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Elastic collisions of gliders on linear air tracks are often used to explore conservation of energy and momentum. If one is interested in the glider behavior over a long time span, the analysis involves repeated collisions and is complicated by reflections from the track end stops. Here we analyze elastic collisions on a novel circular air track; since such a track lacks end stops, the mathematical analysis of repeated collisions is amenable to our students. Our analysis uncovers a variety of interesting behaviors which depend on the ratio of the glider masses. We examine periodic sequences where the gliders return to their initial conditions and progressions where (when plotted in polar coordinates) the collision positions take on the locus of a spiral. One set of initial conditions produces an "angle trap" where one glider remains within a certain angular range. We also explore making one glider's mass hypothetically negative, which results in a novel "chasing" motion. Our results were obtained using a 3D interactive simulation (created using C++ within the Unreal engine), which we make available as supplementary material. Editor's Note: Students in introductory courses often analyze one-dimensional elastic collisions between carts on wheels or gliders on an air track. If the track possesses end stops, and the system is left undisturbed after the initial contact, multiple collisions will occur. The analysis of repeated collisions can be somewhat complicated due to the end-stop reflections. In this article, the authors consider a clever simplification involving a circular track without end stops. This renders the mathematical analysis more tractable for students, and the system presents a variety of interesting behaviors to explore. Students and instructors will enjoy this entertaining application of linear algebra and can freely make use of online computer simulations provided as supplementary material. [ABSTRACT FROM AUTHOR]

Overflow metabolism is a well-known phenomenon that describes the seemingly wasteful and incomplete substrate oxidation by aerobic cells, such as yeasts, bacteria, and mammalian cells, even when conditions allow for total combustion via respiration. This cellular response, triggered by an excess of C-source, has not yet been investigated in archaea. In this study, we conducted chemostat cultivations to compare the metabolic and physiological states of the thermoacidophilic archaeon Sulfolobus acidocaldarius under three conditions, each with gradually increasing nutrient stress. Our results show that S. acidocaldarius has different capacities for the uptake of the two C-sources, monosodium glutamate and glucose. A saturated tricarboxylic acid cycle at elevated nutrient concentrations affects the cell's ability to deplete its intermediates. This includes deploying additional cataplerotic pathways and the secretion of amino acids, notably valine, glycine, and alanine, while glucose is increasingly metabolized via glycogenesis. We did not observe the secretion of common fermentation products, like organic acids. Transcriptomic analysis indicated an upregulation of genes involved in fatty acid metabolism, suggesting the intracellular conservation of energy. Adapting respiratory enzymes under nutrient stress indicated high metabolic flexibility and robust regulatory mechanisms in this archaeon. This study enhances our fundamental understanding of the metabolism of S. acidocaldarius. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of strong potential porous materials to absorb the transmitted energy in a dissipative device containing a wave-bearing cavity. The expansion chamber consists of horizontal as well as vertical elastic boundaries that is filled with a compressible fluid and porous media. The porous media is dealt as an equivalent fluid with complex propagation speed and density, has effects on the eigenfunctions of cavity regions. The vibrational response of the vertical elastic components having different sets of edge conditions are incorporated by mode-matching tailored-Galerkin (MMTG) approach. This approach provides displacement of vertical elastic membrane which deals with various edge conditions. The MMTG approach has point-wise convergence that is conform through generalized orthogonal relations. The MMTG solutions are used to reconstruct matching conditions and to satisfy law of conservation of energy. It confirms the validity of retained solutions and accuracy of performed algebra. It is observed from the curves of TL and P abs that by varying edge conditions the absorbed power and TL are enhanced. [ABSTRACT FROM AUTHOR]

Machining different types of complex parts requires changing speed of the motorized spindle to accommodate the various processes, resulting in temperature rise or decline and then causing thermal deformation of machine tool, which plays a significant impact on the machining accuracy of the parts. According to the Law of Conservation of Energy and Fourier's Law of Heat Conduction, the heat transfer mechanism of the motorized spindle is investigated. Based on the thermo-solid structure coupling theory, the analytic models of the temperature field and thermal deformation for the motorized spindle are established, and the thermal hysteresis phenomenon is explored by means of the case studies. The characteristic experiments were carried out under variable working conditions and the model parameters were identified using Genetic Algorithm (GA). The accuracy and effectiveness of the proposed models for predicting temperature and thermal deformation of the spindle are validated which is applicable to compensate the thermal errors. Moreover, compared with data-driven modeling approach, our study needs lesser data for parameter identification, greatly saving the computation time in modeling. [ABSTRACT FROM AUTHOR]

This work proposes a resource efficient robust control scheme for missile-target engagement scenarios subjected to external disturbances. The robustness is achieved by using an annular event-triggered artificial time-delayed control (ET-TDC) methodology with input saturation. The ET-TDC philosophy uses the TDC strategy through a dynamic predefined triggering mechanism which overcomes the requirement to update the control periodically for every sampling instant, unlike conventional TDC and other robust control schemes. Thus the proposed methodology can tackle uncertainties with minimal a-priori knowledge while significantly reducing the over-utilisation of system resources. In addition, the adopted event-triggered mechanism facilitates further conservation of energy which might be crucial for mid-to-long range engagement scenarios. The closed-loop stability is derived analytically and the simulation results illustrate the efficacy of the proposed guidance framework in comparison with other state-of-art robust control methodologies. [ABSTRACT FROM AUTHOR]

The article presents a combined mathematical model that allows us to determine and investigate the dynamic characteristics of the latest type of non-contact sealing for pump and compressor shafts, which eliminates leakage of pumped products, which are important from the point of view of safe operation. The proposed method is based on the laws of conservation of energy and conservation of matter. The model is based on static and dynamic calculation of operation characteristics, while its key feature is the combination of analytical, variational and numerical solutions. The materials of the article may be useful to developers of new types of contactless seals of centrifugal machines. [ABSTRACT FROM AUTHOR]

Context. The electron-cyclotron maser instability (ECMI) is a significant coherent radio emission mechanism widely utilized in various astrophysical radio phenomena. It is well known that the velocity anisotropic distribution of energetic electrons, which leads to an inverted perpendicular population in the vertical direction with ∂fb/∂v⊥ > 0, can provide the free energy necessary for the ECMI. Aims. The initial velocity distribution of energetic electrons leaving the acceleration region is typically isotropic or beam-like. However, as these energetic electrons travel along the magnetic field as fast electron beams (FEBs) in magnetic plasma, various velocity anisotropic distributions can emerge. In this paper, we examine the impact of temperature anisotropy formed by beam electrons traveling along a flare loop on the ECMI. Methods. By neglecting the energy loss of energetic electrons as they traverse the corona and invoking the conservation of energy and magnetic moments, we established the relationship between momentum dispersion and the magnetic field. Utilizing the magnetic field model of the flare loop, we calculated the evolution of momentum dispersion and the growth rates of the ECMI as FEBs precipitate along the flare loop. Results. The results demonstrate that the temperature anisotropy arising as FEBs descend along the flare loop significantly impacts the ECMI. The maximum growth rates of the excited modes exhibit a gradual increase initially and then decline rapidly after reaching a critical height for β0 = 0.2c and 0.15c. The results also show that the growth rates of the O2 mode are one order of magnitude smaller than those of the O1 and X2 modes. This indicates that the harmonic radiation is X-mode polarized. Notably, the temperature anisotropy of FEBs as they precipitate along the flare loop with different magnetic field models or at different heights has similar effects on the ECMI. [ABSTRACT FROM AUTHOR]

The essence of rock fracture can be broadly categorized into four processes: energy input, energy accumulation, energy dissipation, and energy release. From the perspective of energy consumption, the failure of rock materials must be accompanied by energy dissipation. Dissipated energy serves as the internal driving force behind rock damage and progressive failure. Given that the process of rock loading and deformation involves energy accumulation and dissipation, the rock constitutive model theory is expanded by incorporating energy principles. By introducing the dynamic energy correction coefficient, according to the law of the conservation of energy, the total energy exerted by external loads on rocks is equal to the energy dissipated through the dynamic energy inside the rocks. A new type of energy constitutive model is established through the functional principle and momentum principle. To validate the model's accuracy, a triaxial compression test was conducted on sandstone to examine the stress–strain behavior of the rock during the failure process. A sensitivity analysis of the parameters introduced into the model was conducted by comparing the model results, which helped to clarify the innate laws of significance of these parameters. The results indicated that the energy model more accurately captures the non-linear mechanical behavior of sandstone under high-stress loading conditions. The model curve fits the test data to a high degree. The fitting curve was basically consistent with the changing trend of the test curve, and the correlation coefficients were all above 0.90. Compared with other models, the model based on the energy principle not only accurately reflects the rock's stress–strain curve, but also reflects the energy change law of rock. This has reference value for the safety analysis of rock mass engineering under loading conditions and aids in the development of anchoring and support schemes. The research results can fill in the blanks that exist in the energy method in terms of rock deformation and failure and provide a theoretical basis for deep rock engineering. Moreover, this research can further improve and extend the rock mechanics research system based on energy. [ABSTRACT FROM AUTHOR]

This article reconsiders Hans Driesch's vitalism, as articulated in his English book The Science and Philosophy of the Organism, from a novel perspective. The central thesis posits that Driesch's vitalism was intricately intertwined with contemporary physical sciences, particularly the version of energy physics prevalent in the energetics movement at the turn of the twentieth century. More specifically, based on the conceptual framework provided by energeticists like Wilhelm Ostwald and Georg Helm, Driesch offered an intriguing treatment of the relationship between entelechy and energy within an updated Kantian philosophy of nature. This article reconstructs Driesch's approach by elucidating four points. First, Driesch asserted that an entelechy strictly adhered to the conservation of energy. Second, he posited that the entelechy was not a form of energy and thus did not constitute a special kind of bio-specific vital energy. Third, he identified the entelechy's most critical characteristic as its ability to suspend certain physico-chemical changes. Fourth, Driesch suggested that the entelechy influenced mechanical systems in a manner akin to Maxwell's demon, raising the possibility of contravening the second law of thermodynamics. This article also contextualizes Driesch's treatment within the broader development of energy physics in the latter half of the nineteenth century. In conclusion, this article offers some critical remarks on the peculiar historical phenomenon of chronic vitalism as identified by Driesch and others. [ABSTRACT FROM AUTHOR]

Many approximate solutions of the time-dependent Schrödinger equation can be formulated as exact solutions of a nonlinear Schrödinger equation with an effective Hamiltonian operator depending on the state of the system. We show that Heller's thawed Gaussian approximation, Coalson and Karplus's variational Gaussian approximation, and other Gaussian wavepacket dynamics methods fit into this framework if the effective potential is a quadratic polynomial with state-dependent coefficients. We study such a nonlinear Schrödinger equation in full generality: we derive general equations of motion for the Gaussian's parameters, demonstrate time reversibility and norm conservation, and analyze conservation of energy, effective energy, and symplectic structure. We also describe efficient, high-order geometric integrators for the numerical solution of this nonlinear Schrödinger equation. The general theory is illustrated by examples of this family of Gaussian wavepacket dynamics, including the variational and nonvariational thawed and frozen Gaussian approximations and their special limits based on the global harmonic, local harmonic, single-Hessian, local cubic, and local quartic approximations for the potential energy. We also propose a new method by augmenting the local cubic approximation with a single fourth derivative. Without substantially increasing the cost, the proposed "single-quartic" variational Gaussian approximation improves the accuracy over the local cubic approximation and, at the same time, conserves both the effective energy and symplectic structure, unlike the much more expensive local quartic approximation. Most results are presented in both Heller's and Hagedorn's parametrizations of the Gaussian wavepacket. [ABSTRACT FROM AUTHOR]

This paper reviews observations on processes involving concentration gradients to show that (1) Concentration gradients can do external work during discharge if the system is arranged in a manner that requires it. (2) Work has to be done on the system (i.e. energy has to be added) to create a concentration gradient. (3) Concentration gradients can spontaneously discharge with no change in energy except interaction energy. These three observations are significant since, together, these observations demonstrate an apparent violation of the law of conservation of energy which is resolved by proposing that a probability field is a common element for all concentration gradients. This paper thus introduces two new concepts into thermodynamics: (1) Many spontaneous processes occur because of an increase in probability, not because of a decrease in the energy state of the system. (2) Concentration gradients coincide with a probability field and a constraint-dependent and temperature-dependent potential energy. [ABSTRACT FROM AUTHOR]

Einstein's expression 'Drama of Ideas' to describe the history of fundamental physics is especially suitable for the problem of quantum gravity (QG). The problem was identified by Einstein in 1916 based on an empirico-cosmological argument that was cosmologically flawed and empirically immeasurable. In 1929, the problem was strikingly underestimated by prominent figures in quantum theory, W. Heisenberg and W. Pauli. In 1929, Bohr, basing on the puzzling results of recent nuclear experiments and theoretical quantum limitations, hypothesized that the law of conservation of energy does not hold in nuclear physics. The young Russian physicist Landau enthusiastically supported Bohr's 'beautiful idea' and in 1931 proposed its theoretical justification, which, however, was rejected by Bohr. In late 1932, Landau realized that Bohr's hypothesis was incompatible with Einstein's theory of gravity. This meeting of two fundamental theories prompted Matvei Bronstein to investigate the quantization of gravity in-depth. In 1935, he proposed the first physical theory of QG for the weak gravity and revealed how deep the QG problem was for strong gravity. He showed that the gravitational field at a point in space–time is in principle unobservable and concluded that a complete theory of QG would require the 'rejection of a Riemannian geometry... and perhaps also the rejection of our ordinary concepts of space and time, replacing them by some much deeper and non-evident concepts'. Until now, despite thousands of publications on QG, the problem remains a great challenge in theoretical physics. [ABSTRACT FROM AUTHOR]

Alsatian engineer Gustave-Adolphe Hirn is best known to historians of science for his experimental determination of the mechanical equivalent of heat, first published in 1855. Since the 1840s, that equivalent has been closely associated with the conservation of energy, indeed often conflated with it. Hirn was one of Thomas Kuhn’s twelve ‘pioneers’ whose work he deemed relevant to the ostensible ‘simultaneous discovery’ of energy conservation. Yet Hirn never wholeheartedly embraced energy conservation. After reviewing his experimental work, his philosophical reflections, and his response to developments in heat theory, this article identifies three factors as having played central roles in this regard: Hirn’s deepest concerns were ontological, not energetic; none of the concepts basic to his natural philosophy were appropriate stand-ins for a quantitatively conserved energy; and, accurately reflecting the most common interpretation of the principle of the conservation of energy from the 1860s on – as exemplified already by Helmholtz in 1847 – Hirn associated its corpuscular-mechanical underpinning with the despiritualizing materialism he saw as dominating contemporary science. Hence although Hirn’s natural philosophy embraced sentiments quite in the spirit of the conservation of energy, he never explicitly subscribed to that principle. [ABSTRACT FROM AUTHOR]

1 In the milling process, due to machining materials and process parameters, the material at the edge of the part may break due to shear forces instead of cutting properly, resulting in the irregular pit (defect) at the exit edge. This seriously affects the surface quality of the workpiece. It is vital to understand the forming mechanism of the exit edge defect (EED) before one tries to eliminate or reduce the size of the EED and furthermore to improve the machining accuracy. Therefore, focusing on the milling process at exit edge of a workpiece, this paper presents a novel theoretical model to study the forming principle of the EED and predict the corresponding size. First, the forming process of the EED is separated into two stages. The beginnings of them are symbolized by the initial- and the fracture-negative shear planes. Then, the initial-negative shear plane which is defined by the initial negative shear angle is found. Furthermore, the location of the fracture-negative shear plane is defined using the fracture negative shear angle to study the EED. For the next step, the concentration force of Flamant-Boussinesq problem combined with the yield strength of the material is introduced to obtain the initial negative shear angle. Additionally, using the energy conservation theory, the negative fracture shear angle is calculated. Based on these, the mechanism of the EED is illustrated. Besides, the size (including length and depth) of the EED is predicted based on the geometric relationship between the initial and the fracture negative shear angle. Finally, the correctness of the theoretical model is verified by simulation and experiments. This study provides a promising step to reducing/eliminating the hazards of edge defects. • Exit edge defects can have a significant impact on part surface quality, which in turn has an impact on part performance. • A new theoretical model is proposed to study the formation mechanism of exit edge defects and to predict their size. • The mechanism of defect generation is described based on a mechanical model and the law of conservation of energy. • The correctness of the theoretical model was proved by a three-way comparison experiments. • The effects of spindle speed, depth of cut and feed per tooth on defect size are shown separately. [ABSTRACT FROM AUTHOR]

Taper beams are widely used due to its good damping properties in vibration and noise control field. For dynamic response analysis of taper beams in the high frequency, the energy finite element analysis (EFEA) based on wave theory is the most promising method. However, there is no energy finite element model for taper beams. In this paper, energy finite element model for taper beam is built though two steps. Firstly, the approximate displacement solution of the vibration equation of the taper beam is expressed by the geometry-acoustics approximation method. The expression of the relationship between energy density and power flow of the taper beam is obtained by utilizing the displacement solution. Based on the principle of conservation of energy, the governing equation taken energy density as a variable was derived. Secondly, the stiffness matrix of taper beam element and the solution format of this governing equation are obtained using the Galerkin weighting method, which led to the energy finite element model of the taper beam. Taking a taper beam as an example, the energy finite element model presented in this paper is used to calculate the energy density distribution on the taper beam, and the calculation results are consistent with the finite element calculation results, which proving the correctness of the energy finite element model of the taper beam established in this paper. In order to show the advantages of the EFEA model presented in this paper, a comparison with approximate EFEA model based on constant cross-section elements is performed. The results shown that the EFEA model presented in this paper have higher accuracy and less time consumption, which can reflect the dynamic response characteristics of the taper beam better. [ABSTRACT FROM AUTHOR]

In order to study the plastic deformation law of ship plate frames under the coupling action of internal explosion load and fragment, first, the calculation formula of plastic deformation deflection of the non-porous plate is derived through the law of conservation of energy. According to the numerical calculation results, the influence of the opening position and opening area of the target plate on the deflection gain of the target plate is further explored. The mathematical expression form of the opening area and opening position on the deflection gain of the prefabricated target plate is fitted, and then, the deflection calculation model of the prefabricated target plate is established. It can theoretically predict the deflection of the bulkhead under cabin explosion and has a certain application reference value for ship cabin anti-explosion design and internal explosion damage assessment. [ABSTRACT FROM AUTHOR]

Capacitors short-circuit discharge in an explosive environment can ignite and detonate the surrounding explosive media, causing dangerous accidents. At low voltages, this kind of discharge constitutes a micro-nano discharge; because the discharge gaps here are of the order of only microns to nanometers, the discharge process, electrode energy consumption, explosive media ignition energy, and other energy relationships are unclear. To study the relationships between the capacitor storage energy and various kinds of dissipation energies under short-circuit discharge, a model comprising conical and spherical cylinder microbumps is proposed based on the cathode surface morphology obtained by three-dimensional profiling and scanning electron microscopy, respectively. Then, the second-order non-chi-squared differential equations were established based on the principle of energy conservation and heat balance to deduce the relationships between the cathode surface temperature and height of the microbump, conical angle, and spherical radius; further, the energy consumed by the anode surface is calculated based on the theory of heat transfer. Using heat conduction theory, the energy consumed by the microbumps on the cathode surface is calculated, and the energy consumed on the anode surface is deduced using the surface heat source as the loading heat source. The residual energy of the capacitor is calculated from the discharge time and voltages before and after discharge, and the effective energy of the gas is calculated using the law of conservation of energy. Finally, the discharge channel energy, electrode energy consumption, and end residual energy of the discharge capacitor are used to derive the effective ignition energy of the explosive gas. This research is of great significance for the design of intrinsically safe circuits with high power. [ABSTRACT FROM AUTHOR]

Fundamental processes in plasmas act to convert energies into different forms, for example, electromagnetic, kinetic and thermal. Direct derivation from the Vlasov‐Maxwell equation yields sets of equations that describe the temporal evolution of magnetic, kinetic and internal energies in either the monofluid or multifluid frameworks. In this work, we focus on the main terms affecting the changes in kinetic energy. These are pressure‐gradient‐related terms and electromagnetic terms. The former account for plasma acceleration/deceleration from a pressure gradient, while the latter from an electric field. Although limited spatial and temporal deviations are expected, a statistical balance between these terms is fundamental to ensure the overall conservation of energy and momentum. We use in‐situ observations from the Magnetospheric MultiScale (MMS) mission to study the relationship between these terms. We perform a statistical analysis of those parameters in the context of magnetic reconnection by focusing on small‐scale Electron Diffusion Regions and large‐scale Flux Transfer Events. The analysis reveals a correlation between the two terms in the monofluid force balance, and in the ion force and energy balance. However, the expected relationship cannot be verified from electron measurements. Generally, the pressure‐gradient‐related terms are smaller than their electromagnetic counterparts. We perform an error analysis to quantify the expected underestimation of gradient values as a function of the spacecraft separation compared to the gradient scale. Our findings highlight that MMS is capable of capturing energy and force balance for the ion fluid, but that care should be taken for energy conversion terms based on electron pressure gradients. Key Points: We analyze energy and force balance in the monofluid and multifluid frameworks using MMS dataWe show that MMS is able to capture energy and force balance in the monofluid and ion fluid frameworksThe ratio of spacecraft separation to local gradient scale limits the proper estimation of electron pressure gradient terms [ABSTRACT FROM AUTHOR]

This paper focuses on a pullout failure of anchor rods used to stabilize rock slope at the sides of a road cut in a mountainous terrain. The objectives of this work are to analyze a case study of a pullout type of failure of anchor rods at highly fractured rock slope sides of a road cut called Dhila descent in Saudi Arabia, and also to investigate the possible mechanisms that caused this peculiar type of failure of the rock anchors and the landslides along the descent. Anchor rods exit out of the hole for a distance of few meters. Results of this analysis showed that the mechanism of this rock anchor failure is of the pullout type, caused apparently by the release of the energy stored in anchor rods at the post-tension stage during the construction period. This release is caused by the reduction of the bond strength between the rod and the grout at the anchorage end inside the hole. The displacements of the rods were computed based on the conservation of energy and work-energy principles. The amount of the displacements computed for a range of possibilities are comparable with those observed in the field. The bolt failure process is explained in terms of the debonding between the bolt and the grout. Recommendations were made to improve the design of such anchors. It is recommended to use fully-grouted, inclined, static rock bolts with a more ductile grout, and locked with nuts from both sides of the bearing block. [ABSTRACT FROM AUTHOR]

A previously published paper provided six examples of spontaneous processes for ideal systems that cannot be explained using classical thermodynamics. These six examples include free expansion of an ideal gas, mixing of ideal gases, diffusion of an ideal solute, mixing of ideal solutes, osmosis with ideal solutions, and free discharge of a concentration battery with ideal solutions. The previous paper demonstrated how energy was not a driving force in any of these examples and then proceeded to develop a positional entropy model, S D, that explains why these spontaneous processes occur. This new paper provides a method for calculating positional entropy, S D, for the same six systems, but for real particles that include nonzero volumes, particles with different volumes, and particles with different particle-particle interactions. The important outcome of this work shows that spontaneous discharge of these six example systems, either for ideal or real particles, is the result of a probability field created by the non-equilibrium distribution of the microstates that exists after the constraints on the system are changed, e.g., by removal of a separating partition or the shorting of a concentration cell. The probability field biases the movement of the particles toward the equilibrium distribution, where the bias is a consequence of an increased probability and not because of a decrease in energy. An additional conclusion of this work shows that the discharge of the probability field to the final equilibrium distribution of positional microstates removes the potential energy in the system but does not violate the law of conservation of energy. [ABSTRACT FROM AUTHOR]

Hibernation is a life history strategy for conservation of energy during adverse conditions, primarily of temperature or resource availability. Whilst energy conservation is beneficial in itself, it is less clear whether hibernation confers wider conservation benefits or mitigates or exacerbates a wide range of threats.We briefly review how hibernation manifests in mammalian biology, primarily through energy budgets, activity levels and resource requirements, but then ask how these interact with existing pressures to affect conservation risk. We also explore conservation actions that could alleviate the negative relations between some pressures and hibernation biology and review the available evidence for these measures.Hibernation can convey some protection from disease and predation, though there are notable exceptions, for example white‐nose syndrome. There is well‐established evidence that hibernators are prone to hazards of disturbance during hibernation, necessitating careful mitigation. Hibernators exhibit diverse responses to the pressures related to climate change, including temperature variability and phenological and range mismatches. Yet for each aspect, there are examples of species and populations responding negatively, such as with reduced survival, which suggests that hibernation could exacerbate the negative consequences of climate change.Though there are times when hibernators do not respond as expected, we find several positive conservation actions, such as modern grilles and regulations reducing the disturbance of cave‐hibernating bat species. Understanding and working with hibernation biology can, therefore, successfully mitigate the additional risks it confers. [ABSTRACT FROM AUTHOR]

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of time-scales, and where the relative importance of these processes often varies by orders of magnitude across the computational domain. Here, we present a new implicit–explicit method for numerical RHD that has a number of desirable properties that have not previously been combined in a single method. Our scheme is based on moments and allows machine-precision conservation of energy and momentum, making it highly suitable for adaptive mesh refinement applications; it requires no more communication than hydrodynamics and includes no non-local iterative steps, making it highly suitable for massively parallel and Graphics Processing Unit (GPU)-based systems where communication is a bottleneck; and we show that it is asymptotically accurate in the streaming, static diffusion, and dynamic diffusion limits, including in the so-called asymptotic diffusion regime where the computational grid does not resolve the photon mean-free path. We implement our method in the GPU-accelerated RHD code quokka and show that it passes a wide range of numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the conservation of energy and magnetic helicity of weak solutions for the three-dimensional electron magnetohydrodynamic (EMHD) equations. Firstly, we establish sufficient conditions to guarantee the energy (magnetic helicity) balance of weak solutions for the EMHD equations based on the magnetic field, which can be viewed as an analogue of famous Lions' energy balance criterion of the Navier–Stokes equations for the EMHD equations. Secondly, in the spirit of recent works due to Berselli and Chiodaroli (Nonlinear Anal 192: 111704, 2020), as reported by Berselli (Three-Dimensional Navier–Stokes Equations for Turbulence. Academic Press, London, 2021), Berselli (Mathematics 11(4): 1–16, 2023), Berselli (J Differ Equ 368: 350–375, 2023), Berselli and Georgiadis (Nonlinear Differ Equ Appl 31(33): 1–14, 2024), we present energy (magnetic helicity) preservation criteria in terms of the current density in this system for both the whole space and the torus cases. [ABSTRACT FROM AUTHOR]

To investigate the perforating characteristics of Zr-based bulk metallic glass fragments against thin steel target, ballistic experiments were carried out to measure ballistic the limit velocities of fragments perforating against different thicknesses of targets. The fragments were driven by a 57 mm one-stage light gas gun to impact the thin steel target. The numerical model of Zr-based bulk metallic glass fragments perforating against thin steel target was established using Autodyn2D commercial software, and the perforating process and perforating mechanism were analyzed by numerical simulation. The semi-empirical model to predict the ballistic limit velocity was fitted. An energy model for calculating the residual velocity of a fragment was derived based on the conservation of energy. The theoretical results of the semi-empirical model and the energy model are in good agreement with experiment results and simulation results. And the energy model has good applicability without fitting the parameters for different target thicknesses. [ABSTRACT FROM AUTHOR]

The superconductivity of CaC6 as a function of pressure and Ca isotopic composition was revisited using DFT calculations on a 2c–double hexagonal superlattice. The introduction of superlattices was motivated by previous synchrotron absorption and Raman spectroscopy results on other superconductors that showed evidence of superlattice vibrations at low (THz) frequencies. For CaC6, superlattices have previously been invoked to explain the ARPES data. A superlattice along the hexagonal c-axis direction is also illustrative of atomic orbital symmetry and periodicity, including bonding and antibonding s-orbital character implied by cosine-modulated electronic bands. Inspection of the cosine band revealed that the cosine function has a small (meV) energy difference between the bonding and antibonding regions, relative to a midpoint non-bonding energy. Fermi surface nesting was apparent in an appropriately folded Fermi surface using a superlattice construct. Nesting relationships identified phonon vectors for the conservation of energy and for phase coherency between coupled electrons at opposite sides of the Fermi surface. A detailed analysis of this Fermi surface nesting provided accurate estimates of the superconducting gaps for CaC6 with the change in applied pressure. The recognition of superlattices within a rhombohedral or hexagonal representation provides consistent mechanistic insight on superconductivity and electron−phonon coupling in CaC6. [ABSTRACT FROM AUTHOR]

This study investigates the propagation of fluid–structure coupled waves in a duct featuring both rigid and flexible interfaces. Two cases are considered: in the first case, with a rigid interface, the truncated form of solution preserves the conservation law, while in the second setting, the power balance is not preserved initially, but is rectified as the number of modes, denoted as N, approaches infinity. The discrepancy is explained by specific equations and the presence of delta functions to enforce edge conditions on the membrane at the interface. The Galerkin approach is adopted to address this issue, expressing the membrane’s displacement using a generalized Fourier series. The investigation establishes a framework for modeling higher-order boundary conditions within a duct, employing the mode-matching (MM) method. The study also delves into the scattering components of power, which vary significantly for the two cases. These findings have implications for noise control devices, particularly in active noise control measures utilizing flexible components to dampen both noise and structural vibrations.

In this study, the thermal and drying characteristics of a thin layer food sample were investigated. An indirect type, simple, efficient, and economically feasible solar dryer was fabricated and used for food preservation. However, a dynamic model of a fabricated solar dryer was also presented to gain a better insight into the drying and thermal actions. This model consists of thermal modeling of the drying chamber, solar collector, and solar-dried food sample. The law of conservation of energy was applied to evaluate the temperature at different sections of the solar dryer with respect to drying time. All listed model equations were solved in the MATLAB environment. This study helps to examine the influence of solar radiation on the collector plate temperature, drying chamber temperature, food sample temperature, and performance parameters such as thermal efficiency with respect to drying time. Model data was found in good agreement with experimental data within a 4% error. It is concluded that the drying of food material is affected by air temperature, the collector temperature, mode of heat transfer, and material characteristics such as dimension and mass of the food sample. [ABSTRACT FROM AUTHOR]

Although the probability of a rollover accident is lower than that of other forms of collision, rollover is a serious accident that can break the symmetry of the vehicle and cause serious loss of life and property. There are many factors affecting rollovers, such as the environment, the vehicle, and the driving control. A coach comprises a complex dynamic system; as such, the accuracy and rationality of the used mathematical model are decisive in the study of coach rollover warning and control. By analogy with the modeling method of an automobile collision accident, the general process of a coach rollover accident is analyzed in this study in combination with the contact form and freedom of motion characteristic of the coach body and external environment. According to the principle of conservation of energy, the mathematical models of critical rollover impact force in a collision between vehicles and obstacles and in a collision between two vehicles are established, allowing for analysis of the relationships between the critical tripped rollover impact forces required for a 90° rollover and the continuous action time and collision point height. During the collision between the vehicle and the obstacle, the occurrence of a vehicle rollover is related not only to the impact force in the collision process but also to the collision duration time. Even if the impact force is relatively small, the collision lasts long enough that a second collision may occur until the vehicle rolls over. In the process of a two-vehicle collision, the critical rollover impact force is not only related to the vehicle mass but also to the vehicle wheelbase and the height of the collision point. Based on the law of conservation of momentum, the mathematic models of 90-degree rollover and 180-degree rollover are established, and the critical rollover velocities are calculated. The purpose of this study is to provide reference and guidance for the research methods of vehicle rollover stability and anti-rollover control in the intelligent vehicle era. [ABSTRACT FROM AUTHOR]

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Efficient communication is crucial in reducing injuries and fatalities in coal mine accidents, necessitating the study of simulation methods for mine communication. When transceiver antennas are positioned close to the same side of the tunnel, the simulation results from the Ray Tracing (RT) method exhibit significant errors. Additionally, the Finite-Difference Time-Domain (FDTD) method demands substantial computational resources. In response to these challenges, we propose a RT-FDTD method, guided by the law of conservation of energy. This approach involves dividing the mine tunnel into a cuboidal region, using the RT method to calculate the electric field strength on the cuboid's surface, and then employing this as the excitation source for the FDTD method. Subsequently, the FDTD method is used to calculate the electric field strength within the cuboid. Experimental results demonstrate that the RT-FDTD method effectively mitigates the limitations of the RT and FDTD methods, enhancing both the efficiency and accuracy of simulations in underground mine. [ABSTRACT FROM AUTHOR]

The strength of backfill is greatly influenced by its inclination angle and interlayer concentration. in order to study the influence of inclination angle and interlayer mass concentration on the strength of backfill, a group of layered cemented backfill with cement-sand ratio of 1:4, interlayer mass concentration of 66%, 67% and 68% and inclination angles of 0°, 10°, 20° and 30° were prepared by using tailings as aggregate. The uniaxial compression test was carried out to analyse the effect of interlayer mass concentration and inclination angle on layered cemented backfill. The crack propagation and energy change law of the specimen during compression were analysed by J-integral and energy conservation law. The relationship between the crack initiation and propagation and strain energy of two representative threelayer backfill specimens was analysed by numerical modelling. The results show that the increase in the layer number and the inclination angle of the backfill can weaken the strength of the backfill. In a certain range of inclination angles, the weakening coefficient of the backfill caused by the inclination angle is very consistent with the cosine value of the corresponding angle. Due to the release of crack energy and the existence of interface J integral, the uniaxial compressive strength of different mass concentration backfill is different at various positions. When the displacement reaches a certain value, the crack and strain energy no longer increase. [ABSTRACT FROM AUTHOR]

Three-wave interactions may occur in media with quadratic nonlinearities, which allow for a flow of power between linear waves. The interactions require selection rules similar to conservation of energy and momentum to be satisfied. Equations are presented to solve these selection rules efficiently along the ray trajectory of a pump wave via integration similar to how ray trajectories are determined numerically. This is convenient when dealing with large amplitude beams which may interact with waves along its trajectory. Reformulating the selection rules as a system of ODEs means that the selection rules may be solved using dispersion relations for the three waves, even if the dispersion relations cannot be solved for frequency or wavevector, which would otherwise be needed. In numerical implementations, root-finding algorithms, which may be unstable for complicated dispersion relations, can be avoided. A simple set of equations valid in one-dimensional are presented first. The corresponding equations in arbitrary dimension, including 2D and 3D, are then derived. A set of equations are also derived to find different solutions to the selection rules at a fixed point. Examples with the derived equations applied to plasma physics are presented. [ABSTRACT FROM AUTHOR]

The electrohydrodynamic processes taking place in a cone jet cause ohmic and viscous dissipation, and ultimately self-heating of the liquid. Despite this, previous analyses have modelled cone jets as isothermal systems. To investigate the validity of this assumption, this work applies the leaky-dielectric model to cone jets, while also requiring conservation of energy to reproduce the variation of temperature caused by dissipation and temperature-dependent liquid properties. The main goals are to determine whether there exist electrospraying conditions for which the isothermal assumption is inaccurate, and quantify the temperature field under such conditions. The work confirms that self-heating and thermal effects are important in liquids with sufficiently high conductivities, which is a significant limit because these electrical conductivities are needed to produce jets and droplets with radii of tens of nanometres or smaller. The numerical solution provides accurate expressions for evaluating the dissipation and the temperature increase in cone jets, and confirms that thermal effects cause the apparent breakdown of the traditional scaling law for the current of cone jets of highly conducting liquids. [ABSTRACT FROM AUTHOR]

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential equation for the height of a falling column of water using Torricelli's Law or render a derivation using the principle of the Conservation of Energy. Once the differential equation is obtained the effort turns to solving, parameter estimation, and model validation.We discuss a derived or analytical model compared to an empirical 'just fit' a curve approach. We introduce a strategy for parameter estimation with Excel's Solver command. Discussions of variations on the shape of the cylinder follow. [ABSTRACT FROM AUTHOR]

Negative thermal quenching (NTQ) denotes that the integral emission spectral intensity of a given phosphor increases continuously with increasing temperature up to a certain elevated temperature. NTQ has been the subject of intensive investigations in recent years, and a large number of phosphors are reported to have exhibited NTQ. In this paper, a collection of results in the archival literature about NTQ of specific phosphors is discussed from a macroscopic viewpoint, focusing on the following three aspects: (1) Could the NTQ of a given phosphor be reproducible? (2) Could the associated data for a given phosphor exhibiting NTQ be in line with the law of the conservation of energy? (3) Could the NTQ of a given phosphor be demonstrated in a prototype WLED device? By analyzing typical cases based on common sense, we hope to increase awareness of the issues with papers reporting the NTQ of specific phosphors based on spectral intensity, along with the importance of maintaining stable and consistent measurement conditions in temperature-dependent spectral intensity measurement, which is a prerequisite for the validity of the measurement results. [ABSTRACT FROM AUTHOR]

Contradictory descriptions of the passage of a relativistic particle through a high potential barrier are investigated. The conventional energy-momentum relation yields a real momentum for the particle within the barrier, suggesting classical particle motion. However, this contradicts the law of conservation of energy, which necessitates that the particle's momentum be imaginary, thereby rendering classical motion impossible. This paradox is resolved through the adoption of a novel energy-momentum relation. [ABSTRACT FROM AUTHOR]

A 'scientific worldview' is commonly seen as contradictory to belief in supernatural forces, and there is little research on the supernatural beliefs of individuals who identify with science. In this article, we investigate the supernatural explanations of science-oriented individuals in domains of fundamental concern (suffering, death, and origins), and how supernatural causality is reconciled with belief in science. The open-ended responses of 387 Finns were analysed. The results show that science-oriented Finns endorsed both religion-related and more secular supernatural beliefs (such as belief in evolution as a purposeful process). Following the coexistence model, science-oriented Finns applied synthetic and target-dependent reasoning. In addition, many who invoked supernatural explanations integrated supernatural causality with science. Two forms of integrated reasoning were found: 1) supernatural agency as the ultimate cause and scientific theory as the proximate cause, and 2) a similarity-based heuristic, as seen in afterlife beliefs appealing to the law of conservation of energy. [ABSTRACT FROM AUTHOR]

Currently, there is rapid development of thermophysics of solids associated with the need to create models with a high degree of predictive reliability. This paper presents new approaches to solve relevant issues related to the study of heat transfer in semiconductors and dielectrics, mainly concerning nanostructures. The first of the considered tasks is the creation of a statistical model of the processes of interaction of heat carriers, phonons, with the rough surfaces of solids. For the first time, the authors propose a method based on the statistics of the slopes of the profile of a random surface. The calculation results are the mean free paths of phonon between the opposite boundaries of the sample, which are necessary for calculating the effective thermal conductivity in the ballistic and diffusion–ballistic regime of heat transfer, depending on the roughness parameters. The second task is to develop methods for calculating the processes of heat transfer through the contact surfaces of solids. We are able to show that, taking into account the phonon dispersion and the corresponding restrictions on the frequency values, the modified acoustic mismatch model for calculating Kapitza resistance can be extended to temperatures above 300 K. Previously, the limit of applicability of this method was considered to be a temperature of 30 K. Moreover, the proposed method is also generalized to the case of rough interfaces. The third task is a new approach to determine the thermal conductivity of solids. The authors develop a method of direct Monte Carlo simulation of phonon kinetics with strict consideration of their interaction due to the direct use of the laws of conservation of energy and quasi-momentum. The calculations of the thermal conductivity coefficient for pure silicon in the temperature range from 100 to 300 K show close agreement with the experiment and ab initio calculations of other authors, and also allow considering in details the kinetics of phonons. [ABSTRACT FROM AUTHOR]

We study the reflection and transmission (R/T) characteristics of inhomogeneous plane waves at the interface between two dissimilar fluid-saturated thermoporoelastic media at arbitrary incidence angles. The R/T behaviors are formulated based on the classic Lord–Shulman (LS) and Green–Lindsay (GL) heat-transfer models as well as a generalized LS model, respectively. The latter results from different values of the Maxwell-Vernotte-Cattaneo relaxation times. These thermoporoelastic models can predict three inhomogeneous longitudinal (P1, P2, and T) waves and one shear (S) wave. We first compare the LS and GL models for the phase velocities and attenuation coefficients of plane waves, where the homogeneous wave has a higher velocity but weaker thermal attenuation than the inhomogeneous wave. Considering the oil–water contact, we investigate R/T coefficients associated with phase angles and energy ratios, which are formulated in terms of incidence and inhomogeneity angles, with the latter having a significant effect on the interference energy. The proposed thermoporoelastic R/T model predicts different energy partitions between the P and S modes, especially at the critical angle and near grazing incidence. We observe the anomalous behavior for an incident P wave with the inhomogeneity angle near the grazing incidence. The energy partition at the critical angle is mainly controlled by relaxation times and boundary conditions. Beyond the critical angle, the energy flux predicted by the Biot poroelastic and LS models vanishes vertically, becoming the opposite for the GL and generalized LS models. The resulting energy flux shows a good agreement with the R/T coefficients, and they are well proven by the conservation of energy, where the results are valuable for the exploration of thermal reservoirs. [ABSTRACT FROM AUTHOR]

We consider the linear wave equation V (x) u t t (x , t) − u x x (x , t) = 0 on [ 0 , ∞) × [ 0 , ∞) with initial conditions and a nonlinear Neumann boundary condition u x (0 , t) = (f (u t (0 , t))) t at x = 0. This problem is an exact reduction of a nonlinear Maxwell problem in electrodynamics. In the case where f : R → R is an increasing homeomorphism we study global existence, uniqueness and wellposedness of the initial value problem by the method of characteristics and fixed point methods. We also prove conservation of energy and momentum and discuss why there is no wellposedness in the case where f is a decreasing homeomorphism. Finally we show that previously known time-periodic, spatially localized solutions (breathers) of the wave equation with the nonlinear Neumann boundary condition at x = 0 have enough regularity to solve the initial value problem with their own initial data. [ABSTRACT FROM AUTHOR]

The pressure expansion performance is the key and basis for the diffused self-pumping hydrodynamic mechanical seal to achieve its good cooling performance, self-cleaning performance, and sealing performance. Using the moment of momentum theorem and Stodola's formula, the pressurization effect of the spiral groove on the fluid was analyzed, and the energy head equation of the work done by the spiral groove on the fluid is established. According to the principle of conservation of energy, the energy equation and Bernoulli equation of the work done by the spiral groove on the fluid are derived, the mathematical expression of the conversion of fluid kinetic energy into hydrostatic pressure in the diffuser groove was established, the energy change and energy distribution problems of the fluid after the work of the spiral groove are clarified, and the pressure expansion mechanism is revealed. Through numerical simulation, the relationship between the fluid pressure at the sealing interface, the position and size of the high-pressure field, the opening force, and the leakage rate under different rotational speeds and the structural parameters of the diffuser groove were explored. Finally, the pressure expansion performance of the ordinary self-pumping hydrodynamic mechanical seal and diffused self-pumping hydrodynamic mechanical seal is compared. The results show that the diffuser groove can effectively convert part of the fluid kinetic energy into pressure energy, improve the opening force of the sealing interface, and have a good pressurization effect on the sealing end face. With the widening of the diffuser groove, the pressure peak of the sealing interface increases, the high-pressure field area continues to expand and tends to expand toward the outer diameter of the seal ring, and the opening force also increases significantly; increasing the depth of the diffuser groove will cause the pressure peak of the sealing interface to become smaller, and the area of the high-pressure field will also decrease rapidly, which is not conducive to improving the opening force of the sealing end face. [ABSTRACT FROM AUTHOR]

This paper theoretically investigates the single-particle tunneling current of Dirac electrons in graphene-based junctions. We use the tunneling Hamiltonian approach and strong coupling equations to calculate the single-particle tunneling for three configurations: normal metal-normal metal, normal metal-superconductor, and superconductor-superconductor junctions. Analytical solutions are obtained for the tunneling current by considering the following assumptions and limitations: tunneling primarily involves electrons near the Fermi surface, the system operates at low temperatures, and electron-optical phonon interaction dominates. Notably, our findings reveal that tunneling currents for the normal metal-superconductor and superconductor-superconductor junctions obey the law of conservation of energy and are self-consistent as we take the zero gap limit. [ABSTRACT FROM AUTHOR]

Heterogeneous reactions such as solid–gas reactions are found in various processes that are indispensable to our daily lives, and numerical simulations are becoming more and more widely used to study these processes. In the analysis of processes involving heat transfer, since the conservation equation of energy is solved numerically to obtain temperatures at arbitrary coordinates, the appropriate governing equations should be solved for an accurate understanding of the phenomenon. In this study, the source term of the conservation equation of energy with temperature as a variable is reconsidered for a system with heterogeneous reactions. As a result, it was confirmed that when the source term is inappropriate, temperatures cannot be calculated correctly when chemical species are generated, while temperatures can be calculated correctly when the equation derived in this study is applied. In addition, as an application of the equation derived in this study to solid–gas two-phase flow, a numerical analysis simulating a biomass gasification experiment in a fluidized bed was conducted, and it was confirmed that the equation can represent the experimental result well. The equation derived in this study is expected to ensure the accuracy of analysis of processes related to heat and mass transfer involving heterogeneous reactions.

The present study investigates the scattering of flexural gravity waves due to uneven bottom topography in the context of wave blocking. Emphasis is given to analyzing the effects of multiple propagating wave modes on the solution procedures. The mathematical model is developed for two scenarios: a bottom step and a submerged rectangular breakwater. For the bottom step case, the complete solution in terms of the velocity potential is obtained using the eigenfunction expansion method. Subsequently, the solution associated with the wave transformation by the bottom step is extended to the case of a submerged rectangular breakwater using symmetry characteristics of the velocity potential. The energy balance relation is derived in both cases using the conservation of energy flux in the presence of multiple propagating wave modes. Wave blocking occurs for four different frequencies in both the cases of the bottom step and the submerged breakwater due to variations in water depth. This makes the problem more complex as, depending on the frequency, multiple propagating wave modes can exist in either the reflected region, the transmitted region, or both. The transmitted wave amplitude associated with the lower wavenumber within the blocking frequencies exceeds unity, and this excess energy is balanced by the corresponding energy transfer rate. Additionally, removable discontinuities are observed at the blocking frequencies in the scattering coefficients, where group velocity ceases. In the context of floating ice sheets, the deflection is analyzed in the time domain for frequencies within and outside the blocking limits. [ABSTRACT FROM AUTHOR]

The ordinary diffusion models in continuous media are derived from basic principles: Conservation of energy and momentum. The classical telegraph equation is one of the earliest and most commonly used equation to describe the transmission of electromagnetic waves. In fractal and disordered media, to capture the complex diffusion feature, we consider rather fractional models. Indeed, the mean square displacement in anomalous media is no longer proportional to the time but rather proportional to a power of time whose exponent may be between zero and one or between one and two. This is the case for the present fractional telegraph equation in the presence of non‐negligible voltage wave. Here, the well‐posedness and stability of a telegraph problem with two time‐fractional derivatives is discussed. In addition to being a noninteger problem, the equation in the model is subject to a nonlinear source as well as a nonlinear lower order fractional derivative term. First, the well‐posedness in an appropriate underlying space is established by the use of resolvent operators. Then, it is proved that, despite the presence of these nonlinearities, solutions are Mittag–Leffler stable. This confirms (and extends) the fact that the lower order term plays the role of a damper in the fractional case. To this end, we combine the energy method with some properties of the Caputo fractional derivative. [ABSTRACT FROM AUTHOR]