Magnetic beads attract each other, forming chains. We push such chains into an inclined Hele-Shaw cell and discover that they spontaneously form self-similar patterns. Depending on the angle of ...inclination of the cell, two completely different situations emerge; namely, above the static friction angle the patterns resemble the stacking of a rope and below they look similar to a fortress from above. Moreover, locally the first pattern forms a square lattice, while the second pattern exhibits triangular symmetry. For both patterns, the size distributions of enclosed areas follow power laws. We characterize the morphological transition between the two patterns experimentally and numerically and explain the change in polarization as a competition between friction-induced buckling and gravity.
We have studied the shadows of a Schwarzschild black hole surrounded by a Bach–Weyl ring through the backward ray-tracing method. The presence of Bach–Weyl ring leads to that the photon dynamical ...system is non-integrable and then chaos would appear in the photon motion, which affects sharply the black hole shadow. The size and shape the black hole shadow depend on the black hole parameter, the Bach–Weyl ring mass and the Weyl radius between black hole and ring. Some self-similar fractal structures also appear in the black hole shadow, which originates from the chaotic lensing. We also study the change of the image of Bach–Weyl ring with the ring mass and the Weyl radius. Finally, we analyze the invariant manifolds of Lyapunov orbits near the fixed points and discuss further the formation of the shadow of a Schwarzschild black hole with Bach–Weyl ring.
We fix a positive integer M, and we consider expansions in arbitrary real bases q>1 over the alphabet {0,1,…,M}. We denote by Uq the set of real numbers having a unique expansion. Completing many ...former investigations, we give a formula for the Hausdorff dimension D(q) of Uq for each q∈(1,∞). Furthermore, we prove that the dimension function D:(1,∞)→0,1 is continuous, and has bounded variation. Moreover, it has a Devil's staircase behavior in (q′,∞), where q′ denotes the Komornik–Loreti constant: although D(q)>D(q′) for all q>q′, we have D′<0 a.e. in (q′,∞). During the proofs we improve and generalize a theorem of Erdős et al. on the existence of large blocks of zeros in β-expansions, and we determine for all M the Lebesgue measure and the Hausdorff dimension of the set U of bases in which x=1 has a unique expansion.
Synthetic aperture radar (SAR) images are inherently degraded by the speckle noise due to the coherent imaging, which may affect the performance of subsequent image analysis task. To address this ...problem, a weighted sparse representation-based method is proposed in this article for SAR image despeckling. The homomorphic transformation is first adopted to convert multiplicative noise into additive one. Second, similar patches are grouped together to learn the adaptive dictionaries and sparse coefficients based on nonlocal self-similarity constraint. Moreover, weighted regularizations are adopted for coefficients to boost the performance. Finally, despeckling images are obtained via exponential transformation. Experimental results on synthetic and real-world SAR images demonstrate that our proposed method outperforms several state-of-the-art methods in terms of both quantitative measurements and visual quality.
Abstract We investigate the long-term persistence of solar energetic particle (SEP) time series by means of four different methods: Hurst rescaled range R / S analysis, detrended fluctuation ...analysis, centered moving average analysis, and the fluctuation of natural time under the time reversal method. For these analyses, we use data sets from the Integrated Science Investigation of the Sun instrument suite on board NASA's Parker Solar Probe. Background systematic noise is modeled using cross-correlation analysis between different SEP energy channels and subtracted from the original data. The use of these four methods for deriving the time-series persistence allows us to (i) differentiate between quiet- and active-Sun periods based on the values of the corresponding self-similarity exponents alone; (ii) identify the onset of an ongoing activity well before it reaches its maximum SEP flux; (iii) reveal an interesting fine structure when activity is observed; and (iv) provide, for the first time, an estimate of the maximum SEP flux of a future storm based on the entropy change of natural time under time reversal.
Abstract The X-ray morphologies of clusters of galaxies display significant variations, reflecting their dynamical histories and the nonlinear dependence of X-ray emissivity on the density of the ...intracluster gas. Qualitative and quantitative assessments of X-ray morphology have long been considered a proxy for determining whether clusters are dynamically active or “relaxed.” Conversely, the use of circularly or elliptically symmetric models for cluster emission can be complicated by the variety of complex features realized in nature, spanning scales from megaparsecs down to the resolution limit of current X-ray observatories. In this work, we use mock X-ray images from simulated clusters from The Three Hundred project to define a basis set of cluster image features. We take advantage of the clusters’ approximate self-similarity to minimize the differences between images before encoding the remaining diversity through a distribution of high-order polynomial coefficients. Principal component analysis then provides an orthogonal basis for this distribution, corresponding to natural perturbations from an average model. This representation allows novel, realistically complex X-ray cluster images to be easily generated, and we provide code to do so. The approach provides a simple way to generate training data for cluster image analysis algorithms and could be straightforwardly adapted to generate clusters displaying specific types of features or selected by physical characteristics available in the original simulations.
Deep learning as a parton shower Monk, J. W.
The journal of high energy physics,
12/2018, Letnik:
2018, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton ...shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, which also preserves existing parton splittings by using layer-skipping connections. By applying a shower merging procedure, the network can be evaluated on unshowered events produced by a matrix element calculation. The trained network behaves as a parton shower that qualitatively reproduces jet-based observables.
The mean wake of a three-bladed horizontal axis tidal stream turbine operating at maximum power coefficient has been investigated experimentally in a wide flume with width 11 times the depth, ...providing minimal restriction to transverse wake development and behaviour of large-scale horizontal turbulence structures. This is an important first stage for understanding wake interaction in turbine arrays and hence large-scale power generation. The rotor diameter has a typical value of 60% of the depth and the thrust coefficient is representative of a full-scale turbine. The shear layers originating from the rotor tip circumference show classic linear expansion downstream, with the rate of a plane shear layer vertically and 1.5 times that horizontally. These shear layers merge by around 2.5 diameters downstream forming a self-similar two-dimensional wake beyond eight diameters downstream with a virtual origin at two diameters downstream of the rotor plane. The spreading rate is somewhat less than that for solid bodies. The detailed velocity measurements made in the near wake show rotation and vorticity similar to that measured previously for wind and marine turbines although with asymmetry associated with bed and surface proximity. The longitudinal circulation in a transverse plane is conserved at about 1% of the swept circulation from the blade tip within two diameters downstream, the extent of detailed measurement. Turbines are usually designed using blade element momentum theory in which velocities at the rotor plane are characterised by axial and tangential induction factors and it is now possible to see how this idealisation relates to actual velocities. The axial induction factor corresponds to velocity deficits at 0.4–0.8 radii from the rotor axis across the near wake while the tangential induction factor at the rotor plane corresponds to velocities at 0.4–0.6 radii between 1–2 diameters downstream, indicating some general correspondence. For the two-dimensional self-similar far wake the two parameters defining the centreline velocity deficit and the transverse velocity profiles are likely to be insensitive to Reynolds number in turbulent conditions.
Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions, or supersaturated solutions. Mean field theories predict an asymptotic ...scaling state with a broad particle size distribution. Aqueous foams are good model systems for investigations of coarsening-induced structures, because the continuous liquid as well as the dispersed gas phases are uniform and isotropic. We present coarsening experiments on wet foams, with liquid fractions up to their unjamming point and beyond, that are performed under microgravity to avoid gravitational drainage. As time elapses, a self-similar regime is reached where the normalized bubble size distribution is invariant. Unexpectedly, the distribution features an excess of small roaming bubbles, mobile within the network of jammed larger bubbles. These roaming bubbles are reminiscent of rattlers in granular materials (grains not subjected to contact forces). We identify a critical liquid fraction Formula: see text, above which the bubble assembly unjams and the two bubble populations merge into a single narrow distribution of bubbly liquids. Unexpectedly, Formula: see text is larger than the random close packing fraction of the foam Formula: see text. This is because, between Formula: see text and Formula: see text, the large bubbles remain connected due to a weak adhesion between bubbles. We present models that identify the physical mechanisms explaining our observations. We propose a new comprehensive view of the coarsening phenomenon in wet foams. Our results should be applicable to other phase-separating systems and they may also help to control the elaboration of solid foams with hierarchical structures.
•Hydrogen jet structure in near-field is conical, while in far-field is spherical vortex.•The spread angle is not sensitive to pressure ratios of injection to ambient (PR).•The jet penetration, ...projected area and volume are positively related to PR.•The jet has good self-similarity under all PRs, and the penetration constant is 13.18.•Proposed a scaling correlation of axial penetration for this kind of hydrogen jets.
The hydrogen jet characteristics have effect on the performance of direction injector (DI) hydrogen engines because they can influence the process of mixture formation and heat release. In this study, the hydrogen jet characteristics of an outward-opening injector were studied with high-speed schlieren imaging in a constant volume chamber at different injection and ambient pressure ratios (PRs), which ranged from 10 to 140. Results show that the hydrogen jet in the near-field is a conical structure, while the jet structure develops into a spherical vortex in the far-field. The jet axial penetration, radial penetration, and volume increase with the increasing of the PR. The jet spread angle is not sensitive to the PR except for the low PRs. The entrainment rate decreases with the increasing of the PR. The normalization analysis of jet penetration shows that the hydrogen jets have a good self-similarity under all PRs. A non-dimensional scaling correlation of axial penetration is proposed for this kind of hydrogen jets. In the scaling correlation, the exponents of the non-dimensional penetration and time term are 0.18 and 0.83, while the penetration constant is 13.18. The discovery of the above jet characteristics can predict the free jet shape under any PR in the range of 10 to140. These results can also promote the application of DI hydrogen engines.
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