The human mandible's cancellous bone, which is characterized by its unique porosity and directional sensitivity to external forces, is crucial for sustaining biting stress. Traditional CAD models fail to fully represent bone's anisotropic structure and thus depend on simple isotropic assumptions. For our research, we use the latest versions of nTopology and Creo Parametric software to make biomimetic Voronoi lattice models that accurately reflect the complex geometry and mechanical properties of trabecular bone. The porosity of human cancellous bone is accurately modeled in this work using biomimetic Voronoi lattice models. The porosities range from 70% to 95%, which can be achieved by changing the pore sizes to 1.0 mm, 1.5 mm, 2.0 mm, and 2.5 mm. Finite element analysis (FEA) was used to examine the displacements, stresses, and strains acting on dental implants with a buttress thread, abutment, retaining screw, and biting load surface. The results show that the Voronoi model accurately depicts the complex anatomy of the trabecular bone in the human jaw, compared to standard solid block models. The ideal pore size for biomimetic Voronoi lattice trabecular bone models is 2 mm, taking into account both the von Mises stress distribution over the dental implant, screw retention, cortical bone, cancellous bone, and micromotions. This pore size displayed balanced performance by successfully matching natural bone's mechanical characteristics. Advanced finite element analysis (FEA) improves biomechanical understanding of how bones and implants interact by creating more accurate models of biological problems and dynamic loading situations. This makes biomechanical engineering better.

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

Recent simulation studies have revealed a wealth of distinct crystal polymorphs encountered in the self-organization of polymer systems driven by entropy or free energy. The present analysis, based on the concept of self-avoiding random walks on crystal lattices, is useful to calculate upper bounds for the entropy difference of the crystals that are formed during polymer crystallization and thus provide predictions on polymorph thermodynamic stability. Here, we compare two pairs of crystals sharing the same coordination number, ncoord: hexagonal close packed (HCP) and face centered cubic (FCC), both having ncoord = 12 and the same packing density, and the less dense hexagonal (HEX) and body centered cubic (BCC) lattices, with ncoord = 8. In both cases, once a critical step length is reached, one of the crystals shows a higher number of SAWs compatible with the crystal. We explain the observed trends in terms of the bending and torsion angles corresponding to the different chain geometry as imposed by the geometric constraints of the crystal lattice.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Biomimicry in additive manufacturing often refers to topology optimization and the use of lattice structures, due to the organic shape of the topology-optimized designs, and the lattices often looking similar to many light-weight structures found in nature such as trabecular bone, wood, sponges, coral, to name a few. Real biomimetic design however involves the use of design principles taken in some way from natural systems. In this work we use a methodology whereby high resolution 3D analysis of a natural material with desirable properties is “reverse-engineered” and the design tested for the purpose. This allows more accurate replication of the desired properties, and adaption of the design parameters to the material used for production (which usually differs from the biological material). One such example is the impact-protective natural design of the glyptodont body armour. In this paper we report on the production of body armour models in metal (Ti4Al4V) and analyze the resulting mechanical properties, assessing their potential for impact protective applications. This is the first biomimetic study using metal additive manufacturing to date.

In the present paper, the effect of the non-linear thermal radiation on the neutral gas mixture in the unsteady state is investigated for the first time. The unsteady BGK technique of the Boltzmann kinetic equations for a neutral non-homogenous gas is solved. The solution of the unsteady case makes the problem more general significance than the stationary one. For this purpose, the moments' method, together with the traveling wave method, is applied. The temperature and concentration are calculated for each gas component and mixture for the first time.Furthermore, the study is held for aboard range of temperatures ratio parameter and a wide range of the molar fraction. The distribution functions are calculated for each gas component and the gas mixture. The significant non-equilibrium irreversible thermodynamic characteristics the entire system is acquired analytically. That technic allows us to investigate the consistency of Boltzmann's H-theorem, Le Chatelier principle, and thermodynamics laws. Moreover, the ratios among the different participation of the internal energy alteration are evaluated via the Gibbs formula of total energy. The final results are utilized to the argon-helium non-homogenous gas at different magnitudes of radiation force strength and molar fraction parameters. 3D-graphics are presented to predict the behavior of the calculated variables, and the obtained results are theoretically discussed.

Here we will model the curvature and contraction of space-time using as a basis the equation of state of an ideal gas and the Hawking´s equation for the temperature of a black hole. We will use this mathematical model to hypothesize that the Boltzmann´s constant depends on the state of matter, that is, there is a known Boltzmann´s constant for flat space-time and an effective Boltzmann´s constant for curved space-time. This model will allow us to quantify the structure of space-time and will serve as a basis to determine the origin of gravity and the origin of elementary particles. Using the Shannon-Boltzmann-Gibbs entropy relation, we will demonstrate that information is not lost and depends on the state of matter, the information is encoded and depends on the effective Boltzmann´s constant.

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory

We present an overview over eight brightly luminescent Cu(I) dimers of the type Cu2X2(PN)3 with X = Cl, Br, I and P^N = 2-diphenylphosphino-pyridine (Ph2Ppy), 2-diphenylphosphino-pyrimidine (Ph2Ppym), 1-diphenylphosphino-isoquinoline (Ph2Piqn) including three new crystal structures (Cu2Br2(Ph2Ppy)3, 1-Br, Cu2I2(Ph2Ppym)3, 2-I, and Cu2I2(Ph2Piqn)3, 3-I). However, we mainly focus on their photo-luminescence properties. All compounds exhibit combined thermally activated delayed fluorescence (TADF) and phosphorescence at ambient temperature. Emission color, decay time, and quantum yield varies over large ranges. For deeper characterization, we select Cu2I2(Ph2Ppy)3, 1-I, showing a quantum yield of 81 %. DFT and SOC-TDDFT calculations provide insight into the electronic structures of the singlet S1 and triplet T1 states. Both stem from metal+iodide-to-ligand charge transfer transitions. Evaluation of the emission decay dynamics, measured from 1.2 ≤ T ≤ 300 K, gives ∆E(S1-T1) = 380 cm-1 (47 meV), a transition rate of k(S1→S0) = 2.25×106 s-1 (445 ns), T1 zero-field splittings, transition rates from the triplet substates, and spin-lattice relaxation times. We also discuss the interplay of S1-TADF and T1-phosphorescence. The combined emission paths shorten the overall decay time. For OLED applications, utilization of both singlet and triplet harvesting can be highly favorable for improvement of the device performance.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.