Natural Boundary Research Articles

An analytical method for the vibration characteristics of double panel structures with uniform elastic boundary supports

ABSTRACT In this paper, the methods for solving the free vibration and forced vibration of double panel structures under arbitrary boundaries are studied. Based on the Mindlin plate theory, the natural boundary between plates and plates is constrained by artificial springs, and the theoretical model of the structure is derived. The displacement function of in-plane vibration and bending vibration is expressed by a modified Fourier series expansion. The effectiveness and reliability of this method are verified by a series of numerical calculations and comparison with those of the finite element method. Through the parameter analysis, it can be seen that the vibration isolation effect can be increased by properly increasing the coupling height or making the connecting plate closer to the boundary of the bottom plate. The method presented in this paper can be used in vibration absorption and structural design of such structures.

Modified Shooting with Discretization Validation for Non-Standard Optimal Control Problem: Case Study for Four-Stage Royalty Payment Problem

A modified shooting method augmented by discretization validation is presented in this paper to address the challenges inherent in non-standard optimal control problems. Specifically, a specific case study involving four-stage royalty payment functions is focused on, with the aim of effectively optimizing these complex, non-differentiable functions. The shooting method is adapted and enhanced to compute optimal solutions, and its accuracy is rigorously confirmed through discretization techniques. The primary objectives involve maximizing the performance index and determining optimal control strategies for scenarios where the final state variable remains unknown. In this study, the royalty payment is defined as a four-stage piecewise function. The incorporation of piecewise royalty functions introduces non-differentiability at specific time intervals, necessitating innovative approaches for finding optimal solutions. This, in turn, leads to the utilization of the continuous hyperbolic tangent (tanh) function to address the non-differentiability issue. A hybrid shooting method, combining the Newton and Golden Section Search methods, is employed in the C++ programming language to compute the unknown final state value. A new natural boundary condition, based on established theory, is introduced to further facilitate the investigation. Discretization methods such as Euler, Runge-Kutta, Trapezoidal, and Hermite-Simpson approximations are employed for validation. The validation process entails the use of the AMPL programming language with the MINOS solver. Comparative analyses reveal that the modified shooting method yields more accurate optimal results than discretization methods, thus demonstrating the method’s effectiveness in addressing non-standard optimal control problems. The significance of fundamental theories in addressing real-world challenges is underscored by this research, providing valuable insights for future researchers exploring mathematical approaches in similar contexts. The study contributes to the continued relevance of the academic field, particularly in science and mathematics education.

Analytical solutions for strain-driven Timoshenko nanobeam bending using generalized functions

Static nanobeam bending problems have yielded conflicting results from many researchers. Methods suggested by numerous researchers have shown inconsistencies in capturing size effects and satisfying essential and natural boundary conditions for nanobeam configurations when subjected to different types of loading. This work proposes an alternative approach using Eringen’s strain-driven integral nonlocal elasticity to arrive at analytical solutions. The theory of generalized functions and the Dirac-delta identity are used to revisit Timoshenko nanobeam modeling aspects, focusing on nanobeam elastostatics. Proposed analytical solutions for fundamental and derived quantities based on the strain-driven nonlocal model have been compared with the results of existing approaches. A crucial drawback with the strain-driven models of Eringen in both integral and differential form is its inability to satisfy equilibrium equations, which is addressed extensively in this work.

Accessing the Trail, Interpreting the Forest

The Stephen F. Austin Experimental Forest is the site of the first ADA-compliant US Forest Service project in Texas. Offering information about the history of forest management alongside information on Pineywoods ecosystems, the interpretive trail raises questions about how access is framed across “natural” and “built” environments as well as how distinctions between nature and culture operate within US environmental imaginaries. This article draws on feminist, posthumanist, and disability studies to conduct a close reading of the interpretive trail as text. It tracks the trail’s approach to disability access as well as its presentation of forest ecology, analyzing how the ableist logic of capitalist commodification underwrites the management of multispecies actants in the woods. I read against the grain of the trail in search of feminist, crip, posthumanist configurations of interdependence and more fluid human–nature boundaries. I argue that cripping the Austin requires questioning the unevenness of disability access as well as the utilitarian ideas of nature presented on the trail while also imagining how we might access and relate to this postindustrial forest otherwise.

Inter- and Intra-Annual Variations in Oak Tree Ring δ13C Values across Different Elevations and Their Climatic Responses in Qinling Mountains

The Qinling Mountains, serving as a natural geographical and climatic boundary in China, require comprehensive climatic records to elucidate the trends in climate changes across the country. While stable isotopes in tree rings are widely employed to indicate historical environmental changes, investigations into tree ring isotopes in the Qinling Mountains, particularly within the widespread broad-leaf oaks, remain limited. In this study, we investigated both intra- and inter-annual variations in the δ13C values of tree rings and their correlations with climatic signals over the past two decades for Quercus aliena var. acuteserrata, a dominant species among oak trees on the main peak of the Qinling Mountains. Our results reveal that responses to climate differ among altitudes and individual trees, with trees at higher altitudes exhibiting higher sensitivity to extreme climate, which is low temperatures and rainfall fluctuations during the growth period in intra-annual δ13C variations. Furthermore, the positive correlations are observed between temperature during growing season and both tree growth and the inter-annual δ13C variations. However, the climate signal appears to be hampered by oak-specific factors, such as intense competition among individuals and the age of trees. Therefore, we suggest a more rigorous selection of sampling and propose further investigations into isotopic fractionation processes in oaks for future studies.

Environmental geomorphology of Wadi Al-Batin, Kuwait: Unveiling natural and anthropogenic influences

Wadi Al-Batin is an ancient valley that acts as the natural boundary between Iraq and Kuwait and is part of the larger Wadi Al-Rummah Basin in Saudi Arabia. Since the 1980s, human activities like military zones, oil fields, and camps have caused significant environmental changes in the area's geological, geomorphological, and hydrological conditions. This study investigates changes in the geomorphology, sedimentology, and topography of Wadi Al-Batin, land degradation and environmental changes caused by artificial landforms and natural factors and provides an update to the sedimentological map of Wadi Al-Batin. The study utilized field observations, geographical information systems (GIS), and remote sensing (RS) techniques to develop a geodatabase across various disciplines. A detailed map of the environmental geomorphological changes in Wadi Al-Batin was created using satellite imagery from 2000 to 2023 to provide up-to-date and precise information. The study also considered changes in the normalized difference vegetation index (NDVI) and normalized difference water index (NDWI) as indicators of environmental change. The results indicate that the surface deposits exhibited polymodal and trimodal modes (40% and 36%, respectively), were sandy and medium-coarse-grained, and showed variability in sorting, skewness, and kurtosis. They originated from the Upper Member of the Dibdibah Formation, were frequently fluvially reworked, and predominantly consisted of quartz with lower amounts of calcite. This study contributes to the preservation of environmental systems and assists decision-makers in protecting the rights of future generations to a sustainable environment.

A Jacobi-Ritz Approach for Aeroelastic Analysis of Swept Distributed Propulsion Aircraft Wing

Abstract This paper presents a Jacobi-Ritz approach for conducting flutter and divergence analysis of a complex distributed propulsion aircraft wing like NASA X-57. The general orthogonal Jacobi polynomials are used to approximate the bending displacement and torsional rotation angle in the Ritz method based structural and aeroelastic analysis. The Jacobi polynomials satisfy the orthogonality condition using weight functions which are easily modified to satisfy different essential and natural boundary conditions. Compared to simple polynomials, Jacobi polynomials can eliminate the well-known ill-conditioning numerical issues when considering higher-order polynomials. The Jacobi-Ritz method is also found to alleviate mode switching often encountered in tracking the changes of modes with the varying airspeed. The Jacobi-Ritz method is later used to investigate the flutter and divergence speeds under distributed propulsor mass and their locations, nonuniform aerodynamic model in the presence of multiple propulsors, and the sweep angle. Results show that placing the distributed propulsors on the wing's leading edge increases the flutter speed even though the bending and torsion modal frequencies are decreased compared to those of the wing without propulsors. The presence of pods for the middle high-lift motors causes an extra aerodynamic moment which reduces the flutter speed. Parametric studies also show that the divergence speed is lower than the flutter speed for a uniform and straight distributed propulsor wing. Using swept-back wing configuration and placing the tip propulsor near the wing's leading edge can help to increase both flutter and divergence speeds.

Non-constant functions with zero nonlocal gradient and their role in nonlocal Neumann-type problems

This work revolves around properties and applications of functions whose nonlocal gradient, or more precisely, finite-horizon fractional gradient, vanishes. Surprisingly, in contrast to the classical local theory, we show that this class forms an infinite-dimensional vector space. Our main result characterizes the functions with zero nonlocal gradient in terms of two simple features, namely, their values in a layer around the boundary and their average. The proof exploits recent progress in the solution theory of boundary-value problems with pseudo-differential operators. We complement these findings with a discussion of the regularity properties of such functions and give illustrative examples. Regarding applications, we provide several useful technical tools for working with nonlocal Sobolev spaces when the common complementary-value conditions are dropped. Among these, are new nonlocal Poincaré inequalities and compactness statements, which are obtained after factoring out functions with vanishing nonlocal gradient. Following a variational approach, we exploit the previous findings to study a class of nonlocal partial differential equations subject to natural boundary conditions, in particular, nonlocal Neumann-type problems. Our analysis includes a proof of well-posedness and a rigorous link with their classical local counterparts via Γ-convergence as the fractional parameter tends to 1.

Unravelling arthropod movement in natural landscapes: Small-scale effects of body size and weather conditions.

Arthropod movement has been noticeably understudied compared to vertebrates. A crucial knowledge gap pertains to the factors influencing arthropod movement at habitat boundaries, which has direct implications for population dynamics and gene flow. While larger arthropod species generally achieve greater dispersal distances and large-scale movements are affected by weather conditions, the applicability of these relationships at a local scale remains uncertain. Existing studies on this subject are not only scarce but often limited to a few species or laboratory conditions. To address this knowledge gap, we conducted a field study in two nature reserves in Belgium, focusing on both flying and cursorial (non-flying) arthropods. Over 200 different arthropod species were captured and released within a circular setup placed in a resource-poor environment, allowing quantification of movement speed and direction. By analysing the relationship between these movement variables and morphological (body size) as well as environmental factors (temperature and wind), we aimed to gain insights into the mechanisms driving arthropod movement at natural habitat boundaries. For flying species, movement speed was positively correlated with both body size and tailwind speed. In contrast, movement speed of cursorial individuals was solely positively related with temperature. Notably, movement direction was biased towards the vegetated areas where the arthropods were originally caught, suggesting an internal drive to move towards suitable habitat. This tendency was particularly strong in larger flying individuals and under tailwind conditions. Furthermore, both flying and cursorial taxa were hindered from moving towards the habitat by strong upwind. In conclusion, movement speed and direction at patch boundaries are dependent on body size and prevailing weather conditions, and reflect an active decision-making process.

Administrative and Economic Systems of the Mughal Empire: A Historical Analysis of Governance and Revenue Policies

The Mughal Dynasty commenced in 1526, led by the esteemed Babur, who is renowned as the pioneer and founder of Indian civilization through the process of unification. Due to its vast territorial reach from Kabul to Bengal, with natural boundaries such as the Arabian Sea and Himalayas, this dynasty was able to establish sophisticated formal institutions that surpassed those of other empires worldwide at that time. This study examines the complex governance system of The Mughal Empire, with a focus on the reigns of Babur, Humayun, Akbar, and Aurangzeb. Abul-Fazl Ibn Mubarak, a prominent historian during Akbar's reign, elucidated the Mughals' adoption of the dual strategies of 'JahanBani' (state maintenance) and 'Jahangiri' (imperial expansion). The article also examines Akbar's reforms in land revenue systems, which aimed to provide uniformity and economic stability in order to sustain the Empire's prosperity. The inclusion of women in the Mughal court is examined to highlight their cultural, political, and social achievements. This examination thoroughly explores the functioning of the Mughal administration and how it effectively maintained the empire's supremacy.

Phylogeography of Morella nana: The Wumeng Mountains as a natural geographical isolation boundary on the Yunnan-Guizhou Plateau.

The Yunnan-Guizhou Plateau (YGP) is characterized by the distinctive isolated habitat of the limestone Karst Islands and features the Wumeng Mountains, which divide the YGP into the two Plateaus of Yunnan and Guizhou. This study aimed to assess the effects of geographic isolation and past climate fluctuation on the distribution of flora in the YGP. To achieve this, we carried out the phylogeographical pattern and genetic structure based on chloroplast and nuclear ribosomal DNA sequence in relation to past (Last Glacial Maximum) and present distributions based on ecological niche modeling for Morella nana, an important wild plant resource and endemic to the YGP once considered a vulnerable species. The results suggest that the genetic and chlorotype network structures of M. nana are divided into at least two groups: cpDNA chlorotype H2 (or dominant nrDNA haplotypes h1 and h2), distributed primarily to the east of the Wumeng Mountains, and cpDNA chlorotypes H1 and H3-H10 (or dominant nrDNA haplotype h2 and h3), distributed to the west of the Wumeng Mountains. A deep genetic split was noted within the two groups to reach 25 steps, especially for the cpDNA fragment variation. This east-west divergence reveals the existence of a natural geographical isolation boundary in the form of the Wumeng Mountains, and supports the existence of at least two glacial refuges during the Quaternary glacial period, along with two genetic diversity center, and at least two large geographic protection units for the important species of M. nana. This study indicates that the phylogeographical pattern of M. nana can be attributed to geographic/environmental isolation caused by the Wumeng Mountains and climate fluctuation during the last glacial maximum, and proposes an effective strategy to protecting this important plant resource.

Free vibration response of micromorphic Timoshenko beams

In this paper the authors investigate the free vibration of a two-length-scale nonlocal micromorphic Timoshenko beam, which is shown to overlap with the nonlocal strain gradient Timoshenko beam under certain conditions. Hamilton’s principle is utilized to obtain a system of two coupled fourth-order equations of motion governing the eigen-deflection and the eigen-rotation of the beam. Uncoupling both equations leads to two eight-order differential equations. Using Ferrari’s method, exact solutions are derived for the eigenfrequencies for various boundary conditions, including simply supported, clamped-clamped, clamped-free, and clamped-hinged boundary conditions. The obtained results are compared with those published in the literature using similar nonlocal strain gradient cases. A detailed parametric study is then performed to emphasize the role of the variationally-derived higher-order boundary conditions (natural higher-order boundary conditions or mixed higher-order boundary conditions). It is noted that when the difference in length-scales is large, the effect of the slenderness of the beam on the frequencies is amplified. Finally, the hardening or the softening effect of the beam model can be achieved through a choice of the ratio between the two length-scales.

Eco-Innovation in The Peruvian Amazon: Perspectives and Initiatives for A Resilient Future

The Peruvian Amazon is emerging as a hotspot of innovation and sustainability, driving transformational change that transcends geographic boundaries and attracts global attention. In this dynamic and promising context, this article explores the impact of innovation and sustainable development in the Peruvian Amazon region, highlighting its importance in global competitiveness and its potential to lead a resilient and prosperous future. The objective was to analyze the prospects and initiatives for innovation and sustainable development in the Peruvian Amazon region. In particular, it seeks to delve into how these initiatives could catalyze a transformation in the Amazon, strengthening its competitiveness in the global scenario. This study applied a qualitative-descriptive methodology, using surveys and data analysis with SPSS. This methodological choice was based on the need to obtain an exhaustive understanding of the subject, allowing the exploration of both the perceptions and experiences of the participants and the associated numerical data. The sample population consisted of 75 stakeholders. In conclusion, our study represents a significant contribution to the field by addressing a gap in existing knowledge on innovation and sustainable development in the Peruvian Amazon. By presenting new perspectives and approaches, our work provides a more complete and up-to-date understanding of the challenges and opportunities facing the region as it moves towards a sustainable and globally competitive future. the Peruvian Amazon is seen as a transformative agent with potential that transcends its natural boundaries. By adopting a comprehensive and visionary perspective, the region emerges as a beacon of hope for a sustainable and prosperous future. It is essential that future policies and actions recognize and strengthen these transformative perspectives, ensuring equitable and resilient development that benefits present and future generations. In this way, the Peruvian Amazon not only drives its own global competitiveness, but also inspires and leads the way towards a more prosperous and sustainable world.

Chromosome-level genome assembly of a cliff plant Taihangia rupestris var. ciliata provides insights into its adaptation and demographic history

BackgroundCliffs are recognized as one of the most challenging environments for plants, characterized by harsh conditions such as drought, infertile soil, and steep terrain. However, they surprisingly host ancient and diverse plant communities and play a crucial role in protecting biodiversity. The Taihang Mountains, which act as a natural boundary in eastern China, support a rich variety of plant species, including many unique to cliff habitats. However, it is little known how cliff plants adapt to harsh habitats and the demographic history in this region.ResultsTo better understand the demographic history and adaptation of cliff plants in this area, we analyzed the chromosome-level genome of a representative cliff plant, T. rupestris var. ciliata, which has a genome size of 769.5 Mb, with a scaffold N50 of 104.92 Mb. The rapid expansion of transposable elements may have contributed to the increasing genome and its ability to adapt to unique and challenging cliff habitats. Comparative analysis of the genome evolution between Taihangia and non-cliff plants in Rosaceae revealed a significant expansion of gene families associated with oxidative phosphorylation, which is likely a response to the abiotic stresses faced by cliff plants. This expansion may explain the long-term adaptation of Taihangia to harsh cliff environments. The effective population size of the two varieties has continuously decreased due to climatic fluctuations during the Quaternary period. Furthermore, significant differences in gene expression between the two varieties may explain the varied leaf phenotypes and adaptations to harsh conditions in different natural distributions.ConclusionOur study highlights the extraordinary adaptation of T. rupestris var. ciliata, shedding light on the evolution of cliff plants worldwide.

The dimension coupling method for 3D transient heat conduction problem with variable coefficients

In this study, a dimension coupling method (DCM) is presented to study the variable coefficients transient heat conduction problems. The dimension splitting method (DSM) is introduced to split the 3D domain into some 2D domains, which are discretized by selecting the improved element-free Galerkin (IEFG) method; thus the corresponding discretized equation in each 2D domain is derived, and the finite element method (FEM) is employed to deal with these discretized equations in a third direction, and the time-dependent term is discretized by selecting the finite difference method (FDM), thus the final solved equation of the transient heat conduction problems is obtained. In the first example, the convergence is proved by increasing the nodes and meshes on the influence of relative errors. Some numerical results illustrate that the proposed method can substantially enhance the computational efficiency of the IEFG method. When an exact solution of the numerical example is a nonlinear function about splitting direction with natural boundary condition is given, the proposed method has shorter computing time than the hybrid element-free Galerkin (HEFG) method when dealing with this situation.

Response properties of lattice metamaterials under periodically distributed boundary loads

We discuss response properties of lattice metamaterials to sinusoidal distributed static loads applied on a material edge. Analytical displacement solutions are obtained using a Fourier domain transfer matrix for both essential and natural boundary conditions, which are valid for a state of plane strain in orthorhombic lattices, as well as for planar metasurfaces. These solutions give sinusoidal displacement profiles in the material interior of the same wavenumber (spatial frequency) as the boundary load. Their amplitudes decay in the material interior in one of two possible ways, exponential or oscillatory exponential, depending on the lattice design and on the spatial frequency of the load. There is a tendency for the oscillatory exponential behavior to occur at lower wavenumbers representing smoother boundary loads. As explained on a specific example, comparing the metamaterial’s response amplitudes with those of a homogenous material also allows studying an effective, wavenumber-dependent shear modulus of the lattice, which can take both positive and negative values.

Prospective Spatiotemporal Cluster Detection Using SaTScan: Tutorial for Designing and Fine-Tuning a System to Detect Reportable Communicable Disease Outbreaks.

Staff at public health departments have few training materials to learn how to design and fine-tune systems to quickly detect acute, localized, community-acquired outbreaks of infectious diseases. Since 2014, the Bureau of Communicable Disease at the New York City Department of Health and Mental Hygiene has analyzed reportable communicable diseases daily using SaTScan. SaTScan is a free software that analyzes data using scan statistics, which can detect increasing disease activity without a priori specification of temporal period, geographic location, or size. The Bureau of Communicable Disease's systems have quickly detected outbreaks of salmonellosis, legionellosis, shigellosis, and COVID-19. This tutorial details system design considerations, including geographic and temporal data aggregation, study period length, inclusion criteria, whether to account for population size, network location file setup to account for natural boundaries, probability model (eg, space-time permutation), day-of-week effects, minimum and maximum spatial and temporal cluster sizes, secondary cluster reporting criteria, signaling criteria, and distinguishing new clusters versus ongoing clusters with additional events. We illustrate how to support health equity by minimizing analytic exclusions of patients with reportable diseases (eg, persons experiencing homelessness who are unsheltered) and accounting for purely spatial patterns, such as adjusting nonparametrically for areas with lower access to care and testing for reportable diseases. We describe how to fine-tune the system when the detected clusters are too large to be of interest or when signals of clusters are delayed, missed, too numerous, or false. We demonstrate low-code techniques for automating analyses and interpreting results through built-in features on the user interface (eg, patient line lists, temporal graphs, and dynamic maps), which became newly available with the July 2022 release of SaTScan version 10.1. This tutorial is the first comprehensive resource for health department staff to design and maintain a reportable communicable disease outbreak detection system using SaTScan to catalyze field investigations as well as develop intuition for interpreting results and fine-tuning the system. While our practical experience is limited to monitoring certain reportable diseases in a dense, urban area, we believe that most recommendations are generalizable to other jurisdictions in the United States and internationally. Additional analytic technical support for detecting outbreaks would benefit state, tribal, local, and territorial public health departments and the populations they serve.

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

The non-Oberbeck–Boussinesq effects on the stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equations for air flows up to a temperature difference of $\Delta T=100\,{\rm K}$ . Based on the linear stability results, the neutral curve is shown to be sensitive to the choice of reference temperature. When evaluated using the film temperature $T_f$ , a lower film Grashof number is required to trigger the linear instability for larger $\Delta T$ . The relative contributions of shear and buoyant production to the perturbation kinetic energy budget reveals that the marginally unstable modes are amplified based on different mechanisms: for lower wavenumbers at relatively small Grashof number, the instability is driven by buoyancy; whereas for higher wavenumbers and larger Grashof number, the flow becomes unstable due to a shear instability. The use of reference temperature is found to scale the shear- and buoyant-driven instabilities differently so that no single reference temperature definition would collapse the neutral curves. The linear stability result further demonstrates that at a given Grashof number a higher temperature difference would give a larger amplification rate of the perturbation, which then leads to an earlier onset of the nonlinearities when evaluated at $T_f$ . Finally, by comparing the amplification rates obtained from direct numerical simulation and the linear stability results, the extent of the linear regime is determined for $\Delta T = 100\,{\rm K}$ .

FENNECS: A novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

This paper presents the new 2D electrostatic particle-in-cell code FENNECS developed to study the formation of magnetized non-neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun design, but solves general equations and can be applied in other domains of plasma physics. FENNECS is capable of simulating electron-neutral collisions using a Monte Carlo approach and considers both elastic and inelastic (ionization) processes. It is also capable of solving the Poisson equation on domains with arbitrary geometries with either Dirichlet or natural boundary conditions. The Poisson solver is based on a meshless Finite Element Method, called web-splines, based on b-splines of any order, and used for the first time in the domain of plasma physics. In addition, the effect of fast ions colliding with the electrodes and causing ion induced electron emission at the electrode surfaces has been implemented in the code. In this paper, the governing equations solved by FENNECS and the numerical methods used to solve them are presented. A number of verification cases are then reported. Finally, the parallelization scheme used in FENNECS and its parallel scalability are presented.

On the natural transition of the natural convection boundary layer under a constant heat flux condition

This study investigates the thermo-fluidic characteristics of a natural convection boundary layer over a vertical plate heated under a constant heat flux condition. We used particle image velocimetry to observe the surface convection velocity at the proximity of the plate, which is submerged in a water chamber with Rayleigh number, Ra=7×109 and Prandtl number, Pr = 8.1. The velocity distributions indicated the presence of distinct stripe-like flow structures in the early transition (upstream) region and that of distinct negative–positive Λ-shaped flow structures in the downstream region. In addition, the temporal variation of spanwise and streamwise velocity components was presented. Furthermore, proper orthogonal decomposition (POD) analysis was used to reduce the complexity of the flow structure and retain the most salient characteristics of the flow field. Our results confirmed the existence of a very weak inceptive oscillation in the behaviour of POD time coefficients in the upstream region.