Inverse Radius Research Articles

Characterization of aluminized RDX for chemical propulsion

The chemical response of energetic materials is analyzed in terms of 1) the thermal decomposition under the thermal stimulus and 2) the reactive flow upon the mechanical impact, both of which give rise to an exothermic thermal runaway or an explosion. The present study aims at building a set of chemical kinetics that can precisely model both thermal and impact initiation of a heavily aluminized cyclotrimethylene-trinitramine (RDX) which contains 35% of aluminum. For a thermal decomposition model, the differential scanning calorimetry (DSC) measurement is used together with the Friedman isoconversional method for defining the frequency factor and activation energy in the form of Arrhenius rate law that are extracted from the evolution of product mass fraction. As for modelling the impact response, a series of unconfined rate stick data are used to construct the size effect curve which represents the relationship between detonation velocity and inverse radius of the sample. For validation of the modeled results, a cook-off test and a pressure chamber test are used to compare the predicted chemical response of the aluminized RDX that is either thermally or mechanically loaded.

Short-range order above the Curie temperature in the dynamic spin-fluctuation theory

Based on the dynamic spin-fluctuation theory, we study the spin-density correlations in the ferromagnetic metals. We obtain computational formulae for the correlation function and correlation radius in different approximations of the theory. Using these formulae, we calculate the magnetic short-range order above the Curie temperature in bcc Fe. Results of the calculation confirm our theoretical prediction that the inverse correlation radius increases linearly with temperature for T sufficiently large. The calculated short-range order is small but sufficient to correctly describe neutron scattering experiments. A considerable amount of the short-range order is shown to persist up to temperatures much higher than the Curie temperature.

ℛ2 supergravity

We formulate R2 pure supergravity as a scale invariant theory built only in terms of superfields describing the geometry of curved superspace. The standard supergravity duals are obtained in both “old” and “new” minimal formulations of auxiliary fields. These theories have massless fields in de Sitter space as they do in their non supersymmetric counterpart. Remarkably, the dual theory of R2 supergravity in the new minimal formulation is an extension of the Freedman model, describing a massless gauge field and a massless chiral multiplet in de Sitter space, with inverse radius proportional to the Fayet-Iliopoulos term. This model can be interpreted as the “de-Higgsed” phase of the dual companion theory of R + R2 supergravity.

Inner Processes of Photon Emission and Absorption

Problem- There are deep unanswered questions about photon emission, specifically how the field structures of the photon emerge from the electron. While this problem cannot be answered from within quantum mechanics, due to its premise that particles are zero dimensional points, other theories of physics have better prospects. Purpose- A conceptual theory is developed for the processes of photon emission and absorption, in a non-local hidden-variable (NLHV) design called the Cordus theory. Approach- Logical inference is used to predict the structures of the discrete fields of the photon and electron under this framework. From this is extracted an explanation of how electron bonding constraints require the electron to emit its excess energy, and how the photon is created and emerges from the electron. Findings- Emission is found to be an escapement mechanism whereby matter particles that are over-prescribed in position can get rid of that energy, and the details of this are explained. The results show excellent qualitative agreement with classical electromagnetic wave theory and quantum mechanics, many conceptual features of which can be recovered. Originality- A novel conceptual theory is developed for the processes of photon emission and absorption. Particularly important here is the proposed causality whereby bonding constraints affect geometric span of the particule, which affects frequency. Hence this constrains the energy that the electron can contain, and explains why the emitted photon has a specific quantum of energy. A second contribution is the proposed differentiation between the discrete fields of the photon and electron. This yields an explanation for the exponential nature of the evanescent field, and recovery of the inverse radius squared relationship for the electro-magneto-gravitational fields. The theory also offers a physical interpretation of the fine structure constant α as a measure of the transmission efficacy of the fabric, i.e. α determines the relationship between the electric constant of the vacuum fabric, and the speed of propagation c through the fabric. There is further novelty in achieving this from the non-local hidden-variable sector of physics. Implications- Quantum mechanics originated with the observation that the movement of electrons between orbitals resulted in emission of photons with discrete quanta of energy. However it does not explain how the transitions occur. The original contribution here is showing that a solution does exist in NLHV physics. Assuming this is valid then the implications are that particles have internal structure and that quantum mechanics is merely a quantitative statistical summary of a deeper physics.

Excitation of Mesoscopic Plasmonic Tapers by Relativistic Electrons: Phase Matching versus Eigenmode Resonances.

We investigate the optical modes in three-dimensional single-crystalline gold tapers by means of electron energy-loss spectroscopy. At the very proximity to the apex, a broad-band excitation at all photon energies from 0.75 to 2 eV, which is the onset for interband transitions, is detected. At large distances from the apex, though, we observe distinct resonances with energy dispersions roughly proportional to the inverse local radius. The nature of these phenomena is unraveled by finite difference time-domain simulations of the taper and an analytical treatment of the energy loss in fibers. Our calculations and the perfect agreement with our experimental results demonstrate the importance of phase-matching between electron field and radiative taper modes in mesoscopic structures. The local taper radius at the electron impact location determines the selective excitation of radiative modes with discrete angular momenta.

Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution

We quantify a limitation in the usual accounting of the finite-size effects, where the leading $[(Z\alpha)^4]$ and subleading $[(Z\alpha)^5]$ contributions to the Lamb shift are given by the mean-square radius and the third Zemach moment of the charge distribution. In the presence of any non-smooth behaviour of the nuclear form factor at scales comparable to the inverse Bohr radius, the expansion of the Lamb shift in the moments breaks down. This is relevant for some of the explanations of the "proton size puzzle". We find, for instance, that the de R\'ujula toy model of the proton form factor does not resolve the puzzle as claimed, despite the large value of the third Zemach moment. Without relying on the radii expansion, we show how tiny, milli-percent (pcm) changes in the proton electric form factor at a MeV scale would be able to explain the puzzle. It shows that one needs to know all the soft contributions to proton electric form factor to pcm accuracy for a precision extraction of the proton charge radius from atomic Lamb shifts.

Short-range Order Above TC in Ferromagnetic Metals

We study the spin-density correlations in ferromagnetic metals using the dynamic spin-fluctuation theory. We derive computational formulae for the spatial correlation function and use them to calculate the short-range order above TC in bcc Fe. Results of the calculation confirm our theoretical prediction that the inverse correlation radius increases linearly with temperature for T sufficiently large. The calculated short-range order is small but sufficient to correctly describe neutron scattering experiments. We show that considerable amount of the short-range order persists up to temperatures much higher than TC.

Adsorption of ozone and plasmonic properties of gold hydrosol: the effect of the nanoparticle size.

The impact of the size of gold nanoparticles on the magnitude of the bathochromic shift of their plasmon resonance peak upon ozone adsorption is revealed and analyzed. Namely, the plasmon band position of 7, 10, 14 and 32 nm nanoparticles shifts toward longer wavelengths by 51, 35, 23 and 9 nm respectively, i.e. the smaller the nanoparticles, the greater the shift of the band. Thus, the sensor efficiency of gold hydrosol increases with a decrease in the nanoparticle size. The shift of the Fermi level is a linear function of the inverse radius of nanoparticles. The observed alterations in the gold nanoparticle plasmonic properties and the Fermi level position are explained by a decrease in the electron density of nanoparticles caused by the electrons' partial binding by adsorbed O3 molecules. The insignificance of oxygen and nitrous oxide effects on plasmonic properties of gold hydrosol is observed.

Standard rulers, candles, and clocks from the low-redshift universe.

We measure the length of the baryon acoustic oscillation (BAO) feature, and the expansion rate of the recent Universe, from low-redshift data only, almost model independently. We make only the following minimal assumptions: homogeneity and isotropy, a metric theory of gravity, a smooth expansion history, and the existence of standard candles (supernovæ) and a standard BAO ruler. The rest is determined by the data, which are compilations of recent BAO and type IA supernova results. Making only these assumptions, we find for the first time that the standard ruler has a length of 103.9±2.3h⁻¹ Mpc. The value is a measurement, in contrast to the model-dependent theoretical prediction determined with model parameters set by Planck data (99.3±2.1h⁻¹ Mpc). The latter assumes the cold dark matter model with a cosmological constant, and that the ruler is the sound horizon at radiation drag. Adding passive galaxies as standard clocks or a local Hubble constant measurement allows the absolute BAO scale to be determined (142.8±3.7 Mpc), and in the former case the additional information makes the BAO length determination more precise (101.9±1.9h⁻¹ Mpc). The inverse curvature radius of the Universe is weakly constrained and consistent with zero, independently of the gravity model, provided it is metric. We find the effective number of relativistic species to be N(eff)=3.53±0.32, independent of late-time dark energy or gravity physics.

Molecular dynamics investigation of the size dependence of the heat of melting of metal nanoclusters

The size dependences of the temperature and heat of melting of transition metal nanoclusters (Ni, Au, Cu, Ag) have been investigated using the isothermal molecular dynamics and tight-binding potential. It has been shown that the heat of melting Λ for nanoclusters approximately 1 nm in size should be two to three times less than the macroscopic heat of melting Λ(∞). It has been found that the heat of melting Λ decreases with a decrease in the size of nanoclusters and, in some approximation, depends linearly on their inverse radius R−1.

Tight lower bound for percolation threshold on an infinite graph.

We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Since a hierarchical notion of dimension is needed to ensure that a virtual, indirect orthogonality of dimensions is maintained in higher-dimensional spatial structures, a generic function for furling and unfurling of the fourth dimension in four-dimensional (4D) spatial structures is proposed. The furling allows three extra dimensions (above the regular three) in a 6D algebraic structure to be represented as a single fourth dimension and thus effectively facilitates morphing of the 4D spacetime into its dual 4D timespace. The effect of the furling of the extra three dimensions resembles that of compactification proposed by Kaluza-Klein theory yet without curling of the furled dimension. The furling supports reexpansion of stringy space into yet another dimension and so enables mapping of radius R (of a closed string being squeezed beyond its minimal radius) into an inverse radius 1/R, which was attributed to string duality, but is shown as due to duality of the 4D spatial structures of spacetime and timespace. Mathematically, it may appear as if further squeezing of the minimal string morphs it into an expanding pointletlike energy bubble so that the stringy spacetime reexpands in a new direction/dimension located within the bubbly dual timespace. So vibrating string is a mirror image of an energy bubblet, both of which do represent the same stringlet. By analogy, particle cast in spacetime could appear mathematically as having a mirror image (or its superpartner) cast in the dual timespace.

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Since a hierarchical notion of dimension is needed to ensure that a virtual, indirect orthogonality of dimensions is maintained in higher-dimensional spatial structures, a generic function for furling and unfurling of the fourth dimension in four-dimensional (4D) spatial structures is proposed. The furling allows three extra dimensions (above the regular three) in a 6D algebraic structure to be represented as a single fourth dimension and thus effectively facilitates morphing of the 4D spacetime into its dual 4D timespace. The effect of the furling of the extra three dimensions resembles that of compactification proposed by Kaluza-Klein theory yet without curling of the furled dimension. The furling supports reexpansion of stringy space into yet another dimension and so enables mapping of radius R (of a closed string being squeezed beyond its minimal radius) into an inverse radius 1/R, which was attributed to string duality, but is shown as due to duality of the 4D spatial structures of spacetime and timespace. Mathematically, it may appear as if further squeezing of the minimal string morphs it into an expanding pointletlike energy bubble so that the stringy spacetime reexpands in a new direction/dimension located within the bubbly dual timespace. So vibrating string is a mirror image of an energy bubblet, both of which do represent the same stringlet. By analogy, particle cast in spacetime could appear mathematically as having a mirror image (or its superpartner) cast in the dual timespace.

Size and shape dependent deprotonation potential and proton affinity of nanodiamond

Many important reactions in biology and medicine involve proton abstraction and transfer, and it is integral to applications such as drug delivery. Unlike electrons, which are quantum mechanically delocalized, protons are instantaneously localized on specific residues in these reactions, which can be a distinct advantage. However, the introduction of nanoparticles, such as non-toxic nanodiamonds, to this field complicates matters, as the number of possible sites increases as the inverse radius of the particle. In this paper we present simulations that map the size- and shape-dependence of the deprotonation potential and proton affinity of nanodiamonds in the range 1.8–2.7 nm in average diameter. We find that while the average deprotonation potential and proton affinities decrease with size, the site-specific values are inhomogeneous over the surface of the particles, exhibiting strong shape-dependence. The proton affinity is strongly facet-dependent, whereas the deprotonation potential is edge/corner-dependent, which creates a type of spatial hysteresis in the transfer of protons to and from the nanodiamond, and provides new opportunities for selective functionalization.

Model evaluation of methods for estimating surface emissions and chemical lifetimes from satellite data

Column densities from satellite retrievals can provide valuable information for estimating emissions and chemical lifetimes objectively across the globe. To better understand the uncertainties associated with these estimates, we test four methods using simulated column densities from a point source: a box model approach, a 2D Gaussian fit, an Inverse Radius fit and an Exponentially-Modified Gaussian fit. The model results were simulated using the WRF and CAMx models for the year 2005, for a single point source outside Atlanta in Georgia, USA with specified emissions and three chemical scenarios: no chemical reactions, 12 h chemical lifetime and 1 h chemical lifetime. No other sources were included in the simulations. We find that the box model provides reliable estimates irrespective of plume speed and plume direction, if the plume speed and the chemical lifetime are known accurately. The 2D Gaussian fit was found to be sensitive to plume speed and direction, and requires omnidirectional dispersion in order to have a decent fit. However, the 2D Gaussian fit is only an approximate fit to the data, and the discrepancies mean that the results are dependent on the geographical domain used for the optimization. An Inverse Radius fit is introduced to correct this issue, which is found to provide improved emissions and lifetime estimates. The Exponentially-Modified Gaussian fit also gave improved estimates. It is however dependent on accurate plume rotation such that reported chemical lifetimes with this method could be significantly underestimated.

A reactive flow model for heavily aluminized cyclotrimethylene-trinitramine

An accurate and reliable prediction of reactive flow is a challenging task when characterizing an energetic material subjected to an external shock impact as the detonation transition time is on the order of a micro second. The present study aims at investigating the size effect behavior of a heavily aluminized cyclotrimethylene-trinitramine (RDX) which contains 35% of aluminum by using a detonation rate model that includes ignition and growth mechanisms for shock initiation and subsequent detonation. A series of unconfined rate stick tests and two-dimensional hydrodynamic simulations are conducted to construct the size effect curve which represents the relationship between detonation velocity and inverse radius of the charge. A pressure chamber test is conducted to further validate the reactive flow model for predicting the response of a heavily aluminized high explosive subjected to an external impact.

The α ′ expansion on a compact manifold of exceptional holonomy

In the approximation corresponding to the classical Einstein equations, which is valid at large radius, string theory compactification on a compact manifold $M$ of $G_2$ or $\mathrm{Spin}(7)$ holonomy gives a supersymmetric vacuum in three or two dimensions. Do $\alpha'$ corrections to the Einstein equations disturb this statement? Explicitly analyzing the leading correction, we show that the metric of $M$ can be adjusted to maintain supersymmetry. Beyond leading order, a general argument based on low energy effective field theory in spacetime implies that this is true exactly (not just to all finite orders in $\alpha'$). A more elaborate field theory argument that includes the massive Kaluza-Klein modes matches the structure found in explicit calculations. In M-theory compactification on a manifold $M$ of $G_2$ or Spin(7) holonomy, similar results hold to all orders in the inverse radius of $M$ -- but not exactly. The classical moduli space of $G_2$ metrics on a manifold $M$ is known to be locally a Lagrangian submanifold of $H^3(M,{\mathbf R})\oplus H^4(M,\mathbf{R})$. We show that this remains valid to all orders in the $\alpha'$ or inverse radius expansion.

Bending Strain Effects on the Critical Current in Cu and Cu–Nb–Stabilized YBCO-Coated Conductor Tape

High strength and high electrical conductivity Cu-Nb tape was tested as the new type of stabilizing layer for YBCO-coated conductor. For electrical interconnection of stabilizing layer to coated conductor the soldering process was used and no degradation in critical current, Ic, of laminated coated conductor after soldering process was observed. The dependence of normalized transport critical current, Ic/Ic0, on the bending radius of coated conductors with and without Cu-Nb stabilizing layer was investigated using the bending test probe providing the uniform bend process at 77 K and under self-field conditions. The reversible and irreversible variations of Ic/I0 with inverse bending radius were found and the irreversible bending radius limit was observed to depend on the neutral axis shift. The generation of the cracks appears to be the primary reason for the Ic/Ic0 degradation that was supported by ScanHall technique investigations.

Vortex Tangle Dynamics under the Effect of Mutual Friction in Superfluid HeII

We have studied numerically the vortex tangle under both counterflow and a ttending of mutual friction by using local- induction approximation model (LIA). We find that the vortex lines are gro wn by the effect of normal fluid velocity in the existence of mutual friction. Many numerical experiments are performed to calculate the vortex filaments development in superfluid helium II. We explained how the total length density, the number of vortex points, the velocity, reconnection events and average inverse radius of curvature are affected by both counterflow and temperature. We fin d that the vortex rings extend fast and the helical disturbances of vortex tangle increases as long as the temperature increases. The cubic box with periodic boundary conditions is employed for all our numerical simulations.

Casimir energy for surfaces with constant conductivity

We consider the vacuum energy of the electromagnetic field in systems characterized by a constant conductivity using the zeta-regularization approach. The interaction in two cases is investigated: two infinitely thin parallel sheets and an infinitely thin spherical shell. We found that the Casimir energy for the planar system is always attractive and it has the same characteristic distance dependence as the interaction for two perfect semi-infinite metals. The Casimir energy for the spherical shell depends on the inverse radius of the sphere, but it maybe negative or positive depending on the value of the conductivity. If the conductivity is less than a certain critical value, the interaction is attractive, otherwise the Casimir force is repulsive regardless of the spherical shell radius.