4,906 research outputs found
Percolation properties of growing networks under an Achlioptas process
We study the percolation transition in growing networks under an Achlioptas
process (AP). At each time step, a node is added in the network and, with the
probability , a link is formed between two nodes chosen by an AP. We
find that there occurs the percolation transition with varying and the
critical point is determined from the power-law behavior
of order parameter and the crossing of the fourth-order cumulant at the
critical point, also confirmed by the movement of the peak positions of the
second largest cluster size to the . Using the finite-size scaling
analysis, we get and , which
implies and . The Fisher exponent
for the cluster size distribution is obtained and shown to
satisfy the hyperscaling relation.Comment: 4 pages, 5 figures, 1 table, journal submitte
Lorentz Invariance in Chiral Kinetic Theory
We show that Lorentz invariance is realized nontrivially in the classical
action of a massless spin- particle with definite helicity. We find
that the ordinary Lorentz transformation is modified by a shift orthogonal to
the boost vector and the particle momentum. The shift ensures angular momentum
conservation in particle collisions and implies a nonlocality of the collision
term in the Lorentz-invariant kinetic theory due to side jumps. We show that
2/3 of the chiral-vortical effect for a uniformly rotating particle
distribution can be attributed to the magnetic moment coupling required by the
Lorentz invariance. We also show how the classical action can be obtained by
taking the classical limit of the path integral for a Weyl particle.Comment: 5 pages, 1 figur
Projection-based reduced order modeling of an iterative coupling scheme for thermo-poroelasticity
This paper explores an iterative coupling approach to solve
thermo-poroelasticity problems, with its application as a high-fidelity
discretization utilizing finite elements during the training of
projection-based reduced order models. One of the main challenges in addressing
coupled multi-physics problems is the complexity and computational expenses
involved. In this study, we introduce a decoupled iterative solution approach,
integrated with reduced order modeling, aimed at augmenting the efficiency of
the computational algorithm. The iterative coupling technique we employ builds
upon the established fixed-stress splitting scheme that has been extensively
investigated for Biot's poroelasticity. By leveraging solutions derived from
this coupled iterative scheme, the reduced order model employs an additional
Galerkin projection onto a reduced basis space formed by a small number of
modes obtained through proper orthogonal decomposition. The effectiveness of
the proposed algorithm is demonstrated through numerical experiments,
showcasing its computational prowess
Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
We present an interacting theory of a gauge boson with a quadratic
dispersion relation, which we call the "nonlinear Lifshitz photon theory.'' The
Lifshitz photon is a three-dimensional generalization of the Tkachenko mode in
rotating superfluids. Starting from the Wigner crystal of charged particles
coupled to a dynamical gauge field, after integrating out gapped degrees
of freedom, we arrive at the Lagrangian for the nonlinear Lifshitz photon. The
symmetries of the theory include a global 1-form symmetry and
nonlinearly realized "magnetic" translation and rotation symmetries. The
interaction terms in the theory lead to the decay of the Lifshitz photon, the
rate of which we estimate. We show that the Wilson loop, which plays the role
of the order parameter of the spontaneous breaking of the 1-form global
symmetry, deviates from the perimeter law by an additional logarithmic factor.
We explore potential connections to other condensed matter systems, with a
particular focus on quantum spin ice and ferromagnets. Finally, we generalize
our theory to higher dimensions
Pressure-robust enriched Galerkin methods for the Stokes equations
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for
solving the Stokes equations, which is an enhanced version of the EG scheme for
the Stokes problem proposed in [Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James
H. Adler, An enriched Galerkin method for the Stokes equations, Computers and
Mathematics with Applications, accepted, 2022]. The pressure-robustness is
achieved by employing a velocity reconstruction operator on the load vector on
the right-hand side of the discrete system. An a priori error analysis proves
that the velocity error is independent of the pressure and viscosity. We also
propose and analyze a perturbed version of our pressure-robust EG method that
allows for the elimination of the degrees of freedom corresponding to the
discontinuous component of the velocity vector via static condensation. The
resulting method can be viewed as a stabilized -conforming
- method. Further, we consider efficient block
preconditioners whose performances are independent of the viscosity. The
theoretical results are confirmed through various numerical experiments in two
and three dimensions
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