Inverse Cube Law Research Articles

Return and volatility properties: Stylized facts from the universe of cryptocurrencies and NFTs

Stylized facts of returns and volatility are an important approximation tool for empirical finance studies, especially in the area of young and new assets. In this paper, we examine the return and volatility properties of four non-fungible tokens (NFTs) and four cryptocurrencies from 24th January 2018–2nd August 2022. The results show the following: Firstly, the returns of both NFTs and cryptocurrencies have fat tails, with evidence of tail exponents following the inverse cubic-law, along with clear persistence behavior. Secondly, all returns exhibit volatility clustering, albeit to varying degrees, and the detected absence of inverse volatility-asymmetry challenges the safe-haven property often documented for cryptocurrencies. Thirdly, return-based long-memory is slightly more intense than volatility-based long-memory, especially for NFTs, which demonstrate a predictability contesting market efficiency. These findings are generally consistent with previous findings on equities, implying that the return and volatility behavior of NFTs and cryptocurrencies is leaning towards that of traditional assets.

How the magnetic field behaves during the motion of a highly conducting fluid under its own gravity: A new theoretical, relativistic approach

Within the context of general relativity we study in a fully covariant way the so-called Euler-Maxwell system of equations. In particular, on decomposing the aforementioned system into its 1 temporal and 1 + 2 spatial components at the ideal magnetohydrodynamic limit, we bring it in a simplified form that favors physical insight to the problem of a self-gravitating, magnetized fluid. Of central interest is the decomposition of Faraday's equation which leads to a new general solution governing the evolution of the magnetic field during the motion of the highly conducting fluid. According to the latter relation, the magnetic field generally grows or decays in proportion to the inverse cube law of the scale factor--associated with the continuous contraction or expansion of the fluid's volume respectively. The magnetic field's law of variation, which has remarkable implications for the motion of the whole fluid, is subsequently applied to homogeneous (anisotropic-magnetized) cosmological models--especially to the Bianchi I case--as well as to the study of homogeneous and anisotropic gravitational collapse in a magnetized environment. Concerning the cosmological application, we derive the evolution equations of Bianchi I spacetime permeated by large-scale magnetic fields (these equations reduce to their FRW counterparts at the small/large--scale limit). Also, the compatibility of the new evolution formula for the magnetic field with the standard cosmic nucleosynthesis constraint is examined. As for the application in astrophysics, our results predict that homogeneous gravitational implosion is impeded when the electric Weyl tensor (associated with tidal forces) along the magnetic forcelines overwhelms the magnetic energy density. Lastly, our model denotes that the satisfaction of the aforementioned criterion is ultimately driven into a problem of initial conditions.

An Internet of Things app for monitor unit calculation in superficial and orthovoltage skin therapy

Purpose: We developed an app for Internet of Things (IoT) device such as smartphone or tablet to calculate the monitor unit in superficial and orthovoltage skin therapy. The app can run both on the Windows and Android operation system. Methods: The IoT app was created based on the formula to calculate the monitor unit in skin therapy using kV photon beams. The calculation was based on databases of dose variables such as relative exposure factor and backscatter factor. The calculation also considered the stand-off and stand-in correction according to the inverse-square and inverse-cube law. Verification of the app was carried out by comparing the monitor unit results with those from hand calculations. Results: The frontend window of the app provided a user-friendly interface to the user for inputting prescription dose, beam and treatment setup variables. The user could save the calculation record electronically, generate a printout or send it to other radiation staff using the IoT. Verification of the app showing that deviation between the monitor units calculated by the app and by hand is insignificant. Conclusion: The verified IoT app can effectively calculate the monitor unit in superficial and orthovoltage skin therapy. The app takes advantages of all innate features of IoT such as real time communication, Internet access, data transfer and sharing.

Magnetic field detection using a highly sensitive FBG probe

A partially unclad fiber Bragg grating (FBG) coated with Fe3O4 nanoparticles as a magnetic field sensor is experimentally demonstrated. A series of six FBGs reflecting different wavelengths at an efficient length of 30 mm are fixed on the top and outside of a cylindrical glass chamber. The chamber is equipped with a solenoid that acts as a magnetic field generator and is filled up with air, saline solution, and crude oil separately to detect the changes in the magnetic field. The magnetic–hysteresis loops confirm the super-paramagnetic properties of the synthesized Fe3O4 nanoparticles with size smaller than 20 nm. The sensor response time of ∼21 s confirms the high reliability and repeatability of the sensing scheme. The change in the magnetic field strength depended from FBG–solenoid distance, propagating at different media and function generator frequency leads to shift in the reflected wavelength of each single FBG’s accordingly. The magnetic field strength outside the solenoid obeys the inverse-cubic law, and the decrease in the wavelength shift with an increase in the FBG–solenoid distance is in excellent agreement with the Biot–Savart law. The shift is caused by the interference of different propagating modes that are reflected from the core-cladding and cladding-magnetite layer interfaces; these modes have different phases because of the changes in the refractive index of the magnetite layer resulting from the change in the magnetic field. Our precise fabrication of the FBG probe with a maximum sensitivity of ∼11 000 pm mT−1 and the proposed design of experiment may be appropriate for detecting small changes in magnetic fields in the oil industry.

Virtual phantom magnetic resonance imaging (ViP MRI) on a clinical MRI platform.

The purpose of this study was to implement Virtual Phantom Magnetic Resonance Imaging (ViP MRI), a technique that allows for generating reference signals in MR images using radiofrequency (RF) signals, on a clinical MR system and to test newly designed virtual phantoms. MRI experiments were conducted on a 1.5 T MRI scanner. Electromagnetic modelling of the ViP system was done using the principle of reciprocity. The ViP RF signals were generated using a compact waveform generator (dimensions of 26 cm × 18 cm × 16 cm), connected to a homebuilt 25 mm-diameter RF coil. The ViP RF signals were transmitted to the MRI scanner bore, simultaneously with the acquisition of the signal from the object of interest. Different types of MRI data acquisition (2D and 3D gradient-echo) as well as different phantoms, including the Shepp-Logan phantom, were tested. Furthermore, a uniquely designed virtual phantom - in the shape of a grid - was generated; this newly proposed phantom allows for the investigations of the vendor distortion correction field. High quality MR images of virtual phantoms were obtained. An excellent agreement was found between the experimental data and the inverse cube law, which was the expected functional dependence obtained from the electromagnetic modelling of the ViP system. Short-term time stability measurements yielded a coefficient of variation in the signal intensity over time equal to 0.23% and 0.13% for virtual and physical phantom, respectively. MR images of the virtual grid-shaped phantom were reconstructed with the vendor distortion correction; this allowed for a direct visualization of the vendor distortion correction field. Furthermore, as expected from the electromagnetic modelling of the ViP system, a very compact coil (diameter ~ cm) and very small currents (intensity ~ mA) were sufficient to generate a signal comparable to that of physical phantoms in MRI experiments. The ViP MRI technique was successfully implemented on a clinical MR system. One of the major advantages of ViP MRI over previous approaches is that the generation and transmission of RF signals can be achieved with a self-contained apparatus. As such, the ViP MRI technique is transposable to different platforms (preclinical and clinical) of different vendors. It is also shown here that ViP MRI could be used to generate signals whose characteristics cannot be reproduced by physical objects. This could be exploited to assess MRI system properties, such as the vendor distortion correction field.

Anomalous Lense–Thirring precession in Kerr–Taub–NUT spacetimes

Exact Lense-Thirring (LT) precession in Kerr-Taub-NUT spacetime is reviewed. It is shown that the LT precession does not obey the general inverse cube law of distance at strong gravity regime in Kerr-Taub-NUT spacetime. Rather, it becomes maximum just near the horizon, falls sharply and becomes zero near the horizon. The precession rate increases again and after that it falls obeying the general inverse cube law of distance. This anomaly is maximum at the polar region of this spacetime and it vanishes after crossing a certain `critical' angle towards equator from pole. We highlight that this particular `anomaly' also arises in the LT effect at the interior spacetime of the pulsars and such a signature could be used to identify a role of Taub-NUT solutions in the astrophysical observations or equivalently, a signature of the existence of NUT charge in the pulsars. In addition, we show that if the Kerr-Taub-NUT spacetime rotates with the angular momentum $J=Mn$ (Mass$\times$Dual Mass), inner horizon goes to at $r=0$ and only {\it event horizon} exists at the distance $r=2M$.

Measurement of the magnetic interaction between two bound electrons of two separate ions.

Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin). The magnetic interaction between two electronic spins can therefore impose a change in their orientation. Similar dipolar magnetic interactions exist between other spin systems and have been studied experimentally. Examples include the interaction between an electron and its nucleus and the interaction between several multi-electron spin complexes. The challenge in observing such interactions for two electrons is twofold. First, at the atomic scale, where the coupling is relatively large, it is often dominated by the much larger Coulomb exchange counterpart. Second, on scales that are substantially larger than the atomic, the magnetic coupling is very weak and can be well below the ambient magnetic noise. Here we report the measurement of the magnetic interaction between the two ground-state spin-1/2 valence electrons of two (88)Sr(+) ions, co-trapped in an electric Paul trap. We varied the ion separation, d, between 2.18 and 2.76 micrometres and measured the electrons' weak, millihertz-scale, magnetic interaction as a function of distance, in the presence of magnetic noise that was six orders of magnitude larger than the magnetic fields the electrons apply on each other. The cooperative spin dynamics was kept coherent for 15 seconds, during which spin entanglement was generated, as verified by a negative measured value of -0.16 for the swap entanglement witness. The sensitivity necessary for this measurement was provided by restricting the spin evolution to a decoherence-free subspace that is immune to collective magnetic field noise. Our measurements show a d(-3.0(4)) distance dependence for the coupling, consistent with the inverse-cube law.

Analysis of a viscoplastic flow with field-dependent yield stress and wall slip boundary conditions for a magnetorheological (MR) fluid

The present study theoretically analyzes the Couette–Poiseuille flow of a magnetorheological (MR) fluid flowing through a thin channel, where the externally applied magnetic field can be spatially non-uniform. To this end, a magnetic field-dependent (MFD) bi-viscosity constitutive model is newly proposed and employed in conjunction with the Navier wall slip condition. In this analysis, the MFD yield stress and MFD bi-viscosity are considered to be linearly proportional to the strength of the magnetic field, which obeys the inverse cube law of the normal distance from the magnetic tool. Through a succession of detailed analyses, a total of eight types of Couette–Poiseuille flows are found, including three new flow types that cannot be described with a classical bi-viscosity constitutive model. The analytic solutions for all types of these flows are derived along with the restriction conditions for their existence. Furthermore, the possibility of the existence of these eight types of MFD bi-viscous flows is investigated under four separate characteristic conditions that determine the configuration of the induced magnetic field in the channel. The behaviors of the MFD bi-viscous flows are then investigated through the use of a parametric diagram composed of the Bingham number (Bn) and the Couette number (Co), i.e., Bn–Co diagram, for which some parameters such as the effective distance, nominal viscosity ratio, and wall slip condition are changed.

The point-spread function of fiber-coupled area detectors

The point-spread function (PSF) of a fiber-optic taper-coupled CCD area detector was measured over five decades of intensity using a 20 µm X-ray beam and ~2000-fold averaging. The `tails' of the PSF clearly revealed that it is neither Gaussian nor Lorentzian, but instead resembles the solid angle subtended by a pixel at a point source of light held a small distance (~27 µm) above the pixel plane. This converges to an inverse cube law far from the beam impact point. Further analysis revealed that the tails are dominated by the fiber-optic taper, with negligible contribution from the phosphor, suggesting that the PSF of all fiber-coupled CCD-type detectors is best described as a Moffat function.

Inverse-cubic law of index fluctuation distribution in Indian markets

One of the principal statistical features characterizing the activity in financial markets is the distribution of fluctuations in market indicators such as the index. While the developed stock markets, e.g., the New York Stock Exchange (NYSE) have been found to show heavy-tailed return distribution with a characteristic power-law exponent, the universality of such behavior has been debated, particularly in regard to emerging markets. Here we investigate the distribution of several indices from the Indian financial market, one of the largest emerging markets in the world. We have used tick-by-tick data from the National Stock Exchange (NSE), as well as, daily closing data from both the NSE and Bombay Stock Exchange (BSE). We find that the cumulative distributions of index returns have long tails consistent with a power law having exponent α≈3, at time scales of both 1 min and 1 day. This “inverse-cubic law” is quantitatively similar to what has been observed in developed markets, thereby providing strong evidence of universality in the behavior of market fluctuations.

Intraglottal pressures in a static physical model of the uniform glottis: Entrance loss coefficients and viscous effects

Pressure distributions for the uniform glottis were taken with a static physical model (M5) for the diameters d=0.005, 0.0075, 0.01, 0.02, 0.04, 0.08, 0.16, and 0.32 cm for a number of transglottal pressures of interest for phonation. At each pressure and diameter, entrance loss and exit coefficients are calculated. The pressure dependence and the diameter dependence of these coefficients are catalogued and compared with some standard values from the earlier literature. The accuracy with which tabulations of these coefficients reproduce the M5 pressure distributions is examined. To an excellent approximation, the intraglottal pressures at smaller diameters decrease linearly with the axial distance, and remnants of this behavior are seen at d=0.08 cm and 0.16 cm. It is shown that the intraglottal pressure gradients are linear functions of the glottal flow rates. Thus, dividing the pressure gradients by the flow rates allows one to isolate the geometric dependence of viscous effects. It is shown that an inverse five-halves power law for the diameter dependence of the viscous glottal resistance is a better approximation than the inverse cube law proposed by van den Berg, Zantema, and Doornenbal. [Work supported by NIH R01DC03577.]

Piled-Slab Searches

This paper deals with the conflict between simplicity and optimality in searching for a stationary target whose location is distributed in two dimensions, thus continuing an analysis that was begun in World War II. The search is assumed to be of the “piled-slab” type, where each slab consists of a uniform search of some simple region. The measure of simplicity is the number of regions (smaller is simpler). If each of a fixed number of elliptical regions is searched randomly, we find the optimal region size and the optimal division of effort between regions. Rectangular regions are also considered, as are problems where the regional searches are according to the inverse-cube law, instead of random search. There is a strong tendency for optimal inverse-cube law searches to consist of a single slab. We also consider problems where the amount of effort for each region is optimized myopically, with no consideration for the search of future regions.

On second-order dynamical systems possessing symmetry groups of the inverse cube law equation

On second-order dynamical systems possessing symmetry groups of the inverse cube law equation

Predicting film dose to aid in cassette placement for radiation therapy portal verification film images.

EC film has improved portal localization images with better contrast and improved distinction of bony structures and air-tissue interfaces. A cassette with slower speed screens was used with EC film to image the treatment portal during the entire course of treatment (verification) instead of taking separate films after treatment. Measurements of film density vs source to film distance (SFD) were made using 15 and 25 cm thick water phantoms with both 6 and 18 MV photons from I to 40 cm past the phantom. A characteristic (H & D) curve was measured in air to compare dose to film density. Results show the reduction in radiation between patient and cassette more closely follows an "inverse cube law" rather than an inverse square law. Formulas to calculate radiation exposure to the film, and the desired SFD were based on patient tumor dose, calculation of the exit dose, and the inverse cube relationship. A table of exposure techniques based on the SFD for a given tumor dose was evaluated and compared to conventional techniques. Although the film has a high contrast, there is enough latitude that excellent films can be achieved using a fixed SFD based simply on the tumor dose and beam energy. Patient diameter has a smaller effect. The benefits of imaging portal films during the entire treatment are more reliability in the accuracy of the portal image, ability to detect patient motion, and reduction in the time it takes to take portal images.

Design features for electric communication.

How do the communication discharges produced by electric fish evolve to accommodate the unique design features for the modality? Two design features are considered: first, the limited range of signaling imposed on the electric modality by the physics of signal transmission from dipole sources; and second, the absence of signal echoes and reverberations for electric discharges, which are non-propagating electrostatic fields. Electrostatic theory predicts that electric discharges from fish will have a short range because of the inverse cube law of geometric spreading around an electrostatic dipole. From this, one predicts that the costs of signaling will be high when fish attempt to signal over a large distance. Electric fish may economize in signal production whenever possible. For example, some gymnotiform fish appear to be impedance-matched to the resistivity of the water; others modulate the amplitude of their discharge seasonally and diurnally. The fact that electric signals do not propagate, but exist as electrostatic fields, means that, unlike sound signals, electric organ discharges produce no echoes or reverberations. Because temporal information is preserved during signal transmission, receivers may pay close attention to the temporal details of electric signals. As a consequence, electric organs have evolved with mechanisms for controlling the fine structure of electric discharge waveforms.

Debye-Waller factors and Debye temperatures of alkali halide mixed crystals

The Debye-Waller factors of KxRb(1-x)I and NaClxBr(1-x) mixed crystals have been determined from X-ray diffraction intensities. The mean Debye-Waller factor is found to vary nonlinearly with the composition with positive deviations from linearity. The Debye temperatures (calculated from the Debye-Waller factors) are found to vary slightly non-linearly with composition with negative deviations from linearity. The Debye temperatures of seven alkali halide mixed crystal systems are critically compared with values predicted from six laws for composition variation. Using the estimated standard deviation as the criterion for the goodness of the fit, it is shown that the inverse cube (Kopp-Neumann) law provides the best description for the composition dependence of Debye temperatures of mixed crystals.

Vertical profile of effective turbidity reconstructed from broadening of incoherent body-wave pulses-II.Application to Kamchatka data

SUMMARY The vertical profile of eVective turbidity under Kamchatka is reconstructed from observations of distance-dependent broadening of the inchoherent pulse of highfrequency body waves from small earthquakes, by means of a new approach and data processing scheme developed in Paper I. The key ‘eVective turbidity’ parameter, g e ,u sed is an immediate generalization of the common isotropic turbidity/scattering coeYcient g. Measurements of 200‐600 onset-to-peak delays for P and S waves for five Kamchatka stations are used for interpretation. The estimates based on these data correspond to the 2‐4 Hz frequency band. The inversion of data is performed in terms of the parameters of two generic vertical eVective turbidity structures: a piecewise-constant profile (PCP) and truncated-inverse-power-law profile (TPLP), both used in several variants. The variants of the inversions give consistent results, but also reveal rather limited resolution, not permitting the recovery of detailed profiles or a comparison of results among individual stations. The inversions indicate that the values of eVective turbidity decay from the surface down: within the depth interval h=0‐50 km, the decay is gradual; at greater depths it is much steeper, roughly following the inverse cube law. The estimates of average eVective mean free path l e =1/g e are very close for P and S waves: 50‐60 km (±20 per cent) for the 0‐20 km layer; 250‐300 km (±30 per cent) for the 20‐80 km layer; and at h>60‐80 km, l e #100(h/40)’2‐4 for both P and S waves. The value of both the P- and the S-wave optical thickness (total scattering loss) of the upper 200 km is about 0.75 (±25 per cent), and the lithosphericscattering contribution to t* P is estimated as 0.2 s at 1 Hz. The expected S-wave scattering loss agrees reasonably with the standard regional amplitude attenuation curve, probably reflecting the secondary role of intrinsic loss at 3 Hz. The S-wave scattering Q in the lithosphere of Kamchatka is estimated for f =1 Hz as 125, 205 and 255 for hypocentral distances of shallow events of 30, 100 and 300 km, respectively.

Multichannel effective-range theory with long-range interactions

Effective-range theory, for both single-channel and multichannel scattering by systems interacting with short-range forces at low energies, provides a simple representation of the energy dependence of scattering matrix elements near reaction thresholds in conformity with the Wigner threshold law. A modification of effective-range theory for single-channel electron-atom scattering, required to account for long-range polarization forces, was developed some years ago. A multichannel extension of that theory is presented here, allowing for a superposition of asymptotic power-law potentials, with asymptotic wave functions expressed as sums of Bessel functions. Threshold branch-point singularities are extracted explicitly, leaving modified reaction-matrix elements that vary smoothly with energy. For target states that are not spherically symmetric the asymptotic wave functions account for inverse-cube law interactions that couple the various channels. The theory provides an unambiguous prescription for analytic continuation of scattering parameters from just above to just below a reaction threshold, a feature that may be useful, for example, in studying resonant cross sections based on above-threshold calculations. The present work represents an extension, to a wider class of scattering systems and long-range interactions, of an earlier analysis of threshold behavior [M. Gailitis and R. Damburg, Proc. Phys. Soc. London 82, 192 (1963)] applicable to electron-hydrogen scattering in the field of the inverse-square potential arising from the linear Stark effect.

INVERSE NTH POWER DETECTION LAW FOR WASHBURN'S LATERAL RANGE CURVE

A detection law (the conditional detection rate. ) which corresponds to the model of Washburn's lateral range curve is presented in this paper. The detection law dealt, with here is a general one which includes the inverse cube law and the definite range law. The lateral range curve and the sweep width of this law are derived explicitly. Two met,hods for estimating the parameters of the law are presented and a set of actual data, is analyzed. Applying the model, we investigate the forestalling detection problem in a search-and-search situation. Taking account, of the forestalling detection by the target, the generalized formulas of the lateral range curve and the sweep width are derived.

Entropy-driven expansion of electric double layer repulsion between highly flexible membranes

Most formulations of electric double layer interactions between charged surfaces in electrolyte solutions are essentially “hard—smooth” surface theories. However, there are many situations where the surfaces are “soft” and extremely flexible. In these systems, thermal fluctuations “roughen” the surface topography which augments double layer interactions through direct geometric effects and subtle entropy—driven renormalization. The effects of entropy confinement lead to diminished attraction and expansion of the underlying repulsion to distances much larger than given by the exponential decay. With a self-consistent field approximation, the osmotic equilibrium of a condensed-multilayer assembly of thin flexible membranes has been analyzed to obtain universal predictions for the interaction pressure between layers stabilized by a “bare” exponential repulsion. The results demonstrate a continuous crossover from the direct exponential force to a steric pressure which decays as an inverse-cube law.