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Similitude theory helps engineers and scientists to accurately predict the behaviors of real systems through the application of scaling laws to the experimental results of a scale model related to the real system by similarity conditions. The theory was applied when studying the deep drawing process of a bathtub made from cold rolled low carbon aluminum-killed steel from the point of view of material limits. The bathtub model was created on the basis of geometric, physical, and mechanical similarity on a scale of 1:5. Thus, simulations and physical models were created. The simulation model was used to verify the combination yield locus/hardening law on the basis of comparing the thickness change. As a result, Hill 48/Krupkowski showed the minimal deviation by comparing data evaluated from numerical simulations and that measured on the physical model. Additionally, material anisotropy was modelled when virtual materials were defined from experimentally measured values of the plastic strain ratio. As an outcome, extra deep drawing quality steel with an average plastic strain ratio of rm ≥ 1.47 and an average strain hardening exponent of nm ≥ 0.23 must be used for the deep drawing of the bathtub.

Almanacis a collection of lyrical and narrative poems that celebrate, and mourn the passing of, the world of the small family farm. But while the poems are all involved in some way with the rural Midwest, particularly with the people and land of the northwestern Illinois dairy farm where Austin Smith was born and raised, they are anything but merely regional. As the poems reflect on farm life, they open out to speak about childhood and death, the loss of tradition, the destruction of the natural world, and the severing of connections between people and the land. This collection also reflects on a long poetic apprenticeship. Smith's father is a poet himself, andAlmanacis in part a meditation about the responsibility of the poet, especially the young poet, when it falls to him to speak for what is vanishing. To quote another Illinois poet, Thomas James, Smith has attempted in this book to write poems \"clear as the glass of wine / on [his] father's table every Christmas Eve.\" By turns exhilarating and disquieting, this is a remarkable debut from a distinctive new voice in American poetry.______ FromAlmanac:THE MUMMY IN THE FREEPORT ART MUSEUMAustin Smith Amongst the masterpieces of the small-townPicassos and Van Goghs and photographsof the rural poor and busts of dead Greeksor the molds of busts donated by the ArtInstitute of Chicago to this dyingtown's little museum, there was a mummy,a real mummy, laid out in a dim-litroom by himself. I used to goto the museum just to visit him, a pharaohwho, expecting an afterlifeof beautiful virgins and infinite foodand all the riches and jewelshe'd enjoyed in earthly life,must have wondered how the hellhe'd ended up in Freeport, Illinois.And I used to go alone into that roomand stand beside his sarcophagus and say,\"My friend, I've asked myself the same thing.\"

This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications.

In this article, we introduce an enhanced version of the log-logistic model, termed the Kumaraswamy alpha-power log-logistic (KAPLL) distribution. The KAPLL model expands upon the traditional log-logistic distribution and several well-established distributions. We investigate the mathematical properties of the KAPLL model, highlighting its ability to effectively model various aging and failure criteria. The KAPLL distribution exhibits remarkable flexibility in modeling various types of hazard rate behaviors. It is capable of accommodating a wide range of shapes, including increasing, decreasing, J-shaped, reversed J-shaped, bathtub-shaped, inverted bathtub-shaped, and even more complex forms such as decreasing-increasing-decreasing failure rates. The KAPLL distribution is characterized by its capacity to exhibit both symmetric and asymmetric shapes in its density function. The proposed KAPLL model overcomes key limitations of existing LL-based generalizations by offering enhanced flexibility in modeling diverse hazard rate shapes and tail behaviors. We estimate the KAPLL parameters using eight classical estimation methods. Comprehensive simulation results are presented and ranked to identify the most effective approach for estimating KAPLL parameters, which we believe will be of great interest to engineers and applied statisticians. To further demonstrate the versatility of the KAPLL distribution, we analyze five real-world datasets from reliability, engineering, biomedical, and environmental sciences, highlighting its flexibility relative to other extensions of the log-logistic model. Likelihood ratio tests conducted across five real datasets confirm that the KAPLL model provides a statistically significant improvement over the baseline log-logistic distribution.

Cyclobisbiphenylenecarbonyl (CBBC) represents a readily available chiral figure-eight macrocycle containing two carbonyl groups. However, the transformation of the carbonyl groups has been unexplored. Herein, we conducted the Wittig reaction of CBBC with methylenetriphenylphosphorane to furnish two chiral macrocycles containing one or two exocyclic olefin units. Owing to the transformation of carbonyl groups, the resulting products exhibit several unique physical and chemical properties: (1) the enhancement of configurational stability, (2) the appearance of fluorescence, and (3) the reductive carbon–carbon-bond formation between carbonyl and alkene units.

Given a well-posed linear evolution system settled on a domain Ω of Rd, an observation subset ω⊂Ω and a time horizon T, the observability constant is defined as the largest possible nonnegative constant such that the observability inequality holds for the pair (ω,T). In this article we investigate the large-time behavior of the observation domain that maximizes the observability constant over all possible measurable subsets of a given Lebesgue measure. We prove that it converges exponentially, as the time horizon goes to infinity, to a limit set that we characterize. The mathematical technique is new and relies on a quantitative version of the bathtub principle.

The phenomenon of “lone wolf ” terrorism, which has increasingly attracted the attention of scholars, consists of terror attacks perpetrated without the operational involvement of terrorist organizations in initiating, planning, or executing the attack. This phenomenon lacks a clear center of gravity directing the actions of “lone wolf ” terrorists; and as such, it is crucial to understand the system of motivations influencing independent assailants to perpetrate attacks. This article is based on extensive studies conducted on the motivations of “lone wolf ” terrorists by the International Institute for Counter-Terrorism (ICT) at the Interdisciplinary Center (IDC), Herzliya. It seeks to contribute to the literature on the topic by proposing a new model. The “Bathtub Model” suggests that the process of the formation of the “lone wolf’s” decision to perpetrate an attack can be akin to a container of water (such as a bath), which would be filled up by various sources of water, each representing groups and subgroups of motivations. The upper threshold of the “bathtub” model represents therefore the maximal level of the “lone wolf’s” ability to contain his motivations, frustrations, and emotions.

A living organism can be regarded as a dissipative, self-organizing physical system operating far from thermodynamic equilibrium. Such systems can be effectively described within the framework of Markov jump processes subjected to an external driving force that sustains the system away from equilibrium—leading, in the special case of stabilization, to a non-equilibrium steady state (NESS). By combining the Markov formalism with concepts from stochastic thermodynamics, we demonstrate the temporal evolution of entropy in such systems: entropy decreases during growth and development, stabilizes at maturity under NESS conditions, and subsequently increases during aging, death, and decomposition. This characteristic trajectory, which we term the entropy bathtub, highlights the universal thermodynamic structure of living systems. We further show that the system exhibits continuous yet time-dependent positive entropy production, in accordance with fundamental thermodynamic principles. Perturbations of the driving force—whether reversible or irreversible—naturally capture the impact of external stressors, providing a conceptual analogy to pathological processes in biological organisms. Although the model does not introduce fundamentally new elements to the physics of life, it offers a simple tool for exploring entropy-driven mechanisms in living matter.

Creep is one of the main failure mechanisms of materials at elevated temperatures, and the creep rate curve is a key descriptor of creep deformation and damage evolution. However, existing creep models are mainly phenomenological or stage-wise, and the physical origin of the bathtub-shaped creep rate curve over the full creep process has not been systematically clarified. In this study, creep damage is treated as an aging failure process of a material system, and a physically interpretable hierarchical model is established based on statistical physics for disordered complex systems. By linking the evolution and interaction of microscopic material units with macroscopic creep behavior, the proposed model provides a unified description of the primary, secondary, and tertiary creep stages and offers a theoretical explanation for the bathtub-shaped creep rate curve. Validation using representative metallic and composite material cases shows that the model can reasonably reproduce the overall three-stage creep rate evolution, with residual sums of squares of 1.3088 and 0.5369, respectively. These results demonstrate the ability of the model to capture full-process creep behavior in different material systems. The main advantage of the proposed approach is its physical interpretability within a unified framework, while its current limitation is that the validation remains limited in scale and broader benchmark comparisons with conventional methods are still needed. This work provides a statistical perspective for creep behavior modeling and for understanding the microscopic mechanisms and interactions underlying creep degradation in structural materials.

By multivariate econometric analysis of UK offshore wind farms, we demonstrate a life cycle effect of the capacity factor of offshore wind. From the bathtub curve findings in reliability engineering, we would expect a long, flat segment of stable operation in the middle of the life cycle production schedule. Our general findings deviate from the standard curve as it does not have a long segment where production is stable. Production starts falling too early. Lack of stable operation period is harmful to wind farm economics. It indicates immature technology and a potential for improvement. We examine the effect life cycle production schedules have on project economics and compare with a common assumption of a flat production schedule. We find that project profitability (net present value) is very sensitive to the life cycle profile of production.