Simple Approximate Solutions for Dynamic Response of Suspension System

An approximate simplified analytic solution is proposed for the one DOF (degree of freedom) static and dynamic displacements alongside the stiffness (dynamic and static) and damping coefficients (minimum and maximum/critical values) of a parallel spring-damper suspension system connected to a solid mass-body gaining its energy by falling from height h. The analytic solution for the prescribed system is based on energy conservation equilibrium, considering the impact by a special G parameter. The formulation is based on the works performed by Timoshenko (1928), Mindlin (1945), and the U. S. army-engineering handbook (1975, 1982). A comparison between the prescribed studies formulations and current development has led to qualitative agreement. Moreover, quantitative agreement was found between the current prescribed suspension properties approximate value - results and the traditionally time dependent (transient, frequency) parameter properties. Also, coupling models that concerns the linkage between different work and energy terms, e.g., the damping energy, friction work, spring potential energy and gravitational energy model was performed. Moreover, approximate analytic solution was proposed for both cases (friction and coupling case), whereas the uncoupling and the coupling cases were found to agree qualitatively with the literature studies. Both coupling and uncoupling solutions were found to complete each other, explaining different literature attitudes and assumptions. In addition, some design points were clarified about the wire mounting isolators stiffness properties dependent on their physical behavior (compression, shear tension), based on Cavoflex catalog. Finally, the current study aims to continue and contribute the suspension, package cushioning and containers studies by using an initial simple pre – design analytic evaluation of falling mass- body (like cushion, containers, etc.).

Gravitational Energy Levels: Part Two: مستويات طاقة الجاذبية: الجزء الثاني

We present here a model that explains in a simple, easy and summarized manner, the values, meaning and reasons for the force of gravity, using simple physical tools. According to this model, a gravitational field actually creates different energy levels, similar to the atom, around the center of mass of the gravitational source, and a transition between the energy levels results in the creation of the force of weight acting on each small body which is in the gravitational field. As the body approaches a gravitational field, its energy value decreases to a value of m0u2(R), proportional to the distance R between the centers of the masses, when u(R) is the magnitude of the self-speed of light vector (the progression in the time axis) of the small body, and its value decreases as it approaches the center of the origin of the field. This change in the energy levels is the cause of the force of gravity. A formula is obtained for the concept of potential gravitational energy and the variables on which it depends, and for the time differences between two frames that are in the gravitational field, taking into account the motion and location of each frame. It is obtained from this model that the speed of light is also a variable value as a result of the effect of the gravitational field.

Are Massive Dense Clumps Truly Subvirial? A New Analysis Using Gould Belt Ammonia Data

Dynamical studies of dense structures within molecular clouds often conclude that the most massive clumps contain too little kinetic energy for virial equilibrium, unless they are magnetized to an unexpected degree. This raises questions about how such a state might arise, and how it might persist long enough to represent the population of massive clumps. In an effort to reexamine the origins of this conclusion, we use ammonia line data from the Green Bank Ammonia Survey and Planck-calibrated dust emission data from Herschel to estimate the masses and kinetic and gravitational energies for dense clumps in the Gould Belt clouds. We show that several types of systematic error can enhance the appearance of low kinetic-to-gravitational energy ratios: insufficient removal of foreground and background material; ignoring the kinetic energy associated with velocity differences across a resolved cloud; and overcorrecting for stratification when evaluating the gravitational energy. Using an analysis designed to avoid these errors, we find that the most massive Gould Belt clumps harbor virial motions, rather than subvirial ones. As a by-product, we present a catalog of masses, energies, and virial energy ratios for 85 Gould Belt clumps.

Principles of local realism in a Friedmann universe

The problem of time is a statement of the inability to establish the standard model according to a consistent physical framework based on a valid starting point provided from either the concept of time in quantum mechanics (QM) or general relativity (GR). Using the deterministic local realism approach of Bell’s inequality experiment, a valid mathematical starting point incorporating both QM and GR can be established using the concept of energy conservation within a volume of spacetime. Because Friedmann established a system that correlates the energy level within the volume of spacetime with the proximity between energy mass, with two opposing universal forces that must act on the reconfiguration of particles when considering a realism-based definite position as they evolve in time independent of observation, it is possible to consider QM time evolution as a form of deterministic thermodynamic work. Considering this volume of spacetime in terms of the local realism interpretation allows one to consider the act of time evolution as a reconfiguration that occurs along with the expansion of volume which allows one to establish an energy conservation argument using only the particles that exist within the volume of spacetime to account for both the gravitational energy and the divergent energy usually attributed to the cosmological constant. With this argument time evolution must cost system energy. For energy to be conserved the use of system energy must be for the act of gravitation as a particle evolves in time. The definition of local realism allows Minkowski spacetime diagrams to pertain to the unseen intervals between measurements. This allows a center frame observer to serve as a background clock to measure time rates in correlation to scale factor expansion. This allows one to consider time rates in terms of work that must occur over an interval of a background clock. In the case of local realism, Minkowski mathematics allow a direct correlation between QM time evolution and the second Friedmann equation.

Shapes of a filament on the surface of a bubble

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore, by experiments and theoretical analysis, the morphological phase space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are the geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well. For better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of the filament’s morphological space spanned by one geometric parameter, and one parameter that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.

The thermalization of massive galaxy clusters

ABSTRACT In the hierarchical scenario of structure formation, galaxy clusters are the ultimate virialized products in mass and time. Hot baryons in the intracluster medium (ICM) and cold baryons in galaxies inhabit a dark matter dominated halo. Internal processes, accretion, and mergers can perturb the equilibrium, which is established only at later times. However, the cosmic time when thermalization is effective is still to be assessed. Here, we show that massive clusters in the observed universe attained an advanced thermal equilibrium ∼1.8 Gyr ago, at redshift z = 0.14 ± 0.06, when the universe was 11.7 ± 0.7 Gyr old. Hot gas is mostly thermalized after the time when cosmic densities of matter and dark energy match. We find in a statistically nearly complete and homogeneous sample of 120 clusters from the Planck Early Sunyaev-Zel’dovich (ESZ) sample that the kinetic energy traced by the galaxy velocity dispersion is a faithful probe of the gravitational energy since a look back time of at least ∼5.4 Gyr, whereas the efficiency of hot gas in converting kinetic to thermal energy, as measured through X-ray observations in the core-excised area within r500, steadily increases with time. The evolution is detected at the ∼98 per cent probability level. Our results demonstrate that halo mass accretion history plays a larger role for cluster thermal equilibrium than radiative physics. The evolution of hot gas is strictly connected to the cosmic structure formation.

The Fundamental Discussion between Newton and Einstein

Isaac Newton and Albert Einstein lived in fundamentally different time frames. An interesting question would be: “Who would win the fundamental discussion about the interaction between gravity and light”? Einstein or Newton? Einstein with the fundamental concept of a “curved space-time continuum” within a gravitational field. Or Newton with the fundamental “3rd law of equilibrium between the forces (force-densities)”. It is still the question who was right? Einstein or Newton? Einstein assumes a deformation of the space-time continuum because of a gravitational field. But in general a deformation of any medium will be caused by the change of the energy density within the medium. Like the speed of sound will increase/ decrease when we change the air pressure. However, the speed of sound (which became higher or lower) will still be the same in any direction. The change of the speed of sound will be omni-directional.A gravitational field contains a gravitational energy-density. For that reason the change in the speed of light will be omni-directional within a gravitational field (with a omni-directional gravitational energy density). Einstein however assumes a one-directional change in the speed of light, (only in the direction of the gravitational field). When the change of the speed of light was omni-directional, a beam of light would never be deflected by a gravitational field which is in contradiction with what we measure. Only the absolute value of the speed of light would change omni-directional.The theory of Newton however results in the theory of a 2-directional inertia of photons. The inertia of photons equals zero only in the direction of propagation. Perpendicular to the direction of propagation the mass density of photons is according Einstein’s E = m c^2).The inertia of photons in the direction of propagation will not change within a gravitational field. Gravity can only interact with mass (inertia). Because the mass of the photons in the direction of propagation equals zero, there will ne no interaction with the gravitational field and the photon in the direction of propagation. The speed of light in the direction of propagation will remain unaltered. But according Newton, the photon will have inertia (mass) in the directions perpendicular to the direction of propagation and for that reason the photon will interact with the gravitational field and the photon will be deflected, only in the direction of the gravitational field.And that leads to the consequence that photons will be deflected within a gravitational field when the direction of the gravitational field is perpendicular to the direction of propagation of the photons.To find fundamental mathematical evidence for this concept, we have to make use of Quantum Light Theory. Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.

Temporal (t > 0) Space and Gravitational Waves

I will begin with the nature of our temporal (t > 0) universe, since without temporal space there would be no gravitation force because gravitational field cannot be created within an empty space. When we are dealing with physical realizability of science, Einstein’s relativity theories cannot be ignored since relativistic mechanics is dealing with very large objects. Nevertheless I will show that huge gravitational waves can be created by a gigantic mass annihilation only within a temporal (t > 0) space. Since gravitational energy has never been consider as a significant component within big bang creation, I will show it is a key component to ignite the big bang explosion, contrary to commonly believed that big bang explosion was ignited by time. I will show a huge gravitation energy reservoir induced by a gigantic mass had had been created over time well before the big bang started. Since the assumed singularity mass within a temporal (t > 0) had had gotten heavier and heavier similar to a gigantic black hole that continuingly swallows up huge chunk of substances within the space. From which we see that it is the gravitational force that triggers the thermo-nuclei big bang creation, instead ignited by time as postulated. Aside the thermo-nuclei creation, it had a gigantic gravitational wave release as mass annihilates rapidly by big bang explosion. From which we see that it is the induced gravitational reservoir changes with time, but not the induced gravity changes (i.e., curves) time–space. In other words if there has no temporal (t > 0) space then there will be no gravitational waves.