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We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic…
This review contains an overview over recent results for the electromagnetic iso-vector form factor of the pion obtained in lattice QCD with dynamical fermions. Particular attention is given to the extrapolation to the physical point and an…
The relativistic calculations of the electromagnetic form factors, static moments and lepton decay constant of the $\rho$-meson are given in the framework of the instant form of the relativistic quantum mechanics with different model wave…
Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean--field dynamo, produced by direct numerical simulations of the three--dimensional compressible magnetohydrodynamic equations…
The fringe pattern that allows geometrical and orbital structure information to be extracted from LIED spectra of symmetric molecules is shown to reflect a symmetry conservation principle. We show that under a field polarization which…
We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
We present a method for system identification of flexible objects by measuring forces and displacement during interaction with a manipulating arm. We model the object's structure and flexibility by a chain of rigid bodies connected by…
We present a relativistic analysis of fermions in an external electric field by non-perturbatively solving the Dirac equation with a static gauge. Different from the magnetic field effect, the fermion wave function in an electric field…
Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct…
It is generally accepted that the effective magnetic field acting on a magnetic moment is given by the gradient of the energy with respect to the magnetization. However, in ab initio spin dynamics within the adiabatic approximation, the…
This paper investigates the five-dimensional(5D) spherically symmetric gravitational collapse with positive cosmological constant in the presence of an electromagnetic field. The junction conditions between the 5D non-static interior and…
The field of a uniformly magnetized rotating sphere is studied with special attention to the surface where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the…
We stabilize the flow past a cluster of three rotating cylinders, the fluidic pinball, with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open- and closed-loop…
We propose a magnetic analogy of the Duffing oscillator--magnetic Duffing oscillator--which is characterized by a double-well magnetic potential of a ferromagnet with a uniaxial magnetic anisotropy. Based on the linear stability analysis of…
Stability of flapping flight, a natural requirement for flying insects, is one of the major challenges for designing micro aerial vehicles (MAVs). To better understand how a flying insect could stabilize itself during hover, we have…
We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which…
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…
Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose…
The strong coupling $\alpha_s$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing…