Prototype Case Research Articles

Evaluation of Motorcycle Brands Using Multi-attribute Decision-Making Method Under Single-Valued Neutrosophic Cubic Hypersoft Set Environment

The process of motorcycles evaluation is intricate and influenced by several factors that are uncertain, indeterminate and vague. It is difficult to estimate to what extent the choice will satisfy all requirements and change with the times. The theoretical frameworks such as hypersoft sets, interval and single-valued neutrosophic sets are useful in managing such vagueness and uncertainty. This study introduces a novel theoretical framework; the single-valued neutrosophic cubic hypersoft set (svNCHSS), to mitigate the loss of useful data. In comparison to the frameworks mentioned above, the svNCHSS is more adaptable in handling ambiguous and unpredictable circumstances because it incorporates all of their limitations as a single model. The set-theoretic operations like P-union (⊔P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\sqcup _{P})$$\\end{document}, P-intersection (⊓P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$( \\sqcap _{P})$$\\end{document}, R-union (⊔R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$( \\sqcup _{R})$$\\end{document}, R-intersection (⊓R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\sqcap _{R})$$\\end{document}, AND- and OR-operations are investigated for svNCHSS environment. Two potent algorithms are proposed in the context of a decision-assisted mechanism that employs AND- and OR-operations for the evaluation of motorbikes taking into account multi-argument-based factors. To evaluate the suggested algorithms’ effectiveness, a prototype case study is used for validation. The computed results are then compared. The structural comparison reveals the flexibility of svNCHSS, making its aggregation operations a useful tool for a variety of industrial applications, including risk assessment, process improvement, and decision-making.

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N=1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Integrating the probe and singular sources methods

Abstract The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods.

Frequent Errors in Modeling by Machine Learning: A Prototype Case of Predicting the Timely Evolution of COVID-19 Pandemic

Background: The development and application of machine learning (ML) methods have become so fast that almost nobody can follow their developments in every detail. It is no wonder that numerous errors and inconsistencies in their usage have also spread with a similar speed independently from the tasks: regression and classification. This work summarizes frequent errors committed by certain authors with the aim of helping scientists to avoid them. Methods: The principle of parsimony governs the train of thought. Fair method comparison can be completed with multicriteria decision-making techniques, preferably by the sum of ranking differences (SRD). Its coupling with analysis of variance (ANOVA) decomposes the effects of several factors. Earlier findings are summarized in a review-like manner: the abuse of the correlation coefficient and proper practices for model discrimination are also outlined. Results: Using an illustrative example, the correct practice and the methodology are summarized as guidelines for model discrimination, and for minimizing the prediction errors. The following factors are all prerequisites for successful modeling: proper data preprocessing, statistical tests, suitable performance parameters, appropriate degrees of freedom, fair comparison of models, and outlier detection, just to name a few. A checklist is provided in a tutorial manner on how to present ML modeling properly. The advocated practices are reviewed shortly in the discussion. Conclusions: Many of the errors can easily be filtered out with careful reviewing. Every authors’ responsibility is to adhere to the rules of modeling and validation. A representative sampling of recent literature outlines correct practices and emphasizes that no error-free publication exists.

VISIVIA research project: set-up of the VISIT (Visual Inspection for Safety-deficit Identification and Triage) methodology and application on a prototype case on the road SS13 "Pontebbana".

The purpose of this work is to describe the development of the VISIT methodology (Visual Inspection for Safety- deficit Identification and Triage) and illustrate the first prototypal tests on a real case of the computerized inspection system. The tests were organized at the University of Udine – SPRINT-Lab Safety and Protection Intersectoral Laboratory, and took place on the SS13 “Pontebbana”, a key connection road in the North-Est of Italy. This work illustrates how the new developed VISIT tools permit to acquire and manage the inspection data, in order to process and summarize them in a standardized way for a situational overview dashboard of the National Agency for Safety of Railway and Road Infrastructures (ANSFISA). The VISIT methodology aims to highlight the need for improving road infrastructures safety by the managing entities. The results of the prototype tests were positive. Therefore, the project moved on to the subsequent phases, which will allow the definition of the supervision and intervention request strategies in a contextualized manner, through a unique and innovative system. This system will support ANSFISA in its objectives of vigilance aimed at improving the levels of safety and regularity of road traffic on the Italian network.

Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings

<abstract><p>Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.</p></abstract>

A video-atlas of levodopa-induced dyskinesia in Parkinson's disease: terminology matters.

Dyskinesia is a common complication of long-term levodopa therapy in patients with Parkinson's disease (PD), which often worsens the quality of life. It is usually dose-dependent and emerges possibly due to pulsatile stimulation of dopamine receptors. Delineating the pattern of dyskinesia is crucial for determining the most effective therapeutic approach, a task that often presents challenges for numerous neurologists. This article comprehensively describes various patterns of dyskinesia in PD patients and features video demonstration of some of the common forms of dyskinesia. We have used a real case scenario as an example to lead the discussion on the phenomenology, distinguishing features, and management of various types of dyskinesia. A comprehensive literature search was conducted in PubMed using "dyskinesia" as a keyword. The prototype case with videos highlights the differentiating features of dyskinesia along with the treatment strategies. A wide range of descriptive rubrics have been used for certain dyskinesia which are described in detail in this article. The newer types of dyskinesia associated with continuous dopaminergic stimulation in patients with advanced PD and their implications have been described. As there are distinct ways of managing various types of dyskinesia, understanding the phenomenology and chronology of dyskinesia is vital for the optimal management of dyskinetic PD patients. We suggest that dyskinesia should be classified broadly into peak-dose dyskinesia (PDD), biphasic dyskinesia (BD), and OFF-period dystonia. The occurrence of low-dose dyskinesia and complex dyskinesia of continuous dopaminergic treatments should be known to specialists and will require additional studies.

Valuation and scenario multi criteria analysis of transportation alternative strategies to mitigate the local sprawl

The general research here introduced concerns the phenomenon of urban sprawl unfolding in the last century and defined as “the physical pattern of low- density settlement in urban areas”. The focus, as part of the more general research cited, is the relationship between sprawl and public transportation. The specific study here present is a possible approach to planning and managing policy responses to urban sprawl through the integration of consolidated settlement systems (with a view to their re-revitalization) with rail green public transportation in the framework of TOD (Transit-Oriented Development). A paramount issue emerges about sprawl: there are prototype case in which TOD and rail green public transportation help concentrate settlement instead of sprawl? No cases have been found. Instead the most recent literature recommends to perform new researches concerning solutions through real world applications, given the total shortage of case studies. The general research framework has been applied in a specific Case Study to support the community of Calabria, the southernmost Mediterranean region of mainland Italy in European Union, within the most urbanized sub-regional sub-area, in analyzing the rampant phenomenon of sprawl and, possibly, in addressing and mitigating it relying on TOD and rail green public transportation. In the Case Study of the present research there are three alternatives in sub regional public transportation: A1; A2; A3. A1 is the status quo. A2 is the upgrading of the railway which, although existing, is illogically neglected. A3 is an unexpected new project by the railway managing body for a new route in the south of the area completely away from the most important settlements and outside any transport or mobility or accessibility institutional public plan. The three alternatives were subjected to social discussions well as a qualitative evaluation by a panel of experts. The multiple criteria valuation approach resulted in a preference for Alternative A2 over Alternatives A1 and A3. The preferred Alternative A2 integrates perfectly with the existing settlement by responding to a fundamental criterion placed at the top of the valuation: integrating the urban railway directly into the existing consolidated inhabited centers. This preferable Alternative A2 has among its peculiar characteristics: – directly connects many of the settlements in the area; – can serve approximately MORE THAN 250,000 potential settled residents; – connects coast to coast the narrowest regional and national isthmus; – creates the fastest and shortest possible connection in the national territory between the two fundamental railway backbones Tyrrhenian (Palermo - Milan - Torino) and Ionian-Adriatic (Reggio Calabria - Venice); – thereby helping to connect two of the Trans European Network and pan-European train mega-corridors I (Palermo - Berlin) and VIII (Skopje - Varna). The A2 Alternative has the further distinctive feature of performing both local and supra-local dual service in a unified venue that is both train-tram and long-distance rail, in analogy with continental benchmarks and experiences, such as the German S-Bahn. Subsequently, in the Case Study, the costs of the Alternative A2 for the upgrading (and “modernization”) of the existing railway has an estimated cost of 168 million appraised by the research team with a detailed quantification, and subsequently, in de facto double-blind estimate, surprisingly confirmed by the railway managing body. According to the latest and most up-dated estimates by the same railway managing body, the completely new route project located far south of all the settlements, constituting the Alternative A3, would cost over 485 million, are reported. This is because all the areas have to be acquired and because the route crosses land with technical difficulties to be overcome by carrying out expensive works. In terms of costs, the preferred Alternative 2 seems to be the most balanced, much more even than the status quo Alternative 1 (do nothing). The latter only apparently has no big investment costs, unless ordinary maintenance. In fact it hides enormous private costs and implicit (and not immediately monetary) social suffering, due to: car commuting (un-pooled) of people; their monetizable travel times, enormous due to congestion; air pollution; accident risks; congestion in cities; high private personal costs of using the individual vehicle (car wear; fuel); parking cost and fine risk; etc.

Il sistema verde: soluzioni per la tutela dell’ambiente e la riduzione delle emissioni di CO2. L’esempio di una scuola esistente.

The public school building sector offers great opportunities for energy efficiency and CO2 emissions reduction. In this research a method for the energy evaluation of school buildings is proposed. It implements simple input information connected to dynamic simulations. The main objective is to evaluate the energy, environmental and economic impact of different regeneration proposals, combining a green system integration. The building chosen as a case study, which presents serial and widespread constructive and thermo-physical characteristics, allows to extend the validity of obtained results to similar cases and conditions. Findings highlighted the importance of developing site-specific strategies and green energy solutions, to optimally adapt any intervention to the architectural, typological and plant characteristics of the school. The proposed example is a prototype case so that the Municipalities and Public Administrations, owned by most of the schools in Italy, can use it as basic knowledge for future projects oriented towards the energy transition, but also for specific tailored training.

Flow Characteristics of the Rip Current System near a Shore-Normal Structure with Regular Waves

Rip currents are the strong narrow seaward current produced by waves breaking on the coast. Of the many types of rip currents, the present study investigates, experimentally and numerically, the rip current system produced by the wave reflection on a finite-length shore-normal structure (corresponding to groin, jetty and headland in a real-word environment) with strong wave reflection strength. The incident wave condition of an obliquely propagating monochromatic surface gravity wave is considered for the bottom topographies of planar and barred beaches without or with a rip channel. The corresponding laboratory experiment was conducted and used to validate the numerical model. A set of higher order Boussinesq equations is used to reproduce the experimental observation and produce the results for the related prototype cases, with the latter considering more factors which may influence the formation and evolution of rip current flow patterns. The resulting rip current system contains two parts: the node rips formed due to the presence of the longshore standing wave in the wave reflection field and the deflection rip formed due to the interaction between the incoming longshore current and the reflection wave field mentioned above. A new formation mechanism of the deflection rip has been proposed, i.e., the deflection rip is formed by the meeting and then deflection of the longshore current and lateral flow. The effects of different wave reflection strengths of the structure, wave incident angles and bathymetric conditions on the pattern and flow volume of the deflection rip are also studied.

Waste to Wealth: Vegetable market waste to generate electricity, a design proposal suitable for any medium scale vegetable market in Indian cities

A biogas plant is current energy source and is reasonable to the necessities representing things to come. With the suitable use of the processing innovation, the improvement of financially plausible natural waste biogas digesters which produces power isn't entirely unachievable. The central purpose of the study is to design the proper power generation unit based on organic waste and to calculate the efficiency of power generation at Monda market of Secunderabad, Telangana by taking exemplary and prototype case of Bowenpally market and implementing it. The development of biogas by anaerobic processing of natural waste is an experienced skill that might introduce unmistakable advantages to society. Natural biogas innovation can lighten many grave issues in the agricultural nations, “The model that has been decided for the review, Bowenpally vegetable market, Hyderabad, India has gotten Prime Minister Narendra Modi's consideration for its creative waste administration framework. Modi lauded the one-of-its-sort bioelectricity, bio fuel and bio compost age project in his 73rd episode of radio program Mann Ki Baat on Sunday. The project has scope to foster in areas, for example, country energy shortage, low horticulture yield and waste administration department. Moreover through the usage of biogas innovation harmful ranch waste can be appropriately dealt \ hrough anaerobic processing, age of regular composts and eventually lead to an productive outcome and expansion in result and pay. From examination it will become obvious that markets utilizing digesters frameworks have more prominent profit or advantages than those markets who don't bringing about the conservation and increment practicality of the natural waste.

Dual Photochemistry of Benzimidazole.

Monomers of benzimidazole trapped in an argon matrix at 15 K were characterized by vibrational spectroscopy and identified as 1H-tautomers exclusively. The photochemistry of matrix-isolated 1H-benzimidazole was induced by excitations with a frequency-tunable narrowband UV light and followed spectroscopically. Hitherto unobserved photoproducts were identified as 4H- and 6H-tautomers. Simultaneously, a family of photoproducts bearing the isocyano moiety was identified. Thereby, the photochemistry of benzimidazole was hypothesized to follow two reaction pathways: the fixed-ring and the ring-opening isomerizations. The former reaction channel results in the cleavage of the NH bond and formation of a benzimidazolyl radical and an H-atom. The latter reaction channel involves the cleavage of the five-membered ring and concomitant shift of the H-atom from the CH bond of the imidazole moiety to the neighboring NH group, leading to 2-isocyanoaniline and subsequently to the isocyanoanilinyl radical. The mechanistic analysis of the observed photochemistry suggests that detached H-atoms, in both cases, recombine with the benzimidazolyl or isocyanoanilinyl radicals, predominantly at the positions with the largest spin density (revealed using the natural bond analysis computations). The photochemistry of benzimidazole therefore occupies an intermediate position between the earlier studied prototype cases of indole and benzoxazole, which exhibit exclusively the fixed-ring and the ring-opening photochemistries, respectively.

Strategic Conflict Management using Recurrent Multi-agent Reinforcement Learning for Urban Air Mobility Operations Considering Uncertainties

The rapidly evolving urban air mobility (UAM) develops the heavy demand for public air transport tasks and poses great challenges to safe and efficient operation in low-altitude urban airspace. In this paper, the operation conflict is managed in the strategic phase with multi-agent reinforcement learning (MARL) in dynamic environments. To enable efficient operation, the aircraft flight performance is integrated into the process of multi-resolution airspace design, trajectory generation, conflict management, and MARL learning. The demand and capacity balancing (DCB) issue, separation conflict, and block unavailability introduced by wind turbulence are resolved by the proposed the multi-agent asynchronous advantage actor-critic (MAA3C) framework, in which the recurrent actor-critic networks allow the automatic action selection between ground delay, speed adjustment, and flight cancellation. The learned parameters in MAA3C are replaced with random values to compare the performance of trained models. Simulated training and test experiments performed on a small urban prototype and various combined use cases suggest the superiority of the MAA3C solution in resolving conflicts with complicated wind fields. And the generalization, scalability, and stability of the model are also demonstrated while applying the model to complex environments.

The child-friendly cities concept in China: A prototype case study of a migrant workers’ community

The United Nations International Children’s Emergency Fund (UNICEF) initiatives of Child-Friendly Cities have operated in more than 3000 cities around the world. However, the concept of making the city child-friendly has not been extensively recognized in China. This article aims to report a regeneration project in a migrant workers’ community, the Mingdong, and is used to illustrate the reactions of residents to youth participation (youth civic engagement) and the project through an international workshop. The article concludes with a discussion of how social workers help in the social development of migrant communities by promoting youth participation, community social awareness and social cohesiveness.

Sistem Informasi Manajemen Berkas Perkara Berbasis Web Pada Kejaksaan Negeri Merangin

The Merangin District Prosecutor's Office is a law enforcement agency that is required to play a greater role in enforcing the law. In the current file data management system, it is still done manually, that is, every incoming case file is recorded in the register book and archived into the file cabinet. This makes it difficult for the process of searching for file data and compiling case files which will be processed by the prosecutor's office and making reports. Based on the existing problems, a case file management system is needed in order to assist the Merangin District Attorney in overcoming the existing problems. The purpose of this study is to design a prototype case file management system using system modeling tools, namely UML and the diagrams used include use case diagrams, activity diagrams and class diagrams. The results of this study are a prototype case file management system design that can be applied by the Merangin District Attorney to help expedite case management and provide maximum service to the public.

Vertically layered flow structure at confluence of a reservoir and tributary carrying high sediment loads

Enhanced understanding of flow structure at a river confluence is essential for predictions of sediment transport and morphological evolution. To date, however, the confluent flow structure of a reservoir and tributary carrying high sediment loads has remained poorly understood, and may be vertically layered sharply, featuring subaqueous sediment-laden flow, i.e., turbidity currents underneath subaerial clear water. Here a recently established 2D double layer-averaged model, able to resolve the formation, propagation, and recession of turbidity currents, is used to investigate a series of idealized laboratory-scale cases and a prototype case study of the Guxian Reservoir on the Yellow River, China. Four primary patterns of the stable, vertically layered flow structure at a reservoir-tributary confluence are identified: 1) single layers of sediment-laden inflow in both the main channel and tributary, sustained by sufficient vertical mixing; 2) a double layer in the main channel and a single layer of sediment-laden inflow in the tributary, when the sediment-laden flow in the tributary suffices to block intrusion of flow in the main channel; 3) a single layer of sediment-laden inflow in the main channel and a double layer in the tributary, induced by the intrusion of sediment-laden flow from the main channel into clear-water flow with small discharge in the tributary; and 4) double layers in both the main channel and tributary, which may be further divided into three subpatterns, as turbidity current exists in both the main channel and tributary, or in the main channel (tributary) intruding into the tributary (main channel). In response to unsteady discharge and sediment inputs from upstream, the vertically layered flow structure evolves in time, and may fall into one of the patterns identified above. Although bed deformation in the long term may modify the confluent flow, the vertically layered flow pattern remains so far as the present cases are concerned. The findings have implications for sediment transport and morphological evolution at a reservoir–tributary confluence, for which further studies are suggested to inform the optimization of reservoir operation schemes to mitigate capacity loss caused by sedimentation.

Automatic generation of BIM-based construction schedule: combining an ontology constraint rule and a genetic algorithm

PurposeThe purpose of this study is to automatically generate a construction schedule by extracting data from the BIM (Building Information Modeling) model and combining an ontology constraint rule and a genetic algorithm (GA).Design/methodology/approachThis study developed a feasible multi-phase framework to generate the construction schedule automatically through extracting information from the BIM, utilizing the ontology constraint rule to demonstrate the relationships between all the components and finally using the GA to generate the construction schedule.FindingsTo present the functionality of the framework, a prototype case is adopted to show the whole procedure, and the results show that the scheme designed in this study can quickly generate the schedule and ensure that it can satisfy the requirements of logical constraints and time parameter constraints.Practical implicationsA proper utilization of conceptual framework can contribute to the automatic generation of construction schedules and significantly reduce manual errors in the Architectural, Engineering, and Construction (AEC) industry. Moreover, a scheme of BIM-based ontology and GA for construction schedule generation may reduce additional manual work and improve schedule management performance.Social implicationsThe hybrid approach combines the ontology constraint rule and GA proposed in this study, and it is an effective attempt to generate the construction schedule, which provides a direct indicator for the schedule control of the project.Originality/valueIn this study, the data application process of the BIM model is divided into four modules: extraction, processing, optimization, and output. The key technologies including secondary development, ontology theory, and GA are introduced to develop a multi-phase framework for the automatic generation of the construction schedule and to realize the schedule prediction under logical constraints and duration interference.

High Energy Channeling and Malleable Transition States: Molecular Dynamics Simulations and Free Energy Landscapes for the Thermal Unfolding of Protein U1A and 13 Mutants.

The spliceosome protein U1A is a prototype case of the RNA recognition motif (RRM) ubiquitous in biological systems. The in vitro kinetics of the chemical denaturation of U1A indicate that the unfolding of U1A is a two-state process but takes place via high energy channeling and a malleable transition state, an interesting variation of typical two-state behavior. Molecular dynamics (MD) simulations have been applied extensively to the study of two-state unfolding and folding of proteins and provide an opportunity to obtain a theoretical account of the experimental results and a molecular model for the transition state ensemble. We describe herein all-atom MD studies including explicit solvent of up to 100 ns on the thermal unfolding (UF) of U1A and 13 mutants. Multiple MD UF trajectories are carried out to ensure accuracy and reproducibility. A vector representation of the MD unfolding process in RMSD space is obtained and used to calculate a free energy landscape for U1A unfolding. A corresponding MD simulation and free energy landscape for the protein CI2, well known to follow a simple two state folding/unfolding model, is provided as a control. The results indicate that the unfolding pathway on the MD calculated free energy landscape of U1A shows a markedly extended transition state compared with that of CI2. The MD results support the interpretation of the observed chevron plots for U1A in terms of a high energy, channel-like transition state. Analysis of the MDUF structures shows that the transition state ensemble involves microstates with most of the RRM secondary structure intact but expanded by ~14% with respect to the radius of gyration. Comparison with results on a prototype system indicates that the transition state involves an ensemble of molten globule structures and extends over the region of ~1–35 ns in the trajectories. Additional MDUF simulations were carried out for 13 U1A mutants, and the calculated φ-values show close accord with observed results and serve to validate our methodology.

Limit profiles for singularly perturbed Choquard equations with local repulsion

We study Choquard type equation of the form where Nge 3, I_alpha is the Riesz potential with alpha in (0,N), p>1, q>2 and varepsilon ge 0. Equations of this type describe collective behaviour of self-interacting many-body systems. The nonlocal nonlinear term represents long-range attraction while the local nonlinear term represents short-range repulsion. In the first part of the paper for a nearly optimal range of parameters we prove the existence and study regularity and qualitative properties of positive groundstates of (P_0) and of (P_varepsilon ) with varepsilon >0. We also study the existence of a compactly supported groundstate for an integral Thomas–Fermi type equation associated to (P_{varepsilon }). In the second part of the paper, for varepsilon rightarrow 0 we identify six different asymptotic regimes and provide a characterisation of the limit profiles of the groundstates of (P_varepsilon ) in each of the regimes. We also outline three different asymptotic regimes in the case varepsilon rightarrow infty . In one of the asymptotic regimes positive groundstates of (P_varepsilon ) converge to a compactly supported Thomas–Fermi limit profile. This is a new and purely nonlocal phenomenon that can not be observed in the local prototype case of (P_varepsilon ) with alpha =0. In particular, this provides a justification for the Thomas–Fermi approximation in astrophysical models of self-gravitating Bose–Einstein condensate.

Equilibrium planform of pocket beaches behind breakwater gaps: On the shape of the equilibrium shoreline.

Bay beaches are common coastal landforms along the world's coastlines and have frequently been used as equilibrium coastal systems to mitigate erosion problems and stabilize coasts. Throughout the literature, several formulae can be found to obtain the static equilibrium planform (SEP) of such beaches on the leeward sides of single protruding headland structures. However, equations used to define SEP behind breakwater gaps are rare and based on a limited number of studies, especially when the obliquity angle ( β ) is large. This paper proposes a new formula for modelling the SEP of bay beaches that includes cases with planform shapes characterized by large obliquity angles ( β > 75°) for which the SEP is almost quasi-semicircular. The formula represents a general form of the parabolic bay shape equation (PBSE) with modified coefficients to alter the planform's curvature to be quasi-semicircular, mimicking the behavior of such bays in nature. The coefficients are expressed as functions of both the obliquity angle ( β ) and the curvature-adjustment angle ( φ ), which was determined based on field observations of the best-fitting SEP of 26 bay beaches with ( β > 75°) along the coasts of Spain, Portugal and Brazil. Additionally, 32 beach cases characterized by smaller obliquity angles ( β < 70°) were included in the derivation of the curvature adjustment angle, which was expressed as a function of ( β ). The model showed good results in modelling the SEP, with an RMSE of 0.90° obtained when estimating the planform's curvature-adjustment angle ( φ ) to obtain quasi-semicircular planform shapes for the prototype cases, confirming its utility as a valuable tool for engineering applications. • Static equilibrium planforms (SEPs) characterized by large obliquity angles are modelled. • A new formula was derived to plot the (SEP) of bay beaches behind gaps when (β > 75°). • A curvature-adjustment angle is used to alter the SEP's curvature based on field cases. • The SEP is quasi-semicircular for pocket beaches behind breakwater gaps when (β > 75°). • The curvature-adjustment angle is directly proportional to the obliquity angle (β).