Small Spatial Volume Research Articles

Cartan monopoles

The effective Hamiltonians for chiral supersymmetric gauge theories at small spatial volume are generalizations of the Hamiltonians describing the motion of a scalar or a spinor particle in a field of Dirac monopoles (we are dealing in fact with a certain lattice of monopoles supplemented with a periodic singular potential). The gauge fields in such Hamiltonians belong to the Cartan subalgebras of the corresponding gauge algebras. Such a construction exists for all groups admitting complex representations, i.e., for SU(N≥3), Spin(4n+2) with n≥1 and E6. We give explicit expressions for these Hamiltonians for SU(3), SU(4)≃Spin(6) and for SU(5). The simplified version of such a Hamiltonian, deprived of fermion terms, of the extra scalar potential and when only one node of the lattice is taken into consideration, describe a 3r-dimensional motion (r being the rank of the group) in the field what we call a “Cartan monopole.” As is the case for the ordinary monopole, the Lagrangian of this system enjoys gauge symmetry, rotational symmetry, and the parameter, generalizing the notion of magnetic charge for Cartan monopoles, is quantized. Published by the American Physical Society 2024

Non-Invasive Deep-Brain Stimulations by Spatio-Temporal Fourier Synthesis

A new type of non-invasive deep-brain stimulation is conceived and demonstrated by computer simulations. The process is based on spatio-temporal Fourier synthesis using multiple electrode pairs with sinusoidal current drive to limit skin sensations and concentrate the stimulus power to a small spatial volume and into large rare spikes in the time domain, while the signal power at the skin is steady and small. Exotic time signals are also shown, such as the cases of high-frequency prime harmonics, quasi-random and chirping stimulations. The first one is able to generate sharp spikes with low frequency while its carriers are high-frequency harmonics that easily conduct via the skin and brain tissue. Open questions are, among others, the best shapes and timing of spikes. The answers require experimental tests and explorations in animal models and human subjects.

Predicting peak stresses in microstructured materials using convolutional encoder–decoder learning

This work presents a machine-learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak – which are of critical importance to failure – is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence require computationally expensive training. This work develops a deep-learning-based convolutional encoder–decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.

Fixed-point quantum circuits for quantum field theories

Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically computed ground states in a small spatial volume can be used to determine operators for preparing the ground state in a beyond-classical quantum register, even for interacting scalar field theories. Due to the exponential decay of correlation functions and the double exponential suppression of digitization artifacts, the derived quantum circuits are expected to be relevant already for near-term quantum devices.

Part 2: Review of Tokamak Physics as a Way to Construct a Device Optimal for Graviton Detection and Generation within a Confined Small Spatial Volume, as Opposed to Dyson’s “Infinite Astrophysical Volume” Calculations

Review of arguments in refutation of Dyson’s alleged prohibition against use of device physics as to determining if Gravitons can be determined to exist is followed up by use of a hot Plasma within a Tokamak in a redo of the amplitude of alleged Gravitational waves. This overlaps with gravitons, and we follow up with an analysis of the pertinent form of Gravitons, i.e. do we have massless or massive gravitons. In addition we also obtain GW of amplitude as low as five meters above the Tokamak center such low strain values are extremely close to brane world GW, and strain values in early universe cosmology. This is after our device analysis. Using Grischuk and Sachin (1975) amplitude for the GW generation due to plasma in a toroid, we generalize this result for Tokamak physics. We obtain evidence for strain values up to in a Tokamak center. These values are an order of magnitude sufficient to allow for possible detection of gravitational waves. The critical breakthrough is in utilizing a burning plasma drift current, which relies upon a thermal contribution to an electric field. Such low strain values are extremely close to brane world GW, and strain values in early universe cosmology. We conclude with statements as to comparing our basic results with those of Yan-Gang Miao, Ying-Jie Zhao as to their generalized HUP which gives support to the suppositions given in our comparison of the character of gravitons which are initially at the start of inflation versus those of our present era, as measured by the Tokamak.

A quantum peek inside the black hole event horizon

We solve the Klein-Gordon equation for a scalar field, in the background geometry of a dust cloud collapsing to form a black hole, everywhere in the (1+1) spacetime: that is, both inside and outside the event horizon and arbitrarily close to the curvature singularity. This allows us to determine the regularized stress tensor expectation value, everywhere in the appropriate quantum state (viz., the Unruh vacuum) of the field. We use this to study the behaviour of energy density and the flux measured in local inertial frames for the radially freely falling observer at any given event. Outside the black hole, energy density and flux lead to the standard results expected from the Hawking radiation emanating from the black hole, as the collapse proceeds. Inside the collapsing dust ball, the energy densities of both matter and scalar field diverge near the singularity in both (1+1) and (1+3) spacetime dimensions; but the energy density of the field dominates over that of classical matter. In the (1+3) dimensions, the total energy (of both scalar field and classical matter) inside a small spatial volume around the singularity is finite (and goes to zero as the size of the region goes to zero) but the total energy of the quantum field still dominates over that of the classical matter. Inside the event horizon, but \textit{outside} the collapsing matter, freely falling observers find that the energy density and the flux diverge close to the singularity. In this region, even the integrated energy inside a small spatial volume enclosing the singularity diverges. This result holds in both (1+1) and (1+3) spacetime dimensions with a \emph{milder} divergence for the total energy inside a small region in (1+3) dimensions. These results suggest that the back-reaction effects are significant even in the region \emph{outside the matter but inside the event horizon}, close to the singularity.

IS A GRAVITON DETECTABLE?

IS A GRAVITON DETECTABLE?

Signatures of minor mergers in Milky Way like disc kinematics: ringing revisited

By means of N-body simulations we study the response of a galactic disc to a minor merger event. We find that non-self-gravitating, spiral-like features are induced in the thick disc. As we have shown in a previous work, this "ringing" also leaves an imprint in velocity space (the u-v plane) in small spatial regions, such as the solar neighbourhood. As the disc relaxes after the event, clumps in the u-v plane get closer with time, allowing us to estimate the time of impact. In addition to confirming the possibility of this diagnostic, here we show that in a more realistic scenario, the in-fall trajectory of the perturber gives rise to an azimuthal dependence of the structure in phase-space. We also find that the space defined by the energy and angular momentum of stars is a better choice than velocity space, as clumps remain visible even in large local volumes. This makes their observational detection much easier since one need not be restricted to a small spatial volume. We show that information about the time of impact, the mass of the perturber, and its trajectory is stored in the kinematics of disc stars.

Numerical study of the two color attoworld

We consider QCD at very low temperatures and non-zero quark chemical potential from lattice Monte Carlo simulations of the two-color theory in a very small spatial volume (the attoscale). In this regime the quark number rises in discrete levels in qualitative agreement with what is found analytically at one loop on S3xS1 with radius R_S3 << 1/{\Lambda}_QCD. The detailed level degeneracy, however, cannot be accounted for using weak coupling arguments. At each rise in the quark number there is a corresponding spike in the Polyakov line, also in agreement with the perturbative results. In addition the quark number susceptibility shows a similar behaviour to the Polyakov line and appears to be a good indicator of a confinement-deconfinement type of transition.

Nonequilibrium and quantum coherent phenomena in the electromechanics of suspended nanowires (Review Article)

Strong coupling between electronic and mechanical degrees of freedom is a basic requirement for the operation of any nanoelectromechanical device. In this review we consider such devices and in particular investigate the properties of small tunnel-junction nanostructures that contain a movable element in the form of a suspended nanowire. In these systems, electrical currents and charge can be concentrated to small spatial volumes, resulting in strong coupling between the mechanics and the charge transport. As a result, a variety of mesoscopic phenomena appear, which can be used for the transduction of electrical currents into mechanical operation. Here we will in particular consider nanoelectromechanical dynamics far from equilibrium and the effect of quantum coherence in both the electronic and mechanical degrees of freedom in the context of both normal and superconducting nanostructures.

Characterization of Polymers and Corrosion Products by Raman Spectroscopy

The Raman spectroscopy is a nondestructive lateral surface sensitive analytical technique aimed at characterizing newly developed coatings and examining the quality of corrosion resistance of surface modifications. Due to the small spatial detection volume of 1 μm3, the chemical microstructure of the surface and organic or inorganic layers can be identified. The crystallinity of coatings, the degree of molecular order, orientation and cross-linking, measurable by the stereo selectivity of the Raman spectroscopy was applied for the classification of Polyethylenetherephtalate (PET) coatings. For determining multilayer systems, the confocal measuring technology of the Raman microscope has been performed for depth profiling through transparent PET layers. Furthermore, this confocal measuring technique provided the best results for the local identification of corrosion products by monitoring the corrosion under transparent organic corrosion protection layers. Selected samples displayed the facilities of Raman spectroscopy to characterize the formation of organic surface coatings and inorganic contaminations by lateral and confocal detection properties. Therefore, Raman spectroscopy received special interest in coating and steel applications to analyse the degradation, processing history or interlacing of coatings and to reduce production sources of error.

Multiple occupancy considerations for the SmartPET imaging system

The SmartPET collaboration is investigating the use of two planar high-purity germanium double-sided strip detectors as a Compton imaging positron emission tomography system. Monte Carlo simulations suggest that a large proportion of interactions within the detectors will occur within a small spatial volume, introducing significant ambiguities within the position and energy measurements made by the detectors. Under certain circumstances, the ambiguities will result in multiple interactions being detected as a single interaction. This investigation studied the effect of such multiple occupancies and found that approximately 45% of 511 keV events include multiple interactions within a 5×5×20 mm 3 volume. Nevertheless, the effect on the quality of the final data remains quite acceptable.

Resolved Spectroscopy of M Dwarf/L Dwarf Binaries. II. 2MASS J17072343-0558249AB

We present Infrared Telescope Facility SpeX observations of the M/L binary system 2MASS J17072343-0558249. SpeX imaging resolves the system into a 101 ± 017 visual binary in which both components have red near-infrared colors. Resolved low-resolution (R ~ 150) 0.8-2.5 μm spectroscopy reveals strong H2O, CO, and FeH bands and alkali lines in the spectra of both components, characteristic of late-type M and L dwarfs. A comparison to a sample of late-type field dwarf spectra indicates spectral types M9 and L3. Despite the small proper motion of the system (0100 ± 0009 yr-1), imaging observations over 2.5 yr provide strong evidence that the two components share common proper motion. Physical association is also likely due to the small spatial volume occupied by the two components (based on spectrophotometric distance estimates of 15 ± 1 pc) as compared to the relatively low spatial density of low-mass field stars. The projected separation of the system is 15 ± 3 AU, similar to other late-type M and L binaries. Assuming a system age of 0.5-5 Gyr, we estimate the masses of the binary components to be 0.072-0.083 and 0.064-0.077 M⊙, with an orbital period of roughly 150-300 yr. While this is nominally too long a baseline for astrometric mass measurements, the proximity and relatively wide angular separation of the 2MASS J1707-0558AB pair make it an ideal system for studying the M dwarf/L dwarf transition at a fixed age and metallicity.

Molecular cloud shredding in the Galactic Bar

Seen just outside the innermost regions of the galactic center, the kinematics of molecular gas are dominated by a handful of compact but unusually broad-lined features of enigmatic origin. We show, using previous data, that there is a family of such features whose members are distinguished morphologically by their extreme vertical extension, perpendicular to the inclined plane of the overall gas tilt. Having isolated the features spatially, we mapped them with varying degrees of completeness at high resolution (1´) in lines of 12 CO, 13 CO and CS. Although very broad profiles exist in some individual beams, more generally we resolved the kinematics into spatial gradients which earlier were smeared in broader beams to form wider lines. The largest apparent velocity gradients are typically with respect to galactic latitude but motions are confined to the range of velocities inside the galactic terminal velocity, indicating that it is the galactic gravitational potential which is being tapped to create the observed kinematics. We interpret the broad-lined features qualitatively in terms of recent hydrodynamical models of gas flow in strongly barred galaxies: standing shocks which occur where gas enters the Galactic dust lane can account for the presence of broad lines over small spatial volumes wherever molecular gas is actually engaged in this process. To interpret the dynamical sequencing of the complex behaviour seen within the broad-line features we discuss how the Sun must be oriented with respect to the bar. In doing so, we identify the nuclear star-forming rings seen in other galaxies with the complex of giant H II regions Sgr A, B, C etc. and show that the kinematics are as expected for a ring of radius 175 pc (for a Sun-center distance of 8.5 kpc) rotating at about 210 km s -1 . Gas having clear and strong outward-directed non-circular motion around $l=0$° (the famous “expanding molecular ring”) is then associated with the “spray” of incoming gas at the inner ends of the dust lane, defining a more nearly end-on viewing angle for the bar. Using the inferred geometry, we construct a narrative for the behaviour of the feature most completely mapped here, at $l = 5.4$°, whereby gas basically falls out of the sky and is concentrated into the observed dense, bright molecular core before being shredded and sucked into the inflow of the dust lane 100 pc or more below the nominal galactic equator. From there it is recycled and lifted back into the more nearly equatorial region of the nuclear ring. Of course, the vertical structure of this and the other features, and the overall tilt of the dust lane and inner-galaxy gas layer, all remain to be discussed theoretically.

NEW LOWER BOUNDS FOR WARP DRIVE ENERGY

The introduction of the warp drive metric by Alcubierre1 has aroused great interest over the past few years. Using an uncertainty-type principle, Ford and Pfenning2 proved that the warp drive transport of a spaceship in a regular bubble having a radius of 100 m is unrealistic. However, Van Den Broeck3 has shown that the situation largely improves when one uses a warp drive bubble with a small surface area and large spatial volume. Putting aside many physics problems related to the realization of the warp drive concept, we show in this paper4 how to modify Van Den Broeck's idea to improve his results. We find new lower bounds for the warp drive energy by working on parameters whose latitude has never been considered before. We also consider micro warp drive bubbles which can be treated as physical entities of their own and could possibly be used to transmit information faster than the speed of light. The conditions prevailing just after the Big Bang allow the spontaneous formation of such micro bubbles which could still be present in our period of time.

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschildblack hole of the five--dimensional Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective Friedmann equation for the brane is derived by introducing the necessary surface counterterms required for a well-defined variational principlein the Gauss--Bonnet theory and for the finiteness of the bulk space. The asymptotic dynamics of the brane cosmology is determined and it is found that solutions with vanishingly small spatial volume are unphysical. The finiteness of the bulk action is related to the vanishing of the effective cosmological constant on the brane. An analogy between the Friedmann equation and a generalized Cardy--Verlinde formula is drawn.

Vortices and confinement in hot and cold D = 2+1 gauge theories

We calculate the variation with temperature of the vortex free energy in D=2+1 SU(2) lattice gauge theories. We do so both above and below the deconfining transition at T=Tc. We find that this quantity is zero at all T for large enough volumes. For T<Tc this observation is consistent with the fact that the phase is linearly confining; while for T>Tc it is consistent with the conventional expectation of `spatial' linear confinement. In small spatial volumes this quantity is shown to be non-zero. The way it decreases to zero with increasing volume is shown to be controlled by the (spatial) string tension and it has the functional form one would expect if the vortices being studied were responsible for the confinement at low T, and for the `spatial' confinement at large T. We also discuss in detail some of the direct numerical evidence for a non-zero spatial string tension at high T, and we show that the observed linearity of the (spatial) potential extends over distances that are large compared to typical high-T length scales.

Enzymatic reactions in small spatial volumes: comment on a model of Hess and Mikhailov

Recently Hess and Mikhailov pointed out that in small subcellular compartments diffusion is so fast that mixing is instantaneous on the time scale of many enzymatic reactions. This opens the possibility for synchronizing individual reaction events. To illustrate this fact they discuss as example an irreversible enzymatic reaction with allosteric product activation. Under appropriate conditions their model shows coherent spiking in the number of product molecules, caused by the strong correlation between reaction events. In this model only substrate binding is an indeterministic process, all other subsequent transitions between different enzyme states being deterministic, contrary to real processes. The purpose of the present paper was to investigate this interesting phenomenon by means of a more realistic modification of the original model, with only probabilistic transitions. In an attempt to obtain spiking, which was not observed under these conditions, the model was extended to make a clear distinction between allosteric high and low affinity substrate binding, in contrast to the original model using a product dependent mean binding probability. However no periodic signal was detectable in the indeterministic version of the Hess Mikhailov model or the extended version, either by means of direct visualization or on autocorrelation or Fourier analysis. Reasons why spiking is not observed in indeterministic enzyme models are discussed.

Laser trapping of radioactive francium atoms

The difficult problem of quickly slowing and cooling nuclear reaction products so that they can be injected into a laser trap has been solved by several groups and there are now strong efforts to work with the trapped atoms. The atoms are confined in the trap to a small spatial volume of the order of 1 mm 3, but more importantly, they are also confined in velocity, which makes them an ideal sample for spectroscopic measurements with other lasers. We have recently trapped radioactive francium and have embarked on a program to further study the francium atom as a prelude to a test of the Standard Model analogous to previous work with Cs. Our sample of 3 min 210Fr now contains over 20 000 atoms, and is readily visible with an ordinary TV camera. We work on-line with the accelerator, and continuously load the trap to replace losses due to decay and collisions with background gas. We have maintained a sample of Fr atoms in the trap for over 10 hours, with occasional adjustment of the trapping laser frequency to account for drifts. The proposed test of the Standard Model will require accurate calculation of its atomic properties. We are currently testing these calculations by measuring other predicted quantities.

Transition from molecular chaos to coherent spiking of enzymic reactions in small spatial volumes

Theoretical study of an irreversible enzymic reaction with allosteric product activation reveals that, in small spatial volumes, it can undergo a transition to coherent spiking regime characterized by the presence of strong correlations between reaction events and the states of individual enzyme molecules.