eulerian formulation for dynamic problems of geometrically exact, sliding shells. In contrast to previous researches where the sliding motions are prescribed at sliding boundaries and the existence of configurational forces is not identified, the configurational momentum equation that governs the evolution of sliding motions is derived in a consistent variational framework in the present paper. To this end, the time-varying material domain due to the presence of sliding motion is mapped onto a time-invariant mesh domain, variations at fixed material and at fixed mesh coordinates are introduced, and their relationship with variation of material coordinates at fixed mesh coordinates are derived. Hamilton’s principle of variation of action is employed to derive the strong form of mechanical and configurational momentum equations together with natural boundary conditions at the sliding boundaries. In the finite element formulation, transfinite interpolation is employed to relate material coordinates of nodes inside the domain to the values at the sliding boundaries. The discrete form of Hamilton’s variational principle leads to discrete governing equations of the proposed ALE formulation. The generalized-α scheme is adjusted to integration the resulting mechanical and configurational momentum equations. Numerical examples are presented to validate correctness and efficiency of the proposed formulation.

The Imaginary Line Across Yogyakarta Land as an Ethnomathemathics Study

In attempt to explore Yogyakarta, the heritage city of Indonesia, the well known landmark, Tugu Pal Putih and the Yogyakarta Imaginary Line is explored. The purpose of this paper is to describe that this cultural context may be used as a reference for geometry learning. The method used in this research is a descriptive qualitative involving two historian experts in interviews. The results are that this line can be explored through ethnomathematics studies based on points, straight lines, comparison of distances between points on the imaginary line and the extension of the imaginary line. This line can be illustrated by an imaginary point located at the Tugu Pal Putih as the starting point to focus on thinking of the mathematical object. This line not only divides Yogyakarta imaginatively but also according to natural boundaries such as rivers. The extension of the imaginary line forms an area called the fertility area. The description of the patterns formed on the Yogyakarta Imaginary Line through ethnomathematics is expected to be used further as materials in the mathematics learning process.

Characterizing thermo-hydraulic behaviors of seasonally frozen loess via a combined opto-electronic sensing system: Field monitoring and assessment

Frost damage in mid-latitude loess regions is mainly caused by the coupled soil water and heat transfer during freezing-thawing (FT) processes. In this paper, to better understand the thermo-hydraulic (TH) behaviors of seasonally frozen loess, field monitoring and assessment were performed on the Loess Plateau, China with a quasi-distributed opto-electronic sensing system. This system successfully captured the spatiotemporal variations in multivariables of seasonally frozen soil in near real-time, including in-situ soil temperature, unfrozen water content, and ice content. The monitoring datasets collected during the 2020/2021 winter offer unique insight into the TH behaviors of freezing point (FP) depression, in-situ soil-freezing characteristic curve (SFCC), and cryosuction. The findings highlight the importance of acquiring SFCCs under natural boundary conditions and confirm the applicability of laboratory-obtained FP in determining in-situ soil freezing depth. Furthermore, the study reveals that soil matric suction, considering the presence of ice, is the primary driving force of water migration during FT. Finally, errors in field monitoring are discussed, which arise from two aspects: the special features of loess and imperfections in monitoring schemes. This assessment of the coupled TH responses to climate changes in loess offers valuable theoretical guidance for optimizing engineering construction schemes and mitigating geohazards in mid-latitude loess regions.

An Efficient Legendre–Galerkin Approximation for Fourth-Order Elliptic Problems with SSP Boundary Conditions and Variable Coefficients

Under simply supported plate (SSP) boundary conditions, a numerical method based on the higher-order Legendre polynomial approximation was studied and developed for fourth-order problems with variable coefficients. We first divide the SSP boundary conditions into two types, namely, forced boundary conditions and natural boundary conditions. According to the forced boundary conditions, an appropriate Sobolev space is defined, and a variational formulation and a discrete scheme associated with the original problem are established. Then, the existence and uniqueness of this weak solution and approximate solution are proved. By using the Céa lemma and the tensor Jacobian polynomial approximation, we further obtain the error estimation for the numerical solutions. In addition, we use the orthogonality of Legendre polynomials to construct a set of effective basis functions and derive the equivalent tensor product linear system associated with the discrete scheme, respectively. Finally, some numerical tests were carried out to validate our algorithm and theoretical analysis.

Natural boundaries for scattering amplitudes

Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also have another class of singularities called natural boundaries of analyticity. They create a barrier beyond which analytic continuation cannot be performed. More concretely, we use unitarity to show that 2 \to 22→2 scattering amplitudes in theories with a mass gap can have a natural boundary on the second sheet of the lightest threshold cut. There, an infinite number of ladder-type Landau singularities densely accumulates on the real axis in the center-of-mass energy plane. We argue that natural boundaries are generic features of higher-multiplicity scattering amplitudes in gapped theories.

Effect of shear on local boundary layers in turbulent convection

In Rayleigh Bénard convection, for a range of Prandtl numbers $4.69 \leqslant Pr \leqslant 5.88$ and Rayleigh numbers $5.52\times 10^5 \leqslant Ra \leqslant 1.21\times 10^9$ , we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each $Ra$ , at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities $V_{bl}$ ; (B) bimodal with the first peak between $V_{bl}$ and $V_{L}$ , the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately $V_{L}$ . Type A distributions occur more at lower $Ra$ , while type C occur more at higher $Ra$ , with type B occurring more at intermediate $Ra$ . We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as $V_{L}$ scales with $Ra$ . We then show that the areas of such regions that have velocities of the order of $V_{L}$ increase exponentially with increase in $Ra$ and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as $Re_{bs}$ , the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For $Pr=1$ and aspect ratio $\varGamma =1$ , $Re_{bs} \sim Ra^{0.375}$ for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with $Ra$ as $Ra^{0.35}$ ; since $V_{bl}\sim Ra^{1/3}$ , this suggests a possible shear domination of the boundary layers at high $Ra$ . The effect of shear, however, decreases with increase in $Pr$ and with increase in $\varGamma$ , and becomes negligible for $Pr\geqslant 100$ at $\varGamma =1$ or for $\varGamma \geqslant 20$ at $Pr=1$ , causing $Re_{bs}\sim Ra_w^{1/3}$ .

Cueing natural event boundaries improves memory in people with post-traumatic stress disorder

People with post-traumatic stress disorder (PTSD) often report difficulty remembering information in their everyday lives. Recent findings suggest that such difficulties may be due to PTSD-related deficits in parsing ongoing activity into discrete events, a process called event segmentation. Here, we investigated the causal relationship between event segmentation and memory by cueing event boundaries and evaluating its effect on subsequent memory in people with PTSD. People with PTSD (n = 38) and trauma-matched controls (n = 36) watched and remembered videos of everyday activities that were either unedited, contained visual and auditory cues at event boundaries, or contained visual and auditory cues at event middles. PTSD symptom severity varied substantial within both the group with a PTSD diagnosis and the control group. Memory performance did not differ significantly between groups, but people with high symptoms of PTSD remembered fewer details from the videos than those with lower symptoms of PTSD. Both those with PTSD and controls remembered more information from the videos in the event boundary cue condition than the middle cue or unedited conditions. This finding has important implications for translational work focusing on addressing everyday memory complaints in people with PTSD.

Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials

In this paper, with classic Legendre polynomials, a method of particular solutions (MPS, for short) is proposed to solve a kind of second-order differential equations with a variable coefficient on a unit interval. The particular solutions, satisfying the natural Dirichlet boundary conditions, are constructed with orthogonal Legendre polynomials for the variable coefficient case. Meanwhile, we investigate the a-priori error estimates of the MPS approximations. Two a-priori error estimations in H 1 - and L ∞ -norms are shown to depict the convergence order of numerical approximations, respectively. Some numerical examples and convergence rates are provided to validate the merits of our proposed meshless method.

Hygro-thermo-mechanical analysis of sandwich shallow shells considering the effects of transverse normal strain

The static response of softcore doubly-curved sandwich shallow shells under hygro-thermo-mechanical loading is presented herein using a fifth-order shell theory which considers the effects of transverse normal strains and stresses at the same time. The present theory accounts for non-linear variations of displacements. The strain-displacement relations take into account only small curvatures following a shallow shell description. The present theory ensured the traction-free boundary conditions at the top and the bottom faces of the shell. The governing equations along with the natural and essential boundary conditions are derived using the principle of virtual work. The governing equations are solved by using Navier’s method. Three layered sandwich shallow shells of double curvature subjected to hygro-thermo-mechanical loading are analyzed. The accuracy and efficacy of the present theory are proved by applying it to the benchmark solutions available in the literature and then the present theory is extended for the analysis of softcore sandwich shells of double curvature. Since an exact 3D elasticity solution is not available for many such problems; this paper can be serving as a benchmark reference solution for future researchers working in this area.

Angular unconformity in Pennsylvanian strata from 3-D seismic interpretation, Goldsmith Field, West Texas

The Pennsylvanian unconformity, which is a detrital surface, separates the beds of the Permian-aged strata from the Lower Paleozoic in the Central Basin Platform. Seismic data interpretation indicates that the unconformity is an angular unconformity, overlying multiple normal faults, and accompanied with a thrust fault which maximizes the region's structural complexity. Additionally, the Pennsylvanian angular unconformity creates pinch-outs between the beds above and below. We computed the spectral decomposition and reflector convergence attributes and analyzed them to characterize the angular unconformity and faults. The spectral decomposition attribute divides the broadband seismic data into different spectral bands to resolve thin beds and show thickness variations. In contrast, the reflector convergence attribute highlights the location and direction of the pinch-outs as they dip south at angles between 2° and 6°. After reviewing findings from RGB blending of the spectrally decomposed frequencies along the Pennsylvanian unconformity, we observed channel-like features and multiple linear bands in addition to the faults and pinch-outs. It can be inferred that the identified linear bands could be the result of different lithologies associated with the tilting of the beds, and the faults may possibly influence hydrocarbon migration or act as a flow barrier to entrap hydrocarbon accumulation. The identification of this angular unconformity and the associated features in the study area are vital for the following reasons: 1) the unconformity surface represents a natural stratigraphic boundary; 2) the stratigraphic pinch-outs act as fluid flow connectivity boundaries; 3) the areal extent of compartmentalized reservoirs' boundaries created by the angular unconformity are better defined; and 4) fault displacements are better understood when planning well locations as faults can be flow barriers, or permeability conduits, depending on facies heterogeneity and/or seal effectiveness of a fault, which can affect hydrocarbon production. The methodology utilized in this study is a further step in the characterization of reservoirs and can be used to expand our knowledge and obtain more information about the Goldsmith Field.

Quasiperiodic Sets at Infinity and Meromorphic Extensions of Their Fractal Zeta Functions

We construct an interesting family of unbounded sets at infinity having a quasiperiodic structure in their geometry. We study these sets by analyzing their complex dimensions—a generalization of the classical Minkowski dimension, which are defined analytically—as poles of a suitably defined Lapidus zeta function at infinity introduced in a previous work by the author. We define the tube zeta function at infinity and obtain a functional equation that relates it to the Lapidus zeta function at infinity much as in the classical setting of relative fractal drums. Furthermore, under suitable assumptions, we provide some general results about extending the fractal zeta functions at infinity beyond their abscissae of convergence. We also provide a sufficiency condition for Minkowski measurability as well as a bound from above for the upper Minkowski content directly from the corresponding zeta functions at infinity. We show that complex dimensions of quasiperiodic sets at infinity possess a quasiperiodic structure which can be either algebraic or transcendental. Furthermore, we use the quasiperiodic sets at infinity to construct a maximally hyperfractal set at infinity with prescribed Minkowski dimension, i.e., a set for which the abscissa of convergence of the associated fractal zeta function at infinity becomes its natural boundary.

A refined spectral element model for wave propagation in multiscale hybrid epoxy/carbon fiber/graphene platelet composite shells

The propagation of elastic waves in heterogeneous media is of interest for impact dynamics and non-destructive detection. This work presents a refined spectral element model (RSEM) to study the wave propagation in multiscale hybrid composite (MHC) shells subjected to impulsive loadings. The doubly-curved MHC shell consists of epoxy, carbon fibers, and graphene platelets (GPLs). The GPLs are functionally distributed along the thickness of the shell. For the three-phase MHC, the Halpin-Tsai micromechanical model in conjunction with the Mori-Tanaka approach is exploited to determine the effective material properties. In the framework of four-variable shear deformation theory, the governing equations along with the natural boundary conditions are derived using Hamilton's principle. A two-node spectral shell element is developed according to the closed-from solutions. The accuracy of the RSEM is verified by comparison with published results in aspects of the natural frequency and transient responses. The wave dispersion characteristics, including the wave number, phase velocity, and group velocity are examined. In the context of high frequency and short wavelength, the proposed RSEM achieves high computational efficiency benefiting from its independence of mesh structure. The time domain responses clearly indicate the wave-boundary interactions, e.g., wave reflection, dispersion, and interference. It is revealed that the present model can well capture the fundamental wave modes of the MHC shell. Moreover, the inclusion of GPLs plays a significant role in improving transverse moduli and mitigating the discontinuities of inter-laminar shear stress.

The Boundaries of Human Nature: The Philosophical Animal from Plato to Haraway

The Boundaries of Human Nature: The Philosophical Animal from Plato to Haraway

Assessing free-fare public transport in Chilean cities through optimization models

Many public transport services receive operating subsidies from national, regional, or local Governments, part of which are directed to reducing fares. In recent years, different cities, most of them located in Europe, have advanced in the provision of free-fare public transport, which could help reduce car use and thus limit negative externalities related to its use. Using cost minimization models with variable mode share, in a circular structure with radial lines, optimal fares for bus services were estimated for 33 small and medium-sized cities in Chile. Through a linear regression model, we determined that the optimal fares decrease for cities with higher population, lower average income, a higher proportion of students, and with a CBD surrounded by natural boundaries such as seacoast. Based on the model's results, together with feasibility criteria that included competition of buses with other transportation modes, the regulation of existing systems and the quality of available data, recommendations are provided to select the best cities for a test of free-fare public transport in Chile. The methodology is applicable to cities in other countries, and future research may incorporate the effect of the valuation of crowding by users, as well as the generation of additional trips due to a drop in bus fares.

Investigation of the ecological state of natural resources at agricultural enterprises of various forms of ownership in the eastern region of Opllia

In order to provide sustainable development of agroecosystems and rational nature management, it is essential to make a transition to alternative farming methods. Organization of agricultural area is the first stage in the process of transforming a natural ecosystem into an agroecosystem. The limits of the types of agricultural area organization form natural boundaries of agroecosystems. The basis of conducting the research is the investigation of the ecological state of natural resources of agricultural enterprises of various forms of ownership in the eastern region of Opillia, namely the agroecosystems of two farms as a comparison of a traditional method of farming and a bioorganic one as well as their influence on the ecosystems on the territory of Berezhany district (investigation of the agroecosystems in TzOV “Zhyva Zemlia Potutory” in the village of Potutory Berezhany district (organic farming method), and TOV “Agroprodservis” in the village of Kozliv, Ternopil region). The research is aimed at the substantiation of ecological approaches and the analysis of practical recommendations on the formation of a mechanism of the development of ecologically-safe farming and at providing the ecological assessment of the agricultural landscapes in order to provide organic crop cultivation. Materials and methods corresponded to the methodology of a continuous soil-agrochemical monitoring of agricultural lands in Ukraine. In most cases, alternative farms cannot compete with traditional farms in terms of crop yield. Satisfactory crop yields absolutely depend on the amount of manure and compost applied as well as on the area that farmers can allocate for growing legumes.

A variational approach for estimating the distribution of body temperature in the form of a rectangular parallelepiped under the influence of temperature, heat exchange and heat isolation of some facets

The article describes the use of a variational method involving the finite element method to estimate the law of temperature distribution in a body in the form of a rectangular parallelepiped. The case is considered when a certain temperature is maintained on one of the faces of a rectangular parallelepiped, and heat exchange with the environment occurs on the opposite side. In accordance with the proposed approach, an approximating function in the form of a polynomial of the third degree is proposed. To determine the law of temperature distribution in a solid in the form of a rectangular parallelepiped, a functional is compiled, which consists of terms that take into account temperature, heat exchange with the environment, isolation of the faces of a rectangular parallelepiped, as well as natural boundary conditions. Minimizing this functional, the temperature values at these nodes are determined by the nodal points of a rectangular parallelepiped. Further, substituting these values into the approximating function, we obtain the temperature distribution law. At the same time, variants are investigated when the remaining faces of a rectangular parallelepiped are thermally insulated or vice versa. The temperature distribution law is estimated for different amounts of partitioning of the sides of a rectangular parallelepiped. In addition, a comparison of the temperature distribution law for a rectangular parallelepiped and a rod close in size, other things being equal, was made. Their minor differences are shown.

Effects of environment and metacommunity delineation on multiple dimensions of stream fish beta diversity

IntroductionBeta diversity represents changes in community composition among locations across a landscape. While the effects of human activities on beta diversity are becoming clearer, few studies have considered human effects on the three dimensions of beta diversity: taxonomic, functional, and phylogenetic. Including anthropogenic factors and multiple dimensions of biodiversity may explain additional variation in stream fish beta diversity, providing new insight into how metacommunities are structured within different spatial delineations.MethodsIn this study, we used a 350 site stream fish abundance dataset from South Carolina, United States to quantify beta diversity explainable by spatial, natural environmental, and anthropogenic variables. We investigated three spatial delineations: (1) a single whole-state metacommunity delineated by political boundaries, (2) two metacommunities delineated by a natural geomorphic break separating uplands from lowlands, and (3) four metacommunities delineated by natural watershed boundaries. Within each metacommunity we calculated taxonomic, functional, and phylogenetic beta diversity and used variation partitioning to quantify spatial, natural environmental, and anthropogenic contributions to variations in beta diversity.ResultsWe explained 25–81% of the variation in stream fish beta diversity. The importance of these three factors in structuring metacommunities differed among the diversity dimensions, providing complementary perspectives on the processes shaping beta diversity in fish communities. The effect of spatial, natural environmental, and anthropogenic factors varied among the spatial delineations, which indicate conclusions drawn from variation partitioning may depend on the spatial delineation chosen by researchers.DiscussionOur study highlights the importance of considering human effects on metacommunity structure, quantifying multiple dimensions of beta diversity, and careful consideration of user-defined metacommunity boundaries in beta diversity analyses.

Finished and unfinished rhythm in architectural composition

The rhythm was at all times and in all forms of art. Already in the countries of the Ancient East the composition was ordered, distinguished by strictness, the presence of rhythm. In ancient Egyptian and Greek art rhythm was also the main form of composition.
 In the Renaissance rhythm was considered one of the three main tasks of composition. Knowledge about rhythm as an integral compositional means is constantly expanding, especially after the first theoretical works on architectural composition. Rhythm is an even alternation of ordered elements and is considered one of the most influential means of creating a coherent architectural composition.
 Rhythmic (metrical) order as a regularity can develop endlessly, but in an artistic composition, where integrity and unity of form are an integral attribute, repetition must have certain limits, a series must have a limited length and have a beginning and an end. In this connection a number of creative problems arise when using rhythm in specific architectural compositions of the frontal surface. It is necessary to notice the peculiarity of the combination of three elements in the composition – if there is a clearly expressed axis, then the ternary rhythm (the one consisting of only 3 elements) is considered complete, if there are elements built according to an increasing or decreasing vector, then this type of ternary rhythm must be completed by methods of stopping the rhythm. On the frontal architectural plane the rhythm can appear in an unstoppable form when the idea of the work consists in bringing the viewer's thought out of the compositional field – an opportunity to have own thoughts about the work, to get the answers outside the creation. In this case the rhythm really does not stop visually. In order for such frontal compositions to feel complete the elements of the rhythmic series and the composition in general must be carefully proportioned, or the stop of the rhythm must be manifested by the natural boundaries of the form which is not visible visually but sensuously encompasses the rhythmic series. The finished rhythm can be achieved by the main ways of stopping it in the composition: form, "extreme element", "rhythm – counter rhythm", stopping the vertical rhythm with a horizontal one. The use of methods of stopping the rhythm in compositional practice simplifies the creation of a complete composition.

О ЕСТЕСТВЕННЫХ ГРАНИЧНЫХ УСЛОВИЯХ В ЗАДАЧЕ О ПОТЕРЕ УСТОЙЧИВОСТИ ПЛАСТИНЫ С ЭЛЛИПТИЧЕСКОЙ ВСТАВКОЙ ПРИ РАСТЯЖЕНИИ

This paper studies the issue of determination and influence of natural boundary conditions in the problem of buckling of a thin plate with an elliptical inclusion under tension. First, the naturalness of the boundary conditions of the “free edge” type for a plate with a hole is proved. Then a plate with welded inclusion is considered and natural boundary conditions are derived. The limit cases are checked for an absolutely soft inclusion and for an absolutely rigid one. It is shown that the first case leads to a problem with a hole and the corresponding natural boundary conditions, and in the second case, to the absence of natural conditions, since a problem with a clamped edge occurs. The authors conclude that the use of additional restrictions will lead to the construction of a basis that will rapid up the convergence of the method. Variational methods are widely used in all fields of mechanics, including in the field of machine, aircraft, and rocket engineering. An exact solution to the problems of elasticity theory and structural mechanics is not always possible to construct, therefore, in practice, great importance is attached to various approximate methods. Among them a special place is occupied by variational methods based on the direct minimization of the corresponding energy of the body and making it possible to build approximate analytical solutions in the form of a functional series. The goal of variational methods is to construct a partial sum of this series, which, with a sufficient number of terms, will be maximum close to the solution. However, the issue of convergence is influenced by many factors, and one of them is the natural boundary conditions, which are derived in this paper for the problem of the stability loss of the plate with the elliptical inclusion under tension.

Invading the Greek Seas: Spatiotemporal Patterns of Marine Impactful Alien and Cryptogenic Species

The Greek Seas are greatly exposed to the proliferation of marine alien species. At least 242 alien species have been reported within Greek territorial waters, three-quarters of which are considered established, while their rate of introduction is increasing. Some of these species exhibit high invasiveness, imposing severe impacts on native ecosystems and ecosystem services. The spatiotemporal proliferation of these species outside their natural boundaries depends on several parameters, including their biological characteristics, native distribution range, introduction pathway, and time of initial introduction. Knowing the current and potential alien species distribution is essential for the implementation of effective management actions. To investigate the distribution of impactful cryptogenic and alien species (ICAS) in the Greek Seas, we combined all records available until the end of 2020 from eight types of data sources: (1) scientific literature, (2) grey literature, (3) offline databases, (4) online scientific databases, (5) personal observations of independent researchers, (6) communications with divers and diving centers, (7) in situ underwater sampling, and (8) social networks. The results of 5478 georeferenced records refer to 60 marine ICAS belonging to 16 taxonomic groups. The number of records and the overall number of ICAS present an increasing trend from the northern to the southern parts of our study area, and there is a clear distinction in community composition between the northern and southern subregions. This latitudinal gradient is mainly due to the large number of thermophilous Lessepsian species of West Indo-Pacific origin, which reach the southern parts of the study area through unaided dispersal. On the other hand, transport stowaways appear to be more prevalent in areas located near large ports, which show significant differences in ICAS numbers and community composition compared to sites located far from ports. Most records (>40% of the total) were associated with rocky reefs, partly reflecting the preference of divers for this habitat type but also the presence of conspicuous, reef-associated impactful fish. The number of published records, as well as the number of reported ICAS, shows a dramatic increase with time, highlighting the urgent need for immediate proactive management actions and scientifically informed control measures.