Search Results (343)

This paper introduces a specific matrix spectral problem involving four potentials and derives an associated soliton hierarchy using the zero-curvature formulation. The bi-Hamiltonian formulation is derived via the trace identity, thereby establishing the hierarchy’s Liouville integrability. This is exemplified through two systems: generalized combined NLS-type equations and modified KdV-type equations. Owing to Liouville integrability, each member of the hierarchy admits a bi-Hamiltonian structure and, consequently, possesses infinitely many symmetries and conservation laws. Full article

This study presents a simulation-based damage modeling and fatigue risk assessment of a reusable ceramic matrix composite thruster designed for short-duration, green bipropellant propulsion systems. The thruster is constructed from a fiber-reinforced ultra-high temperature ceramic matrix composite composed of zirconium diboride, silicon carbide, and carbon fibers. Time-resolved thermal and structural simulations are conducted on a validated thruster geometry to characterize the severity of early-stage thermal shock, stress buildup, and potential degradation pathways. Unlike traditional fatigue studies that rely on empirical fatigue constants or Paris-law-based crack-growth models, this work introduces a simulation-derived stress-margin envelope methodology that incorporates ±20% variability in temperature-dependent material strength, offering a physically grounded yet conservative risk estimate. From this, a normalized risk index is derived to evaluate the likelihood of damage initiation in critical regions over the 0–10 s firing window. The results indicate that the convergent throat region experiences a peak thermal gradient rate of approximately 380 K/s, with the normalized thermal shock index exceeding 43. Stress margins in this region collapse by 2.3 s, while margin loss in the flange curvature appears near 8 s. These findings are mapped into green, yellow, and red risk bands to classify operational safety zones. All the results assume no active cooling, representing conservative operating limits. If regenerative or ablative cooling is implemented, these margins would improve significantly. The framework established here enables a transparent, reproducible methodology for evaluating lifetime safety in ceramic propulsion nozzles and serves as a foundational tool for fatigue-resilient component design in green space engines. Full article

In this paper, we investigate the memory effects introduced by the time-fractional Schrödinger equation proposed by Naber on quantum entanglement and quantum dense coding under amplitude damping noise. Two formulations are analyzed: one with fractional operations applied to the imaginary unit and one without. Numerical results show that the formulation without fractional operations on the imaginary unit may be more suitable for describing non-Markovian (power-law) behavior in dissipative environments. This finding provides a more physically meaningful interpretation of the memory effects in time-fractional quantum dynamics and indirectly addresses fundamental concerns regarding the violation of unitarity and probability conservation in such frameworks. Our work offers a new perspective for the application of fractional quantum mechanics to realistic open quantum systems and shows promise in supporting the theoretical modeling of decoherence and information degradation. Full article

The escalating demand for efficient thermal management in lithium-ion batteries necessitates precise characterization of their thermal behavior under diverse operating conditions. This study develops a three-dimensional (3D) electrochemical–thermal coupling model grounded in porous electrode theory and energy conservation principles. The model solves multi-physics equations such as Fick’s law, Ohm’s law, and the Butler–Volmer equation, to resolve coupled electrochemical and thermal dynamics, with temperature-dependent parameters calibrated via the Arrhenius equation. Simulations under varying discharge rates reveal that high-rate discharges exacerbate internal heat accumulation. Low ambient temperatures amplify polarization effects. Forced convection cooling reduces surface temperatures but exacerbates core-to-surface thermal gradients. Structural optimization strategies demonstrate that enhancing through-thickness thermal conductivity reduces temperature differences. These findings underscore the necessity of balancing energy density and thermal management in lithium-ion battery design, proposing actionable insights such as preheating protocols for low-temperature operation, optimized cooling systems for high-rate scenarios, and material-level enhancements for improved thermal uniformity. Full article

This paper explores the complex dynamics of mixed convective flow in a Casson fluid saturated in a non-Darcy porous medium, focusing on the influence of gyrotactic microorganisms, internal heat generation, and multiple convective mechanisms. Casson fluids, known for their non-Newtonian behavior, are relevant in various industrial and biological contexts where traditional fluid models are insufficient. This study addresses the limitations of the standard Darcy’s law by examining non-Darcy flow, which accounts for nonlinear inertial effects in porous media. The governing equations, derived from conservation laws, are transformed into a system of no linear ordinary differential equations (ODEs) using similarity transformations. These ODEs are solved numerically using a finite differencing method that incorporates central differencing, tridiagonal matrix manipulation, and iterative procedures to ensure accuracy across various convective regimes. The reliability of this method is confirmed through validation with the MATLAB (R2024b) bvp4c scheme. The investigation analyzes the impact of key parameters (such as the Casson fluid parameter, Darcy number, Biot numbers, and heat generation) on velocity, temperature, and microorganism concentration profiles. This study reveals that the Casson fluid parameter significantly improves the velocity, concentration, and motile microorganism profiles while decreasing the temperature profile. Additionally, the Biot number is shown to considerably increase the concentration and dispersion of motile microorganisms, as well as the heat transfer rate. The findings provide valuable insights into non-Newtonian fluid behavior in porous environments, with applications in bioengineering, environmental remediation, and energy systems, such as bioreactor design and geothermal energy extraction. Full article

This paper presents a high-order structure-preserving difference scheme for the nonlinear space fractional sine-Gordon equation with damping, employing the triangular scalar auxiliary variable approach. The original equation is reformulated into an equivalent system that satisfies a modified energy conservation or dissipation law, significantly reducing the computational complexity of nonlinear terms. Temporal discretization is achieved using a second-order difference method, while spatial discretization utilizes a simple and easily implementable discrete approximation for the fractional Laplacian operator. The boundedness and convergence of the proposed numerical scheme under the maximum norm are rigorously analyzed, demonstrating its adherence to discrete energy conservation or dissipation laws. Numerical experiments validate the scheme’s effectiveness, structure-preserving properties, and capability for long-time simulations for both one- and two-dimensional problems. Additionally, the impact of the parameter $\epsilon$ on error dynamics is investigated. Full article

Underwater exploration is vital for advancing scientific understanding of marine ecosystems, biodiversity, and oceanic processes. Autonomous underwater vehicles and sensor platforms play a crucial role in continuous monitoring, but their operational endurance is often limited by energy constraints. Various control strategies have been proposed to enhance energy efficiency, including robust and optimal controllers, energy-optimal model predictive control, and disturbance-aware strategies. Recent work introduced a variable structure depth controller for a sensor platform with a variable buoyancy module, resulting in a 22% reduction in energy consumption. This paper extends that work by providing a formal stability proof for the proposed switching controller, ensuring safe and reliable operation in dynamic underwater environments. In contrast to the conventional approach used in controller stability proofs for switched systems—which typically relies on the existence of multiple Lyapunov functions—the method developed in this paper adopts a different strategy. Specifically, the stability proof is based on a novel analysis of the system’s trajectory in the net buoyancy force-versus-depth error plane. The findings were applied to a depth-controlled sensor platform previously developed by the authors, using a well-established system model and considering physical constraints. Despite adopting a conservative approach, the results demonstrate that the control law can be implemented while ensuring formal system stability. Moreover, the study highlights how stability regions are affected by different controller parameter choices and mission requirements, namely, by determining how these aspects affect the bounds of the switching control action. The results provide valuable guidance for selecting the appropriate controller parameters for specific mission scenarios. Full article

Ecological ethics is gaining traction. Can this new attitude towards our ecosystems help to motivate a change in our relationship with land and nature? Can we move towards a legal system that supports the legal personality of land, devoid of human ownership? There are substantial amounts of international environmental laws that have been hovering on the fringes of defining and then redefining our relationship with land, with more emphasis on respecting the land as itself rather than as a vehicle with which humanity can gain wealth. This article briefly explores the conjunction of international environmental law history and ecological ethics in the hope that it will encourage a segue in our approach to conservation, ecology, and being. Full article

The tasar silk production of India’s sericulture industry supports tribal livelihoods and economic sustainability. However, Antheraea mylitta Drury, 1773, the primary species for tasar silk, faces habitat threats due to deforestation, climate change, and anthropogenic pressures. This study evaluates the distribution and habitat suitability of wild tasar silkworm using multi-criteria approach, Geographic Information System (GIS), Remote Sensing (RS), and ecological niche modeling using the MaxEnt algorithm. Field surveys were conducted to collect cocoon samples, and the analysis of environmental parameters and assessment of soil micronutrient influences were also carried out. The MaxEnt model predictions indicate that the Central, Western, and Southern zones of Mayurbhanj, encompassing the Similipal Biosphere Reserve, provide the most suitable habitats. The jackknife test confirmed that these climatic variables collectively contributed 68.7% to the habitat suitability model. This study highlights the impact of habitat fragmentation and deforestation on tasar silkworm populations, emphasizing the need for conservation strategies, sustainable forest management, and afforestation programs. The findings highlight the following key conservation strategies: restoring habitats in Similipal, enforcing anti-deforestation laws, promoting community-led planting of host trees, and adopting climate-resilient silk farming to protect biodiversity and support tribal livelihoods. Full article

This study aims to investigate a chronological review of the term museum, defined by the International Council of Museums (“ICOM”) and Korean laws, and explore how the museum definitions have been revised historically. Then, it argues how the museum architecture has been spatially changed and explores whether the revised social roles and ethical responsibilities would impact the restructuring of the spatial changes. To this end, it scrutinized new ideas, significant issues, orders of words, and implicit intentions of the museum definitions over time. It analyzed the data of spatial change projects, which were collected through web crawling of the Korean National e-Procurement System. Then, the spatial changes were categorized regarding functions and characteristics. Through an in-depth investigation of a literature review and case studies, the findings suggest that museums had been understood as a place for collecting, exhibiting, and enjoying materials. However, they have been required to play diverse roles, such as collecting, conserving, exhibiting, researching, and communicating heritage for education, reflection, and sharing knowledge over time. However, the issue of cultural enjoyment has come into focus in Korean laws after 2007, and, as a result, spatial changes (e.g., creating immersive experience center, renovating exhibition spaces, and improving convenience spaces) have taken place exclusively in national museums. Thus, it is clear that national museums are aware of the need to actively think about their role with regard to the public and how architecture corresponds to this. Full article

This article presents a comprehensive study of the (2+1)-dimensional Zakharov–Kuznetsov (ZK) $(q,p,r)$ equation with time fractional derivativeUtilizing the fractional Lie group method, we derive several results, including the symmetries, similarity reductions and conservation laws for this equation. Our findings not only correct previous errors in the literature but also introduce new results, such as the Lie transformation group and optimal system for this model. The study provides a rigorous mathematical framework for analyzing this fundamental model, which describes nonlinear ion-acoustic wave evolution in magnetized plasmas. Full article

Waves on graphs are a current subject of research interest. As opposed to flows on graphs, the reflection–transmission of waves at the graph’s vertex is a problem that needs to be further modelled mathematically. The literature on the reflection and transmission of waves at a vertex is scarce. Some articles are reviewed and discussed. Water waves are a good topic for comparing different mathematical models, from hyperbolic conservation laws to weakly nonlinear, weakly dispersive systems of partial differential equations on a two-dimensional fattened (thick) graph and the respective one-dimensional graph-model reduction. In this study, we present a particular water wave model in which junction angles are systematically included in the mathematical model. Comparing the solutions with the fattened-graph model gave rise to a more general compatibility condition at the vertex. Current research topics of interest are outlined at the end. Full article

This paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term. Based on Painlevé analysis, sufficient and necessary conditions for the equation’s Painlevé integrability are obtained. Under specific integrability conditions, the Lax pair for this equation is successfully constructed using the extended Ablowitz–Kaup–Newell–Segur system (AKNS system). Furthermore, the Riccati-type Bäcklund transformation (R-BT), Wahlquist–Estabrook-type Bäcklund transformation (WE-BT), and the nonlinear superposition formula are derived. In utilizing these transformations and the formula, explicit one-soliton-like and two-soliton-like solutions are constructed from a seed solution. Moreover, the infinite conservation laws of the equation are systematically derived. Finally, the influence of variable coefficients and the external-force term on the propagation characteristics of a solitory wave is discussed, and soliton interaction is illustrated graphically. Full article

The Boronia Ridge palusmont, Walpole, in southern Western Australia, is situated in the most humid part of the State. It was a unique hilltop wetland complex and the only one of its type in the State. On its margins, the area also supports the ancient sedge Reedia spathacea, a Gondwanan relict endemic to humid southern Western Australia and the Walpole region and a plant that was ultimately recognised as being of national significance and protected under Australia’s strongest conservation law, the Environment Protection and Biodiversity Act (1999). However, prior to the geoheritage and biodiversity values of the area being known, in the late 1980s, a pristine scenic area west of Walpole, adjacent to the Walpole River and Walpole Inlet, classified as a Class A national park, was earmarked for urban development, in spite of there being “very little demonstrated requirement for land in Walpole”. This appeared to be as a result of poor land-use planning, since the urbanisation proposed was to be located on the Walpole River delta and wetlands. Urban infrastructures would also impact on adjoining wetlands and the Walpole Inlet System. With new information available in relation to the soils, wetlands, and environmental values of the area, in 1993, community groups and scientists combined, at a public Local Government meeting, to demonstrate that the proposed urban development, referred to as Lot 650, and later Boronia Ridge, with its above-land surface wastewater treatment, was inappropriate, both from an engineering perspective and due to the high conservation values of the area. With the support of the local government of the day and expert scientists who confirmed local concerns, the community engaged in a 7-year conflict with the development proponent, government agencies involved in decision making, and politicians of the day. Ultimately, the use of state-of-the-art science and traditional geomorphic, stratigraphic, hydrological, and geoheritage principles failed to prevent the urbanisation of the area in favour of preserving the whole area as a wetland complex. The following three reasons for this failure are identified: 1. political, rather than science-based decision making, 2. government agencies staffed without the necessary training in biological or earth sciences to make informed decisions, and 3. little attention to environmental concerns due to a bias towards development. Walpole, with its population of 400, moved from a low priority on the wastewater treatment priority list in Western Australia to a high priority on the deep sewerage priority list to accommodate a proposed residential development. Full article

In this paper, the mechanism of interlayer bonding under a low-temperature environment is systematically revealed in terms of the temperature control difficulties in the continuous multilayer construction of an asphalt concrete core wall in winter. A field simulation paving test was conducted using a temperature-controllable simulated paving system, and the key laws of the temperature transfer and mechanical property evolution were discovered by precisely regulating the surface temperature of the bonded surface (the test range covered from −5 °C to 70 °C). This study shows that a bonding surface temperature of 40 °C is a critical point of engineering importance, at which the material exhibited a unique performance compensation effect. Under this temperature condition, although the mechanical index was reduced compared with the parent material, the flexural strength was reduced by 11.39%, the maximum bending strain was reduced by 9.65%, the tensile strength was reduced by 7.89%, the critical tensile strain was reduced by 16.11%, and the crack curvature coefficient was reduced by 10.06%. However, thanks to the unique structural reorganization characteristics of asphalt materials, these performance losses were effectively compensated, thus ensuring the stability of engineering applications. In particular, a fast rise–stable–slow decline evolution law of the interlayer temperature transfer was found, proving the existence of a temperature-adaptive interval of the bond surface. The research results not only enrich the theory of asphalt concrete interlayer bonding but also provide innovative technical solutions for the construction of water conservancy projects in cold regions. In particular, the fast rise–stable–slow drop evolution law of the interlayer temperature transfer was found, which proves the existence of a temperature-adaptive interval of the bond surface. The research results not only enrich the theory of asphalt concrete interlayer bonding but also provide innovative technical solutions for the construction of water conservancy projects in cold regions. Full article