Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

In a holistic perspective, time is absolute and relativity a direct consequence of the conservation of total energy

We are taught to think that the description of relativistic phenomena requires distorted time and distance. The message of this essay is that, in a holistic perspective, time and distance are universal coordinate quantities, and relativity is a direct consequence of the conservation of energy. Instead of the kinematics/metrics-based approach of the theory of relativity, the dynamic universe (DU) approach starts from the dynamics of space as a whole and expresses relativity in terms of locally available energy instead of locally distorted time and distance. In such an approach, e.g., the frequency of atomic clocks at different states of motion and gravitation is obtained from the quantum mechanical solution of the characteristic frequencies, and the unique status of the velocity of light becomes understood via its linkage to the rest of space. In the kinematic/metrics-based theory of relativity, we postulate the principle of relativity, Lorentz covariance, the equivalence principle, the constancy of the speed of light, and the rest energy of mass objects. The conservation of momentum and energy is honored in local frames of reference, and time and distance are parameters in frame-to-frame observations. In the dynamics-based DU, the whole space is studied as a closed energy system and the energy in local structures is derived conserving the overall energy balance. Any local state of motion and gravitation in space is related, through a system of nested energy frames, to the state of rest in hypothetical homogeneous space, which serves as the universal frame of reference. Relativity of observations appears as a direct consequence of the overall energy balance and the linkage of local to the whole—with time and distance as universal coordinate quantities. DU postulates spherically closed space and zero-energy balance of motion and gravitation. DU does not need the relativity principle or any other postulates of the theory of relativity. Primarily, the theory of relativity is an empirically driven mathematical description of observations, with postulates formulated to support the mathematics. DU relies on mathematics built on the conservation of an overall zero-energy balance as the primary law of nature, which makes DU more like a metaphysically driven theory. Both approaches produce precise predictions. The choice is philosophical—nature is not dependent on the way we describe it.

Energy-Efficient UAV Trajectory Design with Information Freshness Constraint via Deep Reinforcement Learning

Unmanned aerial vehicle (UAV) technique with flexible deployment has enabled the development of Internet of Things (IoT) applications. However, it is difficult to guarantee the freshness of information delivery for the energy-limited UAV. Thus, we study the trajectory design in the multiple-UAV communication system, in which the massive ground devices send the individual information to mobile UAV base stations under the demand of information freshness. First, an energy-efficiency (EE) maximization optimization problem is formulated under the rest energy, safety distance, and age of information (AoI) constraints. However, it is difficult to solve the optimization problem due to the nonconvex objective function and unknown dynamic environment. Second, a trajectory design based on the deep Q-network method is proposed, in which the state space considering energy efficiency, rest energy, and AoI and the efficient reward function related with EE performance are constructed, respectively. Furthermore, to avoid the dependency of training data for the neural network, the experience replay and random sampling for batch are adopted. Finally, we validate the system performance of the proposed scheme. Simulation results show that the proposed scheme can achieve a better EE performance compared with the benchmark scheme.

Analysis of energy expenditure of skiers across the preparatory phase

Energy expenditure was calculated at rest and during physical activity by indirect calorimetry using the Oxyson Pro system in 55 highly elite skiers. The results showed that in 75% of athletes, the measured rest energy expenditure were higher than the calculated rest energy expenditure by 20% and was 2139±363 kcal/day. Daily energy expenditure was 5347±907 kcal. In the structure of rest energy expenditure the part of carbohydrates was 67 % and fats was 33%. Generally, energy expenditure was more 5000 kcal. In addition, in our study, it was observed a progressive increase of contribution of carbohydrate oxidation in energy expenditure during high-intensity exercise. Key words: energy expenditure, high-intensity exercise, carbohydrates, fats, skiers, indirect calorimetry.

MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

Behaviour, temperature and terrain slope impact estimates of energy expenditure using oxygen and dynamic body acceleration

The energy used by animals is influenced by intrinsic (e.g. physiological) and extrinsic (e.g. environmental) factors. Accelerometers within biologging devices have proven useful for assessing energy expenditures and their behavioural context in free-ranging animals. However, certain assumptions are frequently made when acceleration is used as a proxy for energy expenditure, with factors, such as environmental variation (e.g. ambient temperature or slope of terrain), seldom accounted for. To determine the possible interactions between behaviour, energy expenditure and the environment (ambient temperature and terrain slope), the rate of oxygen consumption ($${\dot{\text{V}}\text{O}}_{2}$$ V ˙ O 2 ) was measured in pygmy goats (Capra hircus aegarus) using open-flow indirect calorimetry. The effect of temperature (9.7–31.5 °C) on resting energy expenditure was measured. The relationship between $${\dot{\text{V}}\text{O}}_{2}$$ V ˙ O 2 and dynamic body acceleration (DBA) was measured at different walking speeds (0.8–3.0 km h−1) and on different inclines (0, + 15°, − 15°). The daily behaviour of individuals was measured in two enclosures: enclosure A (level terrain during summer) and enclosure B (sloped terrain during winter) and per diem energy expenditures of behaviours estimated using behaviour, DBA, temperature, terrain slope and $${\dot{\text{V}}\text{O}}_{2}$$ V ˙ O 2 . During rest, energy expenditure increased below 22 °C and above 30.5 °C. $${\dot{\text{V}}\text{O}}_{2}$$ V ˙ O 2 (ml min−1) increased with DBA when walking on the level. Walking uphill (+ 15°) increased energetic costs three-fold, whereas walking downhill (− 15°) increased energetic costs by one third. Based on these results, although activity levels were higher in animals in enclosure A during summer, energy expenditure was found to be significantly higher in the sloped enclosure B in winter (means of enclosures A and B: 485.3 ± 103.6 kJ day−1 and 744.5 ± 132.4 kJ day−1). We show that it is essential to account for extrinsic factors when calculating animal energy budgets. Our estimates of the impacts of extrinsic factors should be applicable to other free ranging ungulates.

Diffusion gravity and its consequences

Diffusion quantum mechanics (DQM), proposed recently (Zakir, 2020-21), describes a conservative diffusion of classical particles in a fluctuating classical scalar field and, in a homogeneous field, derives the formalism of quantum mechanics. In an inhomogeneous scalar field, DQM reproduces gravitation, and in the present paper, the following theory of diffusion gravity and its various consequences are considered. In DQM a part of the energy of the scalar field is transferred to particles as their fluctuation energy (“thermal” energy), appearing as their rest energy (mass). The resulting local decrease in the field’s energy density around a macroscopic body generates “thermal” diffusion flux of particles to this region. The properties of this “thermal” part of conservative diffusion are similar to gravitation. A high matter concentration in some region reduces the local energy density of scalar field sufficiently to reduce the local intensity of fluctuations. Due to the conservativity of diffusion, the increments in the drift velocity of particles are cumulative, and “thermal” diffusion acceleration arises, independent on the particle’s mass. The world lines become curved, and all processes with particles slowdown, which means time dilation. On hypersurfaces of simultaneity t = const, where the scalar field is defined, effective metrics, connection, and curvature arise. They obey to Einstein’s equations following from balance between energies of matter and background scalar field.

Diffusion treatment of quantum mechanics and its consequences

Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.

Universe: the dynamics of the minimum and maximum expansion states

Two hypotheses stand out in describing the evolution of the Universe. The predominant one predicts that the current expansion began at a certain instant and will not preserve any variation of energy that performs work; apparent flat Universe (Ω = 1) is advocated by relativistic calculations and observational data, with an end or thermal death at its maximum expansion (3D Space). The other hypothesis considers that the Universe is cyclical (always alternating phases of expansion and contraction). This proposal aims to demonstrate that both hypotheses can be correct by not being distinct, but complementary. Supported by the immutability of physical laws, analyses of concepts such as space, mass, energy, gravity, spin, and entropy define an exclusive presence of 1D Space in the minimum and maximum expansion states of the Universe. With our 3D Space Universe created and existing between these extreme states, every dynamic is outlined and completes the usual relativity. The concept of complete rest energy (1D Space) was able to be applied, demonstrating that the complete evolution of the Universe is spatially dynamic in a perpetual time dimension, always recreating our Universe.