Faulting of rocks as a critical energy process

Faulting of rocks is a dominant earth process that governs small-scale fracturing, formation of tectonic plate boundaries, and earthquakes occurrence1–4. Since the 18th century, the mechanical settings for rock faulting were commonly analyzed with the Coulomb criterion5 that offers empirical, useful tools for scientific and engineering applications1,6–12. Here we revisit the processes of rock faulting by an alternative approach that incorporates elastic energy, strain-state, and three-dimensional deformation; these mechanical fundamentals are missing in Coulomb criterion. We propose that a stressed rock-body fails as two conditions are met: (1) The elastic energy generated by the loading system equals or exceeds a critical energy intensity that is required for the faulting process; (2) The internal strain of the stressed rock-body due to slip and dilation along the developing faults equals the strain-state created by the loading system to maintain physical continuity13,14. Our simulations reveal that meeting these energy and strain conditions requires an orthorhombic, polymodal fault geometry that is similar to natural and experimental fault systems15–20. The application of our formulation to hundreds of rock-mechanics experiments11,21–28 provides a new, comprehensive benchmark for rock-faulting.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti)

Small bipedal hoppers, including kangaroo rats, are thought to not benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offer novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

Elastic Energy Management Algorithm Using IoT Technology for Devices with Smart Appliance Functionality for Applications in Smart-Grid

Currently, ensuring the correct functioning of the electrical grid is an important issue in terms of maintaining the normative voltage parameters and local line overloads. The unpredictability of Renewable Energy Sources (RES), the occurrence of the phenomenon of peak demand, as well as exceeding the voltage level above the nominal values in a smart grid makes it justifiable to conduct further research in this field. The article presents the results of simulation tests and experimental laboratory tests of an electricity management system in order to reduce excessively high grid load or reduce excessively high grid voltage values resulting from increased production of prosumer RES. The research is based on the Elastic Energy Management (EEM) algorithm for smart appliances (SA) using IoT (Internet of Things) technology. The data for the algorithm was obtained from a message broker that implements the Message Queue Telemetry Transport (MQTT) protocol. The complexity of selecting power settings for SA in the EEM algorithm required the use of a solution that is applied to the NP difficult problem class. For this purpose, the Greedy Randomized Adaptive Search Procedure (GRASP) was used in the EEM algorithm. The presented results of the simulation and experiment confirmed the possibility of regulating the network voltage by the Elastic Energy Management algorithm in the event of voltage fluctuations related to excessive load or local generation.

Experimental and Numerical Simulation of Coal Rock Impact Energy Index Based on Peridynamics

In response to the increasing severity of the rock burst phenomenon and its relatively difficult prediction, peridynamics and indoor uniaxial compression experiments were used to calculate the changes of the internal elastic energy (t) and impact energy (c) for different rock masses during a loading process from an energy perspective. Two traditional indices for judging rock burst tendency—the rock elastic deformation energy index (WET) and the rock impact energy index (WCF)—were combined to define a new actual impact energy index (W) to more accurately determine the occurrence tendency of rock bursts. The LAMMPS software was used to simulate the internal energy changes of rock materials under pressure, and the results were compared with experimental results for verification. The results were as follows: (1) in the uniaxial compression experiments of different specimens, fine sandstone had the strongest impact resistance, followed by coarse sandstone, mudstone, bottom coal seam, and top coal seam, and the obtained material properties provide a reference for predicting the rock bursts of various rock types in practical engineering. (2) The values calculated using the actual impact energy index (W) and the simulation value were 1.75 and 1.77, respectively, which corresponded to a lower error than when the rock impact energy index (WCF) and the rock elastic deformation energy index (WET) were used individually. Thus, this index can better predict the rock burst. (3) The simulated specimen was subjected to a gradual increase in the internal stored elastic energy during compression, which gradually decreased after the ultimate compressive strength was exceeded. The degree of impact damage formed after macroscopic crushing occurred depended on its residual energy.

Utilizing high-p⊥ theory and data to constrain the initial stages of quark-gluon plasma

The scarce knowledge of the initial stages of quark-gluon plasma before the thermalization is mostly inferred through the low-[Formula: see text] sector. We propose a complementary approach in this report — the use of high-[Formula: see text] probes’ energy loss. We study the effects of four commonly assumed initial stages, whose temperature profiles differ only before the thermalization, on high-[Formula: see text][Formula: see text] and [Formula: see text] predictions. The predictions are based on our Dynamical Radiative and Elastic ENergy-loss Approach (DREENA) framework. We report insensitivity of [Formula: see text] to the initial stages, making it unable to distinguish between different cases. [Formula: see text] displays sensitivity to the presumed initial stages, but current experimental precision does not allow resolution between these cases. We further revise the commonly accepted procedure of fitting the energy loss parameters, for each individual initial stage, to the measured [Formula: see text]. We show that the sensitivity of [Formula: see text] to various initial stages obtained through such procedure is mostly a consequence of fitting procedure, which may obscure the physical interpretations. Overall, the simultaneous study of high-[Formula: see text] observables, with unchanged energy loss parametrization and restrained temperature profiles, is crucial for future constraints on initial stages.

Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

The scientific novelty of this work is determined by the rationale for the participation in transformations, along with the kinetic energy of particles, of four types of elastic energy, identified by the peculiarities of their phase changes in the oscillation process. Two types are converted into kinetic energy, while the other two types change the deformed state of particles in accordance with the equations of motion due to internal sources. The result is obtained based on the use of the superposition principle in the space of Lagrange variables with the imposition of forced and free oscillations, as well as a new model of mechanics based on the concepts of space, time, and energy with a new scale of average stresses that takes into account the energy of particles in the initial state. In such a model of mechanics, a generalized measure of the elastic energy of particles is a quadratic invariant of asymmetric tensor whose components are partial derivatives of Euler variables with respect to Lagrange variables. The concept of kinematic energy parameters is introduced, which differ from the corresponding volumetric energy densities by a multiplier equal to the modulus of elasticity, which is directly proportional to the density and heat capacity of the material, and inversely proportional to the volumetric compression coefficient. Comparison of the values of kinematic parameters shows that most of the energy required for oscillations is associated with the deformation of particles and comes from internal sources. The mechanisms of transformation of forced vibrations into their own for transverse, torsional, and longitudinal vibrations are considered, as well as the occurrence of resonance when free and forced vibrations are superimposed with the same or a similar frequency. The formation of a new free wave after each cycle of external influences with an increase in amplitude, which occurs mainly due to internal, and not external, energy sources is justified.

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.