Fundamental Lengths Research Articles

High quality factor, monodisperse micron-sized random lasers based on porous PLGA spheres.

Miniature random lasers with high quality factor are crucial for applications in barcoding, bioimaging, and on-chip technologies. However, achieving monodisperse and size-tunable biocompatible random lasers has been a significant challenge. In this study, we employed poly(lactic-co-glycolic) acid (PLGA), a biocompatible material approved for medical use, as the base material for random lasers. By integrating a dye-doped PLGA solution with a microfluidic system, we successfully fabricated monodisperse and miniature dye-doped PLGA spheres with tunable sizes ranging from 25 to 52 µm. Upon optical pulse excitation, these spheres exhibited strong random lasing emission at 610-640 nm with a threshold of approximately 22 µJ·mm-2. The lasing modes demonstrated a spectral linewidth of 0.2 nm, corresponding to a quality factor of 3100. Fourier transform analysis of the lasing emission revealed fundamental cavity lengths, providing insights into the properties of the random lasers.

Magnetic monopole mass from fundamental lengths

With an assumption of n = 2 in the Dirac quantization condition,when the sequence comprised of the Bohr radius, reduced Compton wavelength and classical electron radius is extended and matched with its velocity sequence, these fundamental lengths are mirrored with a corresponding set of fundamental monopole lengths with the speed of light as the axis ofsymmetry. Monopole charge is g = 137 ecand mass is found to be 1 . 45 × 10- 3 eV / c2 . This result may fit with the extended relativity (tachyon) theory of Recami with a modification of the proposed charge quantization and electromagnetic coupling constant.

What can observations tell us about coronal heating?

The actual source of coronal heating is one of the longest standing unsolved mysteries in all of astrophysics, but it is only in recent years that observations have begun making significant contributions. Coronal loops, their structure and sub-structure, their temperature and density details, and their evolution with time, may hold the key to solving this mystery. Because spatial resolution of current observatories cannot resolve fundamental scale lengths, information about the heating of the corona must be inferred from indirect observations. Loops with unexpectedly high densities and multi-thermal cross-field temperatures were not consistent with results expected from steady uniform heating models. The hot (T>5 MK) plasma component of loops may also be a key observation; a new sounding rocket instrument called the Marshall Grazing Incidence X-ray Spectrometer will specifically target this observable. Finally, a loop is likely to be a tangle of magnetic strands. The High Resolution Coronal Imager observed magnetic braids untwisting and reconnecting, dispersing enough energy to heat the surrounding plasma. The existence of multi-thermal, cooling loops and hot plasma provides observational constraints that all viable coronal heating models will need to explain.

Fundamental Nature of the Fine-Structure Constant

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.

Free vibration analysis of an adhesively bonded functionally graded double containment cantilever joint

In this study, Genetic Algorithms (GAs) combined with the proposed neural networks were implemented to the free vibration analysis of an adhesively bonded double containment cantilever joint with a functionally graded plate. The proposed neural networks were trained and tested based on a limited number of data including the natural frequencies and modal strain energies calculated using the finite element method. GA evaluates a value generated iteratively by an objective function and this value is calculated by the finite element method. The iteration process restricts us apparently to use directly the finite element method in our multi-objective optimisation problem in which the natural frequency is maximised and the corresponding modal strain energy is minimised. The proposed neural networks were used accurately to predict the natural frequencies and modal strain energies instead of calculating directly them by using the finite element method. Consequently, the computation time and efforts were reduced considerably. The adhesive joint was observed to tend vertical bending modes and torsional modes. Therefore, the multi-objective optimisation problem was limited to only the first mode which appeared as a bending mode. The effects of the geometrical dimensions and the material composition variation through the plate thickness were investigated. As the material composition of the horizontal plate becomes ceramic rich, both natural frequency and modal strain energy of the adhesive joint increased regularly. The plate length and plate thickness were more effective geometrical design parameters whereas the support length and thickness were less effective. However, the adhesive thickness had a small effect on the optimal design of the adhesive joint as far as the natural frequencies and modal strain energies are concerned. The distributions of optimal solutions were also presented for the adhesive joints with fundamental joint lengths and material compositions in reference to their natural frequencies and corresponding modal strain energies.

Fundamental Nature of the Fine-Structure Constant

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.

Fundamental times, lengths and physical constants: Some unknown contributions by Ettore Majorana

AbstractWe review the introduction in physics of the concepts of an elementary space length and of a fundamental time scale, analyzing some related unknown contributions by Ettore Majorana. In particular, we discuss the quasi‐Coulombian scattering in presence of a finite length scale, as well as the introduction of an intrinsic (universal) time delay in the expressions for the retarded electromagnetic potentials. Finally, we also review a special model considered by Majorana in order to deduce the value of the elementary charge, in such a way anticipating key ideas later introduced in quantum electrodynamics.

Liquid elasticity length, universal dynamic crossovers, and glass transition

We discuss two main universal dynamic crossovers in a liquid that correspond to relaxation times of 1 psand 10−7–10−6 s. We introduce the concept of liquid elasticity lengthdel. At roomtemperature, del is several Å in water and increases to 0.01 mm in honey and 1 mm in tar. We discuss that on temperaturedecrease, del = dm and del = L correspond to the two dynamic crossovers, wheredm is the medium-rangeorder and L is system size. In this picture, the two important changes in the dynamics of a system aredefined by its fundamental lengths. The second crossover defines all kinetic aspects of theglass transition, whereas the ‘thermodynamic’ glass transition is realized in the limit ofinfinite system size only. In this picture, we also discuss the division of liquids into strongand fragile. One prediction of our theory is the increase of viscosity with thesize of macroscopic system, which we verify by measuring the viscosity of honey.

Position and length operators in a theory with minimal length

Relations between the notions of fundamental and minimal lengths, and duality, in a system with minimal length uncertainty relations are examined. Self-adjoint versions of operators relevant to the problem, and their spectra, are analyzed in detail.

A weak acceleration effect due to residual gravity in a multiply connected universe

Context. Understanding dark energy and measuring the topology of the Universe are two of the biggest open questions in physical cosmology. It was previously shown that multiple connectedness, via the twin paradox of special relativity, provides a novel physical justification for an assumption of the standard FLRW model: it implies a favoured space-time splitting (comoving coordinates). Aims. Could cosmic topology also imply dark energy? Methods. We use a weak field (Newtonian) approximation of gravity and consider the gravitational effect from distant, multiple copies of a large, collapsed (virialised) object today (i.e. a massive galaxy cluster), taking into account the finite propagation speed of gravity, in a flat, multiply connected universe, and assume that due to a prior epoch of fast expansion (e.g. inflation), the gravitational effect of the distant copies is felt locally, from beyond the naively calculated horizon. Results. We find that for a universe with a T' x R 2 spatial section, the residual Newtonian gravitational force (to first order) provides an anisotropic effect that repels test particles from the cluster in the compact direction, in a way algebraically similar to that of dark energy. For a typical test object at comoving distance X from the nearest dense nodes of the cosmic web of density perturbations, the pressure-to-density ratio w of the equation of state in an FLRW universe, is ω ∼ -(X/L) 3 , where L is the size of the fundamental domain, i.e. of the Universe. Clearly, |ω| « 1. For a T 3 spatial section of exactly equal fundamental lengths, the effect cancels to zero. For a T3 spatial section of unequal fundamental lengths, the acceleration effect is anisotropic in the sense that it will tend to equalise the three fundamental lengths. Conclusions. Provided that at least a modest amount of inflation occurred in the early Universe, and given some other conditions, multiple connectedness does generate an effect similar to that of dark energy, but the amplitude of the effect at the present epoch is too small to explain the observed dark energy density and its anisotropy makes it an unrealistic candidate for the observed dark energy.

Cantorian space–time and Hilbert space: Part II—Relevant consequences

Abstract In this paper, we will show the consequences of the link between e (∞) and H (∞) . Starting from El Naschie’s e (∞) nature shows itself as an arena where the laws of physics appear at each scale in a self–similar way, linked to the resolution of the observations; while Hilbert’s space H (∞) is the mathematical support to describe the interaction between the observer and dynamical systems. The present formulation of space–time, based on the non-classical, Cantorian geometry and topology of the space–time, automatically solves the paradoxical outcome of the two-slit experiment and duality. The experimental fact that a wave-particle duality exists is an indirect confirmation of the existence of e (∞) . Another direct consequence of the fact that real space–time is the infinite dimensional hierarchical e (∞) is the existence of the scaling law R ( N ). The present author proposed it as a generalization of the Compton wavelength. This rule gives an answer to segregation of matter at different scales; it shows the role of fundamental constants like the speed of light and Plank’s constant h in the fundamental lengths scale without invoking the methodology of quantum mechanics. In addition, we consider the genesis of E -Infinity. A Cantorian potential theory can be formulated to take into account the geometry and topology of e (∞) in the context of gravitational theories. Consequently, we arrive at the result of the existence of gravitational channels.

Cantorian spacetime and Hilbert space: Part I—Foundations

Abstract We are going to show the link between the e(∞) Cantorian space and the Hilbert spaces H(∞). In particular, El Naschie’s e(∞) is a physical spacetime, i.e. an infinite dimensional fractal space, where time is spacialized and the transfinite nature manifests itself. El Naschie’s Cantorian spacetime is an arena where the physics laws appear at each scale in a self-similar way linked to the resolution of the act of observation. By contrast the Hilbert space H(∞) is a mathematical support, which describes the interaction between the observer and the dynamical system under measurement. The present formulation, which is based on the non-classical Cantorian geometry and topology of spacetime, automatically solves the paradoxical outcome of the two-slit experiment and the so-called particle–wave duality. In particular, measurement (i.e. the observation) is equivalent to a projection of e(∞) in the Hilbert space built on 3 + 1 Euclidean spacetime. Consequently, the wave–particle duality becomes a mere natural consequence of conducting an experiment in a spacetime with non-classical topological and geometrical structures, while observing and taking measurements in a classical smooth 3 + 1 Euclidean spacetime. In other words, the experimental fact that a wave–particle duality exists is an indirect confirmation of the existence of e(∞) and a property of the quantum–classical interface. Another direct consequence of the fact that real spacetime is infinite dimensional hierarchical e(∞) is the existence of scaling law R(N), introduced by the author, which generalizes the Compton wavelength. It gives an answer to the problem of segregation of matter at different scales, and shows the role of fundamental constants such as the speed of light and Plank’s constant h in the fundamental lengths scale without invoking the principles of quantum mechanics.

Dynamics of the magnetization reversal in Au/Co/Au micrometer-size dot arrays

In high-quality Au/Co/Au ultrathin films with high perpendicular magnetic anisotropy, magnetization reversal occurs through easy domain-wall (DW) propagation following rare nucleation events, located at major structural defects. By patterning arrays of dots in such films, we block the DW propagation, and thus sample the intrinsic distribution of nucleation sites, improving precision as the dot diameter decreases. In a Au/Co (1 nm)/Au film we have fabricated large area arrays of round dots, with diameters of 1 and 2 \ensuremath{\mu}m, leaving aside an unpatterned area as a witness of the magnetization reversal in a ``continuous film'' having undergone all patterning steps. Polar magneto-optical (MO) Kerr effect was used in both global and imaging experiments to accurately measure the hysteresis loops and aftereffect phenomena. We show that, despite limited damage induced by patterning, the expected behavior is indeed observed. A statistical model was developed, assuming an intrinsic distribution of nucleation sites in the initially continuous film, a uniform nucleation volume ${V}_{n},$ and a linear dependence of the nucleation energy barrier ${E}_{n}{=2M}_{S}{V}_{n}{(H}_{n}\ensuremath{-}H)$ on both applied field $H$ and nucleation field ${H}_{n}$ at a given site (${M}_{S}$ is the saturation magnetization). Comparison between experiments and theory shows an excellent overall agreement, and allows one to obtain an approximate view of the distribution of nucleation fields. We could extract two fundamental lengths, the nucleation length ${\ensuremath{\xi}}_{n}$ (related to ${V}_{n}$), and the mean distance $l$ between nucleation sites. ${\ensuremath{\xi}}_{n}$ was found to be equal to $26\ifmmode\pm\else\textpm\fi{}1\mathrm{nm},$ in good agreement with previous determinations on similar films. $l,$ equal to about 430 nm, could be viewed as a measure of the typical distance between major structural defects in the ``continuous film.'' Our method is indeed a means to characterize nanometer scale magnetic events (reversal of a nucleation volume), using micrometer scale resolution experiments (MO imaging). This is an example of how microfabrication can help us to understand magnetization reversal in a continuous ultrathin film.

Correlation length used as a predictor of fundamental scale lengths for image characterization

Correlation length used as a predictor of fundamental scale lengths for image characterization

Relaxation phenomena in self-assembled systems

A dynamical model is proposed to study the evolution of the structure factor in the isotropic phase of a frustrated spin model. The study has application to the development of structure in bicontinuous microemulsions. We consider both non-conserved order parameters (NCOP) and the conserved order parameters (COP). In the former case (NCOP), within a self-consistent meanfield theory, we find that in the asymptotic limit ( t→∞) all modes of the structure factor decay with the same characteristic time. This characteristic time scales with the two fundamental lengths d and ξ is present in self-assembled systems such as frustrated magnetic systems and binary alloys. In the latter case (COP), we find that no characteristic time is present within self-consistent mean-field theory and all modes decay algebraically. This is reminiscent of the long time tails in the velocity-velocity autocorrelation function observed for simple fluids.

On the characteristic lengths of the highTcoxide superconductors

Abstract We discuss the fundamental characteristic lengths, namely ζ0 the zero temperature coherence length, ΛL the London penetration depth, and l the carrier mean free path, for the oxide high Tc superconductors in relation to the latest experimental measurements. We examine theoretically why ζ0 is so small and argue that its smallness is independent of the nature of the pairing mechanism of superconductivity. We also compare various measurements from the point of view of Pippard's theory for both the normal and the superconducting states respectively. Several questions are posed by these interpretations of the experimental data.

Direct evidence for a very large penetration depth in superconducting Bi2Sr2CaCu2O8 single crystals

THE temperature-dependent magnetic penetration depth λ(T) and the superconducting coherence length ξ(T) are the two fundamental lengths in superconductivity1, and it is clearly important to determine these two quantities in the new high-transition-temperature (high-Tc) oxide superconductors2. Here we report a direct determination of λ(0) for high-quality single crystals of Bi2Sr2CaCu2O8 with a Tc of 85 K, for the particular case in which the screening currents responsible for the diamagnetism flow perpendicular to the CuO2 planes. The measured value, λc(0) = 100 ± 10 (μm, is surprisingly large, but it is consistent with the anisotropy in the electrical resistivity above Tc, measured on the same batch of single crystals, and approximately consistent with the anisotropy in lower critical field, Hc1 measured by others3. Such a large value may have important consequences for the physical properties of polycrystalline samples and thin films.

Analysis of brain gene expression in schizophrenia by molecular cloning techniques

The paper describes an investigation of some possible “dimensional” systems for the designation of physical concepts. The usual system, based on the primary concepts of length, mass, and time, results in a large number of ambiguities (Table II) and is therefore unsatisfactory. The introduction of an additional primary concept for heat and another for electromagnetism is an improvement, but many ambiguities still remain (Table III). The trouble is caused by our failure to distinguish between distances in different directions.By introducing two fundamental lengths lr and lt (radial and tangential) in place of the usual l, we eliminate the former difficulty and obtain distinct designation symbols for the concepts of energy and torque, for normal stress and shear stress, for pharosage (radiant energy per unit area) and hellos (brightness).There are six types of practical application for idon theory (“dimensions”), all of which are handled as well (or better) by the lr,lt-system as by the old method. Examples are given of the use of the new method in checking equations and in deriving new equations by idonic analysis. Tables of designation symbols are given for the principal concepts of physics (Table VI to X). Finally, an alternative system is outlined which employes the fundamental lengths lr, lt, and l, and which discriminates between vectors and scalars in physical space (Table XI). This vector system is useful in certain problems, though in most cases the simpler lr/lt-system is adequate.

Ultrafine Metal Particles in Porous and Dense Silica Gels

The present trend of developing electronic devices with increasingly fine dimensions borders on a number of fundamental scientific questions about the very nature of how materials at ultrafine dimensions behave. This article addresses some of these questions. The fabrication of discrete metallic phases in porous and nonporous glassy matrices presents a number of exciting device possibilities. Methods of fabricating ultrafine metallic phases in silica via the sol-gel route are presented.In attempting to fabricate materials with ultrafine physical dimensions for a wide variety of applications, several fundamental questions arise about the nature of materials behavior. For example, how many metal atoms are necessary to form a cluster exhibiting “metallic“ properties? Moreover, does the number of atoms necessary depend upon which metallic property is examined? This question has been partly addressed by D.C. Johnson and co-workers with regard to magnetism in osmium clusters. Their results show a threefold increase in magnetic susceptibility between clusters containing 3–10 osmium atoms.Another important question, especially when considering device applications, is how the relative contributions of surface and bulk thermodynamics affect such properties as phase transformations. In addition, ultrafine phase dimensions interact with the fundamental unit lengths of a wide range of processes, including the wavelength of visible light, the mean free path lengths of conduction processes, the wavelengths of phonon vibrations, etc. How do these interactions affect optical, thermal, and electronic properties?Fabrication of ultrafine metallic particles in porous and nonporous matrices may lead to many possible device applications including heterogeneous catalysts, nonlinear optic devices, highvoltage switching devices based on interparticle tunneling, and perhaps even new types of charge storage devices (capacitors).

Fundamental correlation lengths of coherent speckle in medical ultrasonic images

Refinements to previous analyses of the natural correlation lengths within simple images and between images to be compounded are presented. Comparison of theoretical and experimental results show very good agreement for the case of Rayleigh scattering media: the correlation length within a simple image is comparable to the resolution cell size; the correlation length between images to be spatially compounded is comparable to, but smaller than, the transducer on array aperture; and the correlation length between images to be frequency-compounded becomes a frequency comparable to their bandwidth. Complications arising from the presence of specular scattering or due to the presence of just a few scatterers are considered. It is shown that straightforward solutions exist for either of these problems taken by itself. When they occur in combination, calibration techniques may lead to unambiguous identification of the contributions to the scattering from diffuse or incoherent scattering and from specular or coherent scattering, and to estimation of the density of diffuse scatterers.