Finite Threshold Research Articles

Mathematical framework for the plastic flow of fine-grained solids, from yield to fracture

A newly proposed mathematical approach to plastic flow, holding from yield to fracture, of a fine-grained polycrystal with no voids or cracks is reviewed and applied to commercial steels. The formalism models the polycrystal by a continuum array of random deformable polyhedra leaving no voids between them, which can slide past each other along the shared faces when the shear stress resolved in the face plane exceeds a finite threshold. Grain reshaping for preserving matter continuity induces local forces assumed much weaker than those causing sliding. The relative velocity of adjacent sliding grains is taken as proportional to the local shear stress resolved in the common boundary plane. Explicit equations are derived for the plastic deformation, from yield to fracture. The analysis of mechanical tests of two commercial stainless steels is shown to illustrate how well the theory agrees with practice.

Mathematical model for the plastic flow and ductile fracture of polycrystalline solids

It is mathematically shown that ductile fracture after finite plastic strain is a necessary consequence of the polycrystalline nature of the materials. A closed–form equation for the plastic strain to fracture of a fine–grained polycrystal with no voids is derived. The mathematical model for the plastic deformation is grounded on the physical hypothesis that adjacent grains slide with a relative velocity proportional to the local shear stress resolved in the plane of the shared grain boundary, when exceeds a finite threshold. Hence plastic flow is governed predominantly by the in–plane shear forces making grain boundaries to slide, and the induced local forces responsible for the continuous grain reshaping are much weaker. The process is shown to produce a monotonic hydrostatic pressure variation with strain that precludes a stationary flow. The hydrostatic pressure dependence on strain has two solutions. One of them leads to superplasticity, the other one is shown to diverge logarithmically at a finite fracture strain and then represents ductile behaviour. Emphasis is done in the mathematical aspects of the deformation of the polycrystal up to the initiation of fracture. Although theoretical predictions agree well with mechanical tests of commercial alloys, technical issues like the effects of the presence and evolution of porosity and other imperfections, or how fracture evolves after initiation are left for a more specific communication.

Replica-Symmetry Breaking Transitions in the Large Deviations of the Ground-State of a Spherical Spin-Glass

We derive, within the replica formalism, a generalisation of the Crisanti–Sommers formula to describe the large deviation function (LDF) L(e)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{L}(e)$$\\end{document} for the speed-N atypical fluctuations of the intensive ground-state energy e of a generic spherical spin-glass in the presence of a random external magnetic field of variance Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}. We then analyse our exact formula for the LDF in much detail for the Replica symmetric, single step Replica Symmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations. Our main qualitative conclusion is that the level of RSB governing the LDF may be different from that for the typical ground-state. We find that while the deepest ground-states are always controlled by a LDF of replica symmetric form, beyond a finite threshold e≥et\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e\\ge e_{t}$$\\end{document} a replica-symmetry breaking starts to be operative. These findings resolve the puzzling discrepancy between our earlier replica calculations for the p=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=2$$\\end{document} spherical spin-glass (Fyodorov and Le Doussal in J Stat Phys 154:466, 2014) and the rigorous results by Dembo and Zeitouni (J Stat Phys 159:1306, 2015) which we are able to reproduce invoking an 1-RSB pattern. Finally at an even larger critical energy ec≥et\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_{c}\\ge e_{t}$$\\end{document}, acting as a “wall”, the LDF diverges logarithmically, which we interpret as a change in the large deviation speed from N to a faster growth. In addition, we show that in the limit Γ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma \\rightarrow 0$$\\end{document} the LDF takes non-trivial scaling forms (i) L(e)∼G((e-ec)/Γ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{L}(e) \\sim G((e-e_c)/\\Gamma )$$\\end{document} in the vicinity of the wall (ii) L(e)∼ΓηνF((e-etyp)/Γν)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{L}(e) \\sim \\Gamma ^{\\eta \ u } F((e-e_{\ extrm{typ}})/\\Gamma ^{\ u })$$\\end{document} in the vicinity of the typical energy, characterised by two new exponents η≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\ge 1$$\\end{document} and ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} characterising universality classes. Via matching the latter allows us to formulate several conjectures concerning the regime of typical fluctuations, identified as e-etyp∼N-1/η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e-e_{\ extrm{typ}} \\sim N^{-1/\\eta }$$\\end{document} and Γ∼N-1/(ην)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma \\sim N^{-1/(\\eta \ u )}$$\\end{document}.

Fast-slow wave transitions induced by a random mean flow.

Motivated by recent asymptotic results in atmosphere-ocean fluid dynamics, we present an idealized numerical and theoretical study of two-dimensional dispersive waves propagating through a small-amplitude random mean flow. The objective is to delineate clearly the conditions under which the cumulative Doppler shifting and refraction by the mean flow can change the group velocity of the waves not only in direction, but also in magnitude. The latter effect enables a possible transition from fast to slow waves, which behave very differently. Within our model we find the conditions on the dispersion relation and the mean flow amplitude that allow or rule out such fast-slow transitions. For steady mean flows we determine a finite mean flow amplitude threshold below which such transitions can be ruled out indefinitely. For unsteady mean flows a sufficiently rapid rate of change means that this threshold goes to zero, i.e., in this scenario all waves eventually undergo a fast-slow transition regardless of mean flow amplitude, with corresponding implications for the long-term fate of these waves.

Decoding the projective transverse field Ising model

The competition between noncommuting projective measurements in discrete quantum circuits can give rise to entanglement transitions. It separates a regime where initially stored quantum information survives the time evolution from a regime where the measurements destroy the quantum information. Here we study one such system---the projective transverse field Ising model---with a focus on its capabilities as a quantum error correction code. The idea is to interpret one type of measurement as an error and the other type as a syndrome measurement. We demonstrate that there is a finite threshold below which quantum information encoded in an initially entangled state can be retrieved reliably. In particular, we implement the maximum likelihood decoder to demonstrate that the error correction threshold is distinct from the entanglement transition. This implies that there is a finite regime where quantum information is protected by the projective dynamics, but cannot be retrieved by using syndrome measurements.

Stability of line-node semimetals with strong Coulomb interactions and properties of the symmetry-broken state

We study the stability and phenomenology of line-node semimetals in the presence of Coulomb interactions. Our results indicate a phase transition to a chiral insulating state that occurs at a finite interaction threshold, which we determine. We also compute the Landau levels for out-of-plane and in-plane magnetic fields in the symmetric and symmetry-broken phases. We find that the magnetic field couples to the chiral order parameter, implying that this degree of freedom can be manipulated in situ in experiments. Finally, we check the existence of edge states in the symmetry-broken phase. On the system's boundary, we note that the metallic ``drum-head'' states that exist in the symmetric phase are gapped out. However, the symmetry-broken phase permits topological defects in the macroscopic order parameter in the form of domain walls, which host metallic ``interface states.'' These consist of linelike gap-closings that occur on the two-dimensional interfaces.

Shear Flows of Dilatant Fluids with Limited Shear Rates: Analytical Results and Linear Stability Analysis

In this paper, we study the simple shear flows of a class of dilatant fluids with a limited shear rate. This class of fluids is characterized by shear thickening behavior in which the apparent viscosity tends to infinity as the modulus of the stress approaches a finite threshold. The apparent viscosity function is a logarithmic type with two material parameters. We considered this specific form because it fits very well with the flow curves of some granular suspensions for specific values of the material parameters. Despite the nonlinearity of the constitutive law, it is possible to determine explicit steady-state solutions for a simple shear flow, namely (i) the channel flow; (ii) the flow between coaxial cylinders, and (iii) the flow down an inclined plane. We performed a two-dimensional linear stability analysis to investigate the onset of possible instabilities of the steady basic flow, putting into evidence the dependency of the critical Reynolds number on the material parameters.

Stiffening or softening of elastic media: Anomalous elasticity near phase transitions.

We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous transition the elasticity is anomalous in unusual ways: the system either significantly stiffens with a hitherto unknown unique, positional order logarithmically stronger than quasi-long-range order, or, as the inversion asymmetry of the order parameter in its coupling with strain increases, it destabilizes when system size L exceeds a finite threshold. In three dimensions, stronger inversion-asymmetric couplings induce instability to the long-range positional order for all L. Sufficiently strong order parameter-displacement couplings can also turn the phase transition first order at all dimensions, concomitant with finite jumps in the elastic modulii across the transition. Our theory establishes a one-to-one correspondence between the order of the phase transitions and anomalous elasticity near the transitions.

Steady state propulsion of isotropic active colloids along a wall

Active drops emit/absorb chemical solutes, whose concentration gradients cause interfacial flows driving their own transport and the propulsion of the droplet. Such non-linear coupling enables active drops to achieve directed self-propulsion despite their isotropy, if the ratio of advective-to-diffusive solute transport, i.e. the Peclet number Pe, is larger than a finite critical threshold. In most experimental situations, active drops are non-neutrally buoyant and thus swim along rigid surfaces; yet theoretical descriptions of their non-linear motion focus almost exclusively on unbounded domains to circumvent geometric complexity. To overcome this gap in understanding, we investigate the spontaneous emergence and nonlinear saturation of propulsion of an isotropic phoretic colloid along a rigid wall, to which it is confined by a constant external force (e.g., gravity). This phoretic particle model is considered here as a limiting case for a viscous active drop. We show that, for moderate Pe, the particle motion and associated chemical transport reduce the chemically-induced wall repulsion, thereby causing the particle to swim progressively closer to the wall as Pe increases. Far from hindering self-propulsion, this reduction in the particle-wall separation is accompanied by a wall-induced efficient rearrangement of the solute concentration gradients driving the particle, thus augmenting its swimming speed.

Mathematical Model of the Decomposition of Unstable Gas Hydrate Accumulations in the Cryolithozone

We present a generalization of the mathematical model of gas discharge from frozen rocks containing gas-saturated ice and gas hydrates in a metastable state (due to the self-preservation effect) caused by the drop in external stress associated with various geodynamic factors. These factors can be attributed, for example, to a decrease in hydrostatic pressure on a gas-bearing formation due to glacier melting, causing an isostatic rise, or to the formation of linear depressions in the bottom topography on the shelf due to iceberg ploughing. A change in external pressure can also be associated with seismic and tectonic deformation waves propagating in the lithosphere as a result of ongoing strong earthquakes. Starting from the existing hydrate destruction model, operating at the scale of individual granules, we consider a low-permeable hydrate and ice-saturated horizontal reservoir. Generalization is associated with the introduction of a finite threshold for the external pressure drop, which causes the destruction of the gas hydrate and gas-saturated microcavities of supramolecular size. This makes it possible to take into account the effect of anomalously high pressures occurring in the released gas as a result of partial hydrate dissociation. Numerical and approximate analytical solutions to the problem were found in the self-similar formulation. A parametric study of the solution was carried out, and regularities of the hydrate decomposition process were revealed.

Degrees of Freedom of a K-User Interference Channel in the Presence of an Instantaneous Relay.

In this paper, we study the degrees of freedom (DoF) of a frequency-selective K-user interference channel in the presence of an instantaneous relay (IR) with multiple receiving and transmitting antennas. We investigate two scenarios based on the IR antennas’ cooperation ability. First, we assume that the IR receiving and transmitting antennas can coordinate with each other and that the transmitted signal of each transmitting antenna can depend on the received signals of all receiving antennas, and we derive lower and upper bounds for the sum DoF of this model. In an interference alignment scheme, we divide receivers into two groups called clean and dirty receivers. We design our scheme such that a part of the messages of clean receivers can be de-multiplexed at the IR. Thus, the IR can use these message streams for an interference cancellation at the clean receivers. Next, we consider an IR, the antennas of which do not have coordination with each other and where the transmitted signal of each transmitting antenna depends only on the received signal of its corresponding receiving antenna. We also derive lower and upper bounds for the sum DoF for this model of IR. We show that the achievable sum DoF decreases considerably compared with the coordinated case. In both of these models, our schemes achieve the maximum K sum DoF if the number of transmitting and receiving antennas is more than a finite threshold.

Facilitating Load-Dependent Queueing Analysis Through Factorization (Extended Abstract)

We construct novel exact and approximate solutions for meanvalue analysis and probabilistic evaluation of closed queueing network models with limited load-dependent (LLD) nodes. In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For single-class models, we provide an explicit formula for the normalizing constant that applies to models with arbitrary LLD functions, whilst retaining constant complexity with respect to the total population size. From this result, we then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between a load-independent solution and a limited load-dependent one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks.

Phase diagrams of SO( N ) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions

We study the zero-temperature phase diagrams of Majorana-Hubbard models with SO($N$) symmetry on two-dimensional honeycomb and $\pi$-flux square lattices, using mean-field and renormalization group approaches. The models can be understood as real counterparts of the SU($N$) Hubbard-Heisenberg models, and may be realized in Abrikosov vortex phases of topological superconductors, or in fractionalized phases of strongly-frustrated spin-orbital magnets. In the weakly-interacting limit, the models feature stable and fully symmetric Majorana semimetal phases. Increasing the interaction strength beyond a finite threshold for large $N$, we find a direct transition towards dimerized phases, which can be understood as staggered valence bond solid orders, in which part of the lattice symmetry is spontaneously broken and the Majorana fermions acquire a mass gap. For small to intermediate $N$, on the other hand, phases with spontaneously broken SO($N$) symmetry, which can be understood as generalized N\'eel antiferromagnets, may be stabilized. These antiferromagnetic phases feature fully gapped fermion spectra for even $N$, but gapless Majorana modes for odd $N$. While the transitions between Majorana semimetal and dimerized phases are strongly first order, the transitions between Majorana semimetal and antiferromagnetic phases are continuous for small $N \leq 3$ and weakly first order for intermediate $N \geq 4$. The weakly-first-order nature of the latter transitions arises from fixed-point annihilation in the corresponding effective field theory, which contains a real symmetric tensorial order parameter coupled to the gapless Majorana degrees of freedom, realizing interesting examples of fluctuation-induced first-order transitions.

WALLABY pilot survey: Public release of H i data for almost 600 galaxies from phase 1 of ASKAP pilot observations

Abstract We present WALLABY pilot data release 1, the first public release of H i pilot survey data from the Wide-field ASKAP L-band Legacy All-sky Blind Survey (WALLABY) on the Australian Square Kilometre Array Pathfinder. Phase 1 of the WALLABY pilot survey targeted three $60\,\mathrm{deg}^{2}$ regions on the sky in the direction of the Hydra and Norma galaxy clusters and the NGC 4636 galaxy group, covering the redshift range of $z \lesssim 0.08$ . The source catalogue, images and spectra of nearly 600 extragalactic H i detections and kinematic models for 109 spatially resolved galaxies are available. As the pilot survey targeted regions containing nearby group and cluster environments, the median redshift of the sample of $z \approx 0.014$ is relatively low compared to the full WALLABY survey. The median galaxy H i mass is $2.3 \times 10^{9}\,{\rm M}_{{\odot}}$ . The target noise level of $1.6\,\mathrm{mJy}$ per 30′′ beam and $18.5\,\mathrm{kHz}$ channel translates into a $5 \sigma$ H i mass sensitivity for point sources of about $5.2 \times 10^{8} \, (D_{\rm L} / \mathrm{100\,Mpc})^{2} \, {\rm M}_{{\odot}}$ across 50 spectral channels ( ${\approx} 200\,\mathrm{km \, s}^{-1}$ ) and a $5 \sigma$ H i column density sensitivity of about $8.6 \times 10^{19} \, (1 + z)^{4}\,\mathrm{cm}^{-2}$ across 5 channels ( ${\approx} 20\,\mathrm{km \, s}^{-1}$ ) for emission filling the 30′′ beam. As expected for a pilot survey, several technical issues and artefacts are still affecting the data quality. Most notably, there are systematic flux errors of up to several 10% caused by uncertainties about the exact size and shape of each of the primary beams as well as the presence of sidelobes due to the finite deconvolution threshold. In addition, artefacts such as residual continuum emission and bandpass ripples have affected some of the data. The pilot survey has been highly successful in uncovering such technical problems, most of which are expected to be addressed and rectified before the start of the full WALLABY survey.

Effect of a uniform random external magnetic field with spatiotemporal variation on compensation in Ising spin-1/2 trilayered square ferrimagnets.

Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a Metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatiotemporal variations. In two distinct configurations, the surface layers are made up of A and the middle layer is made up of B atoms in an ABA-type stacking while in AAB-type stacking, the top layer and the middle layer is made up of A atoms while the bottom layer is made up of B atoms. The magnetic coupling between the like atoms (A-A and B-B) is ferromagnetic while between the unlike atoms (A-B), it is antiferromagnetic. For the time-dependent external uniform random field, the mean is always set to zero and the standard deviation is varied until spin-field energy is comparable to the dominant cooperative energy of the system. The findings show that the observed compensation and critical points shift and steady-state magnetic behaviors shift among N, L, P, and Q, etc., type of ferrimagnetic behaviors, depending on the strength of external uniform random field. The compensation phenomenon even vanishes after crossing a finite threshold of standard deviation of the magnetic field for particular choices of the other controlling parameters. Thus islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case, in the two-dimensional Hamiltonian parameter space. For both the configurations, the areas of such islands even grow with increasing standard deviation of the external field, σ, obeying a scaling relation of the form: f(σ,A(σ))=σ^{-b}A(σ) with b_{ABA}=1.958±0.122 and b_{AAB}=1.783±0.118.

Performance Evaluation Model for Matrix Calculation on GPU

Establishment of a performance evaluation model is a hotspot of current research. In this paper, the performance bottleneck is analyzed quantitatively, which provided programmers with a guidance to optimize the performance bottleneck. This paper takes a matrix as an example; the matrix is divided into a dense matrix or a sparse matrix. For dense matrix, the performance is first analyzed in a quantitative way, and an evaluation model is developed, which includes the instruction pipeline, shared memory, and global memory. For sparse matrix, this paper aims at the four formats of CSR, ELL, COO, and HYB, through the observation data obtained from the actual operation of large datasets, finds the relationship between the running time, dataset form, and storage model, and establishes their relational model functions. Through practical test and comparison, the error between the execution time of the test dataset that is predicted by the model function and the actual running time is found to be within a stable finite deviation threshold, proving that the model has certain practicability.

Gaussian continuous-variable isotropic state

Inspired by the definition of the non-Gaussian two-parametric continuous variable analogue of an isotropic state introduced by Mi\v{s}ta et al. [Phys. Rev. A, 65, 062315 (2002); arXiv:quant-ph/0112062], we propose to take the Gaussian part of this state as an independent state by itself, which yields a simple, but with respect to the correlation structure interesting example of a two-mode Gaussian analogue of an isotropic state. Unlike conventional isotropic states which are defined as a convex combination of a thermal and an entangled density operator, the Gaussian version studied here is defined by a convex combination of the corresponding covariance matrices and can be understood as entangled pure state with additional Gaussian noise controlled by a mixing probability. Using various entanglement criteria and measures, we study the non-classical correlations contained in this state. Unlike the previously studied non-Gaussian two-parametric isotropic state, the Gaussian state considered here features a finite threshold in the parameter space where entanglement sets in. In particular, it turns out that it exhibits an analogous phenomenology as the finite-dimensional two-qubit isotropic state.

Dynamics and nonmonotonic drag for individually driven skyrmions

We examine the motion of an individual skyrmion driven through an assembly of other skyrmions in the absence of quenched disorder. The skyrmion behavior is determined by the ratio of the damping and Magnus terms, known as the intrinsic skyrmion Hall angle. For fixed drive in the damping dominated regime, the effective viscosity decreases monotonically with increasing skyrmion density. In contrast, in the Magnus dominated regime, the velocity varies nonmonotonically with density, and there is a regime in which the skyrmion moves faster with increasing density, as well as a pronounced speed-up effect in which a skyrmion traveling through a dense medium moves more rapidly than for low densities or the single-particle limit. The velocity-force curves in the Magnus-dominated regime exhibit an overshoot effect and other differences from the damping-dominated regime. We find a finite threshold force for skyrmion motion which increases with density as well as a drive-dependent skyrmion Hall angle. We map dynamic phase diagrams showing the threshold for motion, nonlinear flow, speed-up, and saturation regimes. In some cases, increasing the density can reduce the skyrmion Hall angle while producing a velocity boost, which could be valuable for applications.

Longitudinal modes of bunched beams with weak space charge

Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameterless integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the rf bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny coupled-bunch interaction makes the beam unstable; such growth rates for all the modes are analytically obtained for arbitrary multipolarity. In practice, however, the finite threshold of this loss of Landau damping is set either by the high-frequency impedance roll-off or intrabeam scattering. Above the threshold, growth of the leading collective mode should result in persistent nonlinear oscillations.

The diffusive epidemic process on Barabasi–Albert networks

We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time t max, exponentially distributed with mean inversely proportional to the node population in order to model the individuals’ interactions. Our simulation results of the modified model on Barabasi–Albert networks are compatible with a continuous absorbing-active phase transition when increasing the average concentration. The transition obeys the mean-field critical exponents β = 1, γ′ = 0 and ν ⊥ = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents on the order parameter and its fluctuations, respectively. The most evident implication of our simulation results is if the individuals avoid social interactions in order to not spread a disease, this leads the system to have a finite threshold in scale-free graphs.