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  • 1.
    Al-Naseri, Haidar
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Applicability of the Klein-Gordon equation for pair production in vacuum and plasma2023In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 108, no 5, article id 055205Article in journal (Refereed)
    Abstract [en]

    In this paper, a phase-space description of electron-positron pair-creation will be applied, based on a Wigner transformation of the Klein-Gordon equation. The resulting theory is similar in many respects to the equations from the Dirac-Heisenberg-Wigner formalism. However, in the former case, all physics related to particle spin is neglected. In the present paper we compare the pair-production rate in vacuum and plasmas, with and without spin effects, in order to evaluate the accuracy and applicability of the spinless approximation. It is found that for modest frequencies of the electromagnetic field, the pair production rate of the Klein-Gordon theory is a good approximation to the Dirac theory, provided the matter density is small enough for Pauli blocking to be neglected, and a factor of two related to the difference in the vacuum energy density is compensated for.  

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  • 2.
    Al-Naseri, Haidar
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Radiation reaction effects in relativistic plasmas: the electrostatic limit2023In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 107, no 3, article id 035203Article in journal (Refereed)
    Abstract [en]

    We study the evolution of electrostatic plasma waves, using the relativistic Vlasov equation extended by the Landau-Lifshitz radiation reaction, accounting for the back-reaction due to the emission of single particle Larmor radiation. In particular, the Langmuir wave damping is calculated as a function of wave number, initial temperature, and initial electric field amplitude. Moreover, the background distribution function loses energy in the process, and we calculate the cooling rate as a function of initial temperature and initial wave amplitude. Finally, we investigate how the relative magnitude of wave damping and background cooling varies with the initial parameters. In particular, it is found that the relative contribution to the energy loss associated with background cooling decreases slowly with the initial wave amplitude.

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  • 3.
    Al-Naseri, Haidar
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Zamanian, Jens
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Plasma dynamics and vacuum pair creation using the Dirac-Heisenberg-Wigner formalism2021In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 104, no 1, article id 015207Article in journal (Refereed)
    Abstract [en]

    We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.

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  • 4. Aslak, Ulf
    et al.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lehmann, Sune
    Constrained information flows in temporal networks reveal intermittent communities2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 6, article id 062312Article in journal (Refereed)
    Abstract [en]

    Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and dissolve based on multiple factors, including their lectures, interests, and friends. Such dynamic systems can be represented as multilayer networkswhere each layer represents a snapshot of the temporal network. In this representation, it is crucial that the links between layers accurately capture real dependencies between those layers. Often, however, these dependencies are unknown. Therefore, current methods connect layers based on simplistic assumptions that do not capture node-level layer dependencies. For example, connecting every node to itself in other layers with the same weight can wipe out dependencies between intermittent groups, making it difficult or even impossible to identify them. In this paper, we present a principled approach to estimating node-level layer dependencies based on the network structure within each layer. We implement our node-level coupling method in the community detection framework Infomap and demonstrate its performance compared to current methods on synthetic and real temporal networks. We show that our approach more effectively constrains information inside multilayer communities so that Infomap can better recover planted groups in multilayer benchmark networks that represent multiple modeswith different groups and better identify intermittent communities in real temporal contact networks. These results suggest that node-level layer coupling can improve the modeling of information spreading in temporal networks and better capture intermittent community structure.

  • 5.
    Blöcker, Christopher
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping flows on bipartite networks2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 5, article id 052305Article in journal (Refereed)
    Abstract [en]

    Mapping network flows provides insight into the organization of networks, but even though many real networks are bipartite, no method for mapping flows takes advantage of the bipartite structure. What do we miss by discarding this information and how can we use it to understand the structure of bipartite networks better? The map equation models network flows with a random walk and exploits the information-theoretic duality between compression and finding regularities to detect communities in networks. However, it does not use the fact that random walks in bipartite networks alternate between node types, information worth 1 bit. To make some or all of this information available to the map equation, we developed a coding scheme that remembers node types at different rates. We explored the community landscape of bipartite real-world networks from no node-type information to full node-type information and found that using node types at a higher rate generally leads to deeper community hierarchies and a higher resolution. The corresponding compression of network flows exceeds the amount of extra information provided. Consequently, taking advantage of the bipartite structure increases the resolution and reveals more network regularities.

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  • 6.
    Brodin, Gert
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Al-Naseri, Haidar
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Zamanian, Jens
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Torgrimsson, Greger
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Eliasson, Bengt
    SUPA, Department of Physics, University of Strathclyde, Glasgow, United Kingdom.
    Plasma dynamics at the Schwinger limit and beyond2023In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 107, no 3, article id 035204Article in journal (Refereed)
    Abstract [en]

    Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms in the regime of ultrastrong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined. Finally, comparisons with competing mechanisms such as radiation reaction and Breit-Wheeler pair production are made.

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  • 7.
    Calatayud, Joaquín
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernardo-Madrid, Ruben
    Neuman, Magnus
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rojas, Alexis
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Exploring the solution landscape enables more reliable network community detection2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 100, no 5, article id 052308Article in journal (Refereed)
    Abstract [en]

    To understand how a complex system is organized and functions, researchers often identify communities in the system's network of interactions. Because it is practically impossible to explore all solutions to guarantee the best one, many community-detection algorithms rely on multiple stochastic searches. But for a given combination of network and stochastic algorithms, how many searches are sufficient to find a solution that is good enough? The standard approach is to pick a reasonably large number of searches and select the network partition with the highest quality or derive a consensus solution based on all network partitions. However, if different partitions have similar qualities such that the solution landscape is degenerate, the single best partition may miss relevant information, and a consensus solution may blur complementary communities. Here we address this degeneracy problem with coarse-grained descriptions of the solution landscape. We cluster network partitions based on their similarity and suggest an approach to determine the minimum number of searches required to describe the solution landscape adequately. To make good use of all partitions, we also propose different ways to explore the solution landscape, including a significance clustering procedure. We test these approaches on synthetic networks and a real-world network using two contrasting community-detection algorithms: The algorithm that can identify more general structures requires more searches, and networks with clearer community structures require fewer searches. We also find that exploring the coarse-grained solution landscape can reveal complementary solutions and enable more reliable community detection.

  • 8.
    Ekman, Robin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Asenjo, F. A.
    Zamanian, Jens
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 2, article id 023207Article in journal (Refereed)
    Abstract [en]

    In this paper, we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long-scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in (h) over bar. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as "hidden momentum" and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

  • 9. Holkundkar, Amol R.
    et al.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Transition from wakefield generation to soliton formation2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 4, article id 043204Article in journal (Refereed)
    Abstract [en]

    It is well known that when a short laser pulse propagates in an underdense plasma, it induces longitudinal plasma oscillations at the plasma frequency after the pulse, typically referred to as the wakefield. However, for plasma densities approaching the critical density, wakefield generation is suppressed, and instead the EM-pulse (electromagnetic pulse) undergoes nonlinear self-modulation. In this article we have studied the transition from the wakefield generation to formation of quasi-solitons as the plasma density is increased. For this purpose we have applied a one-dimensional relativistic cold fluid model, which has also been compared with particle-in-cell simulations. A key result is that the energy loss of the EM-pulse due to wakefield generation has its maximum for a plasma density of the order 10% of the critical density, but that wakefield generation is sharply suppressed when the density is increased further.

  • 10.
    Keta, Yann-Edwin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Département de Physique, École Normale Supérieure de Lyon,France; Département de Physique, Université Claude Bernard Lyon 1, France.
    Olsson, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Translational and rotational velocities in shear-driven jamming of ellipsoidal particles2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 5, article id 052905Article in journal (Refereed)
    Abstract [en]

    We study shear-driven jamming of ellipsoidal particles at zero temperature with a focus on the microscopic dynamics. We find that a change from spherical particles to ellipsoids with aspect ratio alpha = 1.02 gives dramatic changes of the microscopic dynamics with much lower translational velocities and a new role for the rotations. Whereas the velocity difference at contacts-and thereby the dissipation-in collections of spheres is dominated by the translational velocities and reduced by the rotations, the same quantity is in collections of ellipsoids instead totally dominated by the rotational velocities. By also examining the effect of different aspect ratios we find that the examined quantities show either a peak or a change in slope at alpha approximate to 1.2, which thus gives evidence for a crossover between different regions of low and high aspect ratio.

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  • 11.
    Lundow, Per-Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Campbell, I. A.
    Ising spin glasses in two dimensions: Universality and nonuniversality2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 4, article id 042107Article in journal (Refereed)
    Abstract [en]

    Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising spin glass (ISG) models in two dimensions [Lundow and Campbell, Phys. Rev. E 93, 022119 (2016)]. Here we further analyze the bimodal and Gaussian data together with data on two other continuous interaction distribution two-dimensional ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an "antidiluted" model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent eta equivalent to 0 but that to within the present numerical precision they share the same critical exponent. also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and the present data strongly indicate that they differ from one discrete distribution model to another. This is evidence that discrete distribution ISG models in two dimensions have nonzero values of the critical exponent. and do not lie in a single universality class.

  • 12.
    Lundow, Per-Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Markström, Klas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Revisiting the cavity-method threshold for random 3-SAT2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 2, article id 022106Article in journal (Refereed)
    Abstract [en]

    A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies α3≤4.262. If the assumption is correct, this means that the actual threshold value for k=3 is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large k. Our result thus indicate that there are distinct behaviors for k above and below some critical kc, and the cavity method may provide a correct mean-field picture for the range above kc.

  • 13. Misra, Amar P.
    et al.
    Chatterjee, Debjani
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Effects of group velocity and multiplasmon resonances on the modulation of Langmuir waves in a degenerate plasma2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 5, article id 053209Article in journal (Refereed)
    Abstract [en]

    We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrodinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multiplasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where hk similar to mv(F) with _ h denoting the reduced Planck's constant, m the electron mass, and v(F) the Fermi velocity; however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multiplasmon effects are forbidden.

  • 14.
    Nyberg, Markus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lizana, Ludvig
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Persistence of non-Markovian Gaussian stationary processes in discrete time2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 4, article id 040101Article in journal (Refereed)
    Abstract [en]

    The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n. Few results are known for the persistence P0(n) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n)∼θn. Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n) analytically in z-transform space in terms of the autocorrelation function A(n). If A(n)→0 as n→∞, we extract θ numerically, while if A(n)=0, for finite n>N, we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A(n)=0 for n>1, the double exponential-correlated "second order autoregressive process", where A(n)=c1λn1+c2λn2, and power-law-correlated variables, where A(n)∼n−μ. Apart from the power-law case when μ<5, we find excellent agreement with simulations.

  • 15.
    Nyberg, Markus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lizana, Ludvig
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Ambjörnsson, Tobias
    Zero-crossing statistics for non-Markovian time series2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 3, article id 032114Article in journal (Refereed)
    Abstract [en]

    In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.

  • 16.
    Olsson, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Relaxation times, rheology, and finite size effects for non-Brownian disks in two dimensions2022In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 105, no 3, article id 034902Article in journal (Refereed)
    Abstract [en]

    We carry out overdamped simulations in a simple model of jamming - a collection of bidisperse soft core frictionless disks in two dimensions - with the aim to explore the finite size dependence of different quantities, both the relaxation time obtained from the relaxation of the energy and the pressure equivalent of the shear viscosity. The motivation for the paper is the observation [Nishikawa, J. Stat. Phys. 182, 37 (2021) 10.1007/s10955-021-02710-8] that there are finite size effects in the relaxation time, τ, that give problems in the determination of the critical divergence, and the claim that this is due to a finite size dependence, τ∼lnN, which makes τ an ill-defined quantity. Beside analyses to determine the relaxation time for the whole system we determine particle relaxation times which allow us to determine both histograms of particle relaxation times and the average particle relaxation times - two quantities that are very useful for the analyses. The starting configurations for the relaxation simulations are of two different kinds - completely random or taken from steady shearing simulations - and we find that the difference between these two cases are bigger than previously noted and that the observed problems in the determination of the critical divergence obtained when starting from random configurations are not present when instead starting the relaxations from shearing configurations. We also argue that the the effect that causes the lnN dependence is not as problematic as asserted. When it comes to the finite size dependence of the pressure equivalent of the shear viscosity we find that our data don't give support for the claimed strong finite size dependence, but also that the finite size dependence is at odds with what one would normally expect for a system with a diverging correlation length, and that this calls for an alternative understanding of the phenomenon of shear-driven jamming.

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  • 17.
    Olsson, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Slow and fast particles in shear-driven jamming: critical behavior2023In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 108, no 2, article id 024904Article in journal (Refereed)
    Abstract [en]

    We do extensive simulations of a simple model of shear-driven jamming in two dimensions to determine and analyze the velocity distribution at different densities φ around the jamming density φJ and at different low shear strain rates, γ˙. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity η, which diverges as the jamming density is approached from below, consists of two different terms, and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process, whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different γ˙ and φ at and around the shear-driven jamming transition has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.

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  • 18.
    Olsson, Peter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Teitel, S.
    Dynamic length scales in athermal, shear-driven jamming of frictionless disks in two dimensions2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 4, article id 042906Article in journal (Refereed)
    Abstract [en]

    We carry out numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, xi and l, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function and argue that the more divergent length l is a consequence of a dangerous irrelevant scaling variable and that it is xi, which is the correlation length that determines the divergence of the system viscosity as jamming is approached from below in the liquid phase. We find that xi similar to (phi(J) - phi)(-v) diverges with the critical exponent v = 1. We provide evidence that xi measures the length scale of fluctuations in the rotation of the particle velocity field, while l measures the length scale of fluctuations in the divergence of the velocity field.

  • 19.
    Servin, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Marklund, Mattias
    Parametric excitation of Alfvén waves by gravitational radiation2000In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 62, p. 8493-8500Article in journal (Refereed)
    Abstract [en]

    We consider the parametric excitation of Alfvén waves by gravitational radiation propagating on a Minkowski background, parallel to an external magnetic field. As a starting point, standard ideal magnetohydrodynamics equations incorporating the curvature of space-time has been derived. The growth rate of the Alfvén waves has been calculated, using the normal-mode approach. Various astrophysical applications of our investigations are discussed, and finally we demonstrate that the coupling coefficients of the interacting modes fulfill the Manley-Rowe relations.

  • 20.
    Smiljanic, Jelena
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics, University of Belgrade, Serbia.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics. Gothenburg Global Biodiversity Centre, Gothenburg, Sweden; Department of Biological and Environmental Sciences, University of Gothenburg, Sweden.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping flows on sparse networks with missing links2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 1, article id 012302Article in journal (Refereed)
    Abstract [en]

    Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based communities in sparse networks with missing links using the map equation. Since the map equation builds on Shannon entropy estimation, it assumes complete data such that analyzing undersampled networks can lead to overfitting. To overcome this problem, we incorporate a Bayesian approach with assumptions about network uncertainties into the map equation framework. Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.

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  • 21. Vagberg, Daniel
    et al.
    Olsson, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Teitel, S.
    Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 5, article id 052903Article in journal (Refereed)
    Abstract [en]

    We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction phi, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate (gamma) over dot. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (phi, Q) plane for small (gamma) over dot, we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing (gamma) over dot, the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (phi,(gamma) over dot) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing (gamma) over dot at fixed phi, we find that discontinuous shear thickening can result if (gamma) over dot is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of (gamma) over dot.

  • 22. Vågberg, Daniel
    et al.
    Olsson, Peter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Teitel, S.
    Effect of collisional elasticity on the Bagnold rheology of sheared frictionless two-dimensional disks2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 1, article id 012902Article in journal (Refereed)
    Abstract [en]

    We carry out constant volume simulations of steady-state, shear-driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction phi and a parameter Q that measures the elasticity of binary particle collisions. We find a Q*(phi) that marks the clear crossover from a region characteristic of strongly inelastic collisions, Q < Q*, to a region characteristic of weakly inelastic collisions, Q > Q*, and give evidence that Q*(phi) diverges as phi -> phi(J), the shear-driven jamming transition. We thus conclude that the jamming transition at any value of Q behaves the same as the strongly inelastic case, provided one is sufficiently close to fJ. We further characterize the differing nature of collisions in the strongly inelastic vs weakly inelastic regions, and recast our results into the constitutive equation form commonly used in discussions of hard granular matter.

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