This work analytically calculates the first moment of lateral pressure in a bent bilayer using a model that treats lipid molecules as flexible elastic chains. The key point is that lateral pressure in a curved lipid membrane influences membrane elastic constants, particularly the bending modulus, which is related to lateral pressure through its first moment. Although the bending modulus is well known, little is known about its theoretical estimate. The microscopic model presented here enables calculation of the bending modulus for the lipid bilayer, the bending modulus for the lipid monolayer, an area-stretching modulus, a bending-stretching modulus, the spontaneous bending moment for the lipid monolayer, and the position of the neutral surface (non-expanded surface). We obtain these theoretical estimates from an analytical expression for the first correction to the lateral pressure profile in the bent lipid membrane, calculated using a well-known condensed-matter-physics method: perturbation theory in the small parameter L0J, where L0 is the unperturbed monolayer thickness, and J is the curvature. The results are compared with available data and fall within the range of experimental values and molecular dynamics data.

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Kshana, or moment, is an exceedingly small, indivisible, and constant quantum of time defined by Maharishi Vyasa in his commentary on Patanjali Yogdrashan. The determined value of the number of kshana ‘n’ using the concept of birth time delay ‘Tb’ in the photoionisation process confirmsthe value of the number of kshana ‘n’ in a second, as determined by the author’s previous values. Kshana is even smaller than the experimentally observed zeptosecond birth time delay of photoelectrons in photoionization. Kshana, or moment, is not merely a theoretical concept. It is an experimentally measurable time in the future, and it may be used as a unit of time measurement at the subatomic level in physical science that studies non-living systems, matter, energy, and the fundamental laws of nature.

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We investigate trade-off relations governing genuine four-qubit nonlocality in multipartite quantum systems. By analyzing the reduced four-qubit density operators obtained from five-qubit generalized GHZ and MS states, we establish nontrivial constraints on the expectation values of the SeevinckSvetlichny operators associated with these subsystems. In particular, we demonstrate that genuine four-qubit nonlocal correlations across different four-qubit reductions are not mutually independent. For both classes of five-qubit states considered, we show that the sum of the maximal squared expectation values of the Seevinck-Svetlichny operators over all four-qubit reductions is subject to a state-dependent upper bound. Furthermore, this collective bound is shown to be tighter than the bounds obtained by independently imposing the maximal allowed expectation value of the Svetlichny operator on each four-qubit subsystem. These results reveal a monogamy-like trade-off structure for genuine four-qubit nonlocal correlations and provide tighter constraints on their simultaneous manifestation in multipartite quantum systems.

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This work underscores the fundamental role of selfenergy in reinterpreting the Schwarzschild radius. In close analogy with the classical electron radius, the Schwarzschild radius defines the unattainable region, thus eliminating the problem of the singularity of gravitation. The simplicity and the physical foundations of an alternative elementary derivation of General Relativity results based on the Equivalence Principle and Special Relativity are reasserted.

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Classical subatomic particle simulations were applied to protons, neutrons, and electrons to simulate an individual atom using pseudo-potentials to simulate the nucleus and electrons distributed around the nucleus. We applied molecular dynamics algorithms to subatomic particles to simulate complete atoms of Hydrogen, Carbon, and Uranium, as reported in our previous studies. Investigation of the Carbon atom’s energy as a function of time reveals quantised, discrete energy values rather than the continuous energies expected in classical simulations. Changes in an atom’s total energy were found to occur in discrete steps as it transitionsto higher/lower energy states, and the energy values are observed to be quantised rather than continuous. Further analysis examined individual electron energies to determine how electrons behave during an atom’s quantum energy shifts. Only one electron’s energy profile had undergone a step change, leaving the other five electrons unaffected in a Carbon atom. To study the energy quantisation property in other atoms, the Fluorine, Magnesium, and Chlorine atoms were considered and found to exhibit similar quantised, discrete energy properties. The energy quantisation property of an individual atom was already accounted for in classical mechanics/models. This study uses classicalmechanics simulations of subatomic particles to investigate why atomic energies are quantised in nature, as observed in discrete lines in atomic emission/absorption spectra.

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