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Himalayan avalanches are examined for agreement with power-law behavior between frequency of outfall and rock volume. The data support a scaling state beyond the size ranges in which corresponding sandpile experiments have suffered from finite-size effects. Large-scale data (12 orders of magnitude in rock volume) additionally suggest a possible role for the numerically predicted 'snowball effects' of large rocks triggering more net dislodging events.
We report on the sustained behavior of a candle flame in microgravity determined in the glovebox facility aboard the First United States Microgravity Labomtofy. In a quiescent, microgmvjfy environment, diffusive transport becomes the dominant mode of heat and mass transfer; whether the diffusive transport rate is fast enough to sustain low-gravity candle flames in air was unknown to this series of about 70 tests. After an initial transient in which soot is observed, the microgravity candle flame in air becomes and remains hemispherical and blue (apparently soot-Ne) with a large flame standoff distance. Near flame extinction, spontaneous flame oscillations are regularly observed; these are explained as a flashback of flame through a premixed combustible gas followed by a retreat owed to flame quenching. The frequency of oscillations can be related to diffusive transport rates, and not to residual buoyant convective flow. The fact that the flame tip is the last point of the flame to survive suggests that it is the location of maximum fuel reactivity; this is unlike normal gravity, where the location of maximum fuel reactivity is the flame base. The flame color, size, and shape behaved in a quasi-steady manner; the finite size of the glovebox, combined with the restricted passages of the candlebox, inhibited the observation of true steady-state burning. Nonetheless, through calculations, and inference from the series of shuttle tests, if is concluded that a candle can burn indefinitely in a large enough ambient of air in microgravity. After igniting one candle, a second candle in close pximity could not be lit. This may be due to wax coating the wick and/or local oxygen depletion around the second, unlit candle. Post-mission testing suggests that simultaneous ignition may overcome these behaviors and enable both candles to be ignited.
We set the scale of SU(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.
The massively parallel processor is used to perform Monte Carlo simulations for the two dimensional XY model on lattices of sizes up to 128 x 128. A parallel random number generator was constructed, finite size effects were studied, and run times were compared with those on a CRAY X-MP supercomputer.
In this work, a nonlocal dispersive optical model analysis is carried out for neutrons and protons in 208 Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, neutron and proton numbers, the charge distribution, and the binding energy are fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we determine the charge and matter distributions in 208 Pb. The predicted spectroscopic factors are consistent with results from the ($\textit{e,e}'\textit{p}$) reaction and inelastic-electron-scattering data to very high-spin states. Sensible results for the high-momentum content of neutrons and protons are obtained, with protons appearing more correlated, in agreement with experiment and ab initio calculations of asymmetric matter. A neutron skin of 0.25 ± 0.05 fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a nonnegligible role in the formation of the neutron skin in finite nuclei.
Under certain conditions, such as in thin liquid films or microgravity, surface tension variations along a free surface can induce convection. Convection onset due to surface tension variation is important to many terrestrial technological processes in addition to microgravity materials processing applications. Examples include coating, drying crystallization, solidification, liquid surface contamination, and containerless processing. In double-diffusive and multicomponent systems, the spatial variations of surface tension are associated with two or more stratifying agencies, respectively. For example, both temperature and species (concentration) gradients are associated with convection in the solidification of binary alloys or salt ponds. The direction of the two (or more) gradients has a profound effect on the nature of the flow at or slightly beyond the onset of convection. Our recent work at the NASA Lewis Research Center focused on characterizing surface-tension-induced onset of convection, often referred to as Marangoni-Benard convection. Exact solutions for the stationary neutral stability of multicomponent fluid layers with interfacial deformation were derived. These solutions also permit the computation of a boundary curve that separates the long and finite wavelength instabilities. Computing points along this boundary using the exact solution (when possible) is more efficient than the typical numerical approaches, such as finite difference or spectral methods. Above the curve, a long wavelength instability was predicted, suggesting that convection would occur principally through one large flow cell in the layer, whereas below the curve, finite wavelength instabilities occur which suggest multiple finite-sized circulation cells. For many common liquids with layer depths greater than 100 mm, finite wave instability is predicted under terrestrial conditions; however, with little exception, long wavelength instability is predicted in microgravity for the identical fluid systems.
Understanding the condensed-phase behavior of chiral molecules is important in biology as well as in a range of technological applications, such as the manufacture of pharmaceuticals. Here, we use molecular dynamics simulations to study a chiral four-site molecular model that exhibits a second-order symmetry-breaking phase transition from a supercritical racemic liquid into subcritical D-rich and L-rich liquids. We determine the infinite-size critical temperature using the fourth-order Binder cumulant, and we show that the finite-size scaling behavior of the order parameter is compatible with the 3D Ising universality class. We also study the spontaneous D-rich to L-rich transition at a slightly subcritical temperature of T = 0.985Tc, and our findings indicate that the free energy barrier for this transformation increases with system size as N2/3, where N is the number of molecules, consistent with a surface-dominated phenomenon. The critical behavior observed herein suggests a mechanism for chirality selection in which a liquid of chiral molecules spontaneously forms a phase enriched in one of the two enantiomers as the temperature is lowered below the critical point. Furthermore, the increasing free energy barrier with system size indicates that fluctuations between the L-rich and D-rich phases are suppressed as the size of the system increases, trapping it in one of the two enantiomerically enriched phases. Such a process could provide the basis for an alternative explanation for the origin of biological homochirality. We also conjecture the possibility of observing nucleation at subcritical temperatures under the action of a suitable chiral external field.
Here, we explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size $\textit{N}$, disorder strength Δ, and temperature $\textit{T}$. The conductivity $κ_N$, obtained for finite length ($\textit{N}$), saturates to a value $κ_∞$ > 0 in the large $\textit{N}$ limit, for all values of disorder strength Δ and temperature $\textit{T}$ > 0. We show evidence that for any Δ > 0 the conductivity goes to zero faster than any power of $\textit{T}$ in the ($\textit{T}$/Δ) → 0 limit, and find that the form $κ_∞$ ~ $e^{{–B|\text{ln}(CΔ/T)|}^{3}}$ fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be $κ_N < κ_∞$ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or $κ_N > κ_∞$ due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.
It is well known that a vector quantizer is an efficient coder offering a good trade-off between quantization distortion and bit rate. The performance of a vector quantizer asymptotically approaches the optimum bound with increasing dimensionality. A vector quantized image suffers from the following types of degradations: (1) edge regions in the coded image contain staircase effects, (2) quasi-constant or slowly varying regions suffer from contouring effects, and (3) textured regions lose details and suffer from granular noise. All three of these degradations are due to the finite size of the code book, the distortion measures used in the design, and due to the finite training procedure involved in the construction of the code book. In this paper, we present an adaptive technique which attempts to ameliorate the edge distortion and contouring effects.
Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.
Models of gas bubble dynamics for studying decompression sickness have been developed by considering the bubble to be immersed in an extravascular tissue with diffusion-limited gas exchange between the bubble and the surrounding unstirred tissue. In previous versions of this two-region model, the tissue volume must be theoretically infinite, which renders the model inapplicable to analysis of bubble growth in a finite-sized tissue. We herein present a new two-region model that is applicable to problems involving finite tissue volumes. By introducing radial deviations to gas tension in the diffusion region surrounding the bubble, the concentration gradient can be zero at a finite distance from the bubble, thus limiting the tissue volume that participates in bubble–tissue gas exchange. It is shown that these deviations account for the effects of heterogeneous perfusion on gas bubble dynamics, and are required for the tissue volume to be finite. The bubble growth results from a difference between the bubble gas pressure and an average gas tension in the surrounding diffusion region that explicitly depends on gas uptake and release by the bubble. For any given decompression, the diffusion region volume must stay above a certain minimum in order to sustain bubble growth.
Fluorescent molecules emit light in a dipole radiation pattern that can be used to infer their orientation through defocused fluorescence microscopy. Proper measurement of the orientation requires mathematical modeling of the radiation pattern expected for a dipole in the geometry of interest and subsequent comparison against experimental data. We point out an ambiguity in common calculations of these patterns that appears to compromise orientation measurements for molecules that are especially near dielectric surfaces. This results in a rotation of the measured emission dipole toward the surface for near-interface molecules, which can be mistaken for a preferentially horizontal orientation among the emitters. The proper treatment for on-surface emitters requires consideration of finite-sized current elements between two dielectric media, and we show that the theoretical ambiguity can be lifted via finite-element modeling. A prescription is provided for correcting measured orientations at arbitrary interfaces.
Various boundary layer parameters and transducer shape effect on Measurement error of random pressure field by finite size transducer
The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size N b . We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\mathcal{O}$(N b 2 ) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with N b up to 2.88 × 10 6 , and the wall clock time is less than 100 s using 17 280 CPU cores. Finally, this enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.
Microlensing of stars places significant constraints on subplanetary-mass compact objects, including primordial black holes, as dark matter candidates. As the lens’ Einstein radius in the source plane becomes comparable to the size of the light source, however, source amplification is strongly suppressed, making it challenging to constrain lenses with a mass at or below 10 –10 solar masses, i.e., asteroid-mass objects. Current constraints, using Subaru Hyper Suprime Cam (HSC) observations of M31, assume a fixed source size of one solar radius. However, the actual stars in M31 bright enough to be used for microlensing are typically much larger. We correct the HSC constraints by constructing a source size distribution based on the M31 PHAT survey and on a synthetic stellar catalog and by correspondingly weighting the finite-size source effects. In this work, we find that the actual HSC constraints are weaker by up to almost 3 orders of magnitude in some cases, broadening the range of masses for which primordial black holes can be the totality of the cosmological dark matter by almost 1 order of magnitude.
We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E 1 and E 2 representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and—as we highlight—the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, ν, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for ν = ± 1, but vanishes for | ν | > 1. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, R ≥ ℏ / p f, the thermal Hall conductivity is finite for chiral order with | ν | ≥ 2, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.
In the framework of the statistical multifragmentation model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the ratio between the probabilities of observing n fragments in each event, for each of the sources, follows a scaling law, similar to the traditional nuclear isoscaling. However, the corresponding slope is sensitive to the source sizes. This property is explained analytically using the grand-canonical ensemble. Furthermore, the extent to which our findings are affected by finite size effects and by the deexcitation of the hot primary fragments is investigated. The scaling turns out to be robust and weakly affected by effects implied by these two aspects. We also find that the Poisson distribution is a fairly good approximation to the above mentioned probabilities, associated with both the primordial fragments, produced at the breakup stage, and the final ones, found at the end of the fragment deexcitation process.
Stresses were calculated for finite size orthotropic laminates loaded by a frictionless steel pin in a circular hole of the same diameter. The calculations were based on finite element analyses for six laminates. Stress concentration factors, based on nominal bearing stress, were determined for wide ranges of the ratios of width to diameter, w/d and edge distance to diameter, e/d. An infinite laminate case was analyzed for each laminate. Orthotropy had a significant influence on the tensile stress concentration at the hole. For example, the stress concentration factors for the infinite laminate cases ranged from 0.82 to 2.16, compared with 0.87 for the quasi-isotropic laminate. The finite widths and edge distances strongly influenced the tensile stress concentration. For the practical range w/d or = 3, the peak tensile stresses were as much as 80% larger than the infinite laminate reference value. For e/d or = 3, these stresses were amplified by as much as 50%. In contrast, the finite width and edge distance had little effect on shear-out and bearing stress concentrations.